Phase 4: quantum-like semantic metrics and human judgments

Theory-guided analytical notebook with methodological rationale, salience variants, annex condition analyses, and human-aligned results

1 Purpose and analytical strategy

This notebook is not only a results report. It is a theory-guided analytical notebook whose purpose is to document what was done, why it was done, which arbitrary decisions were made, and how the results should be interpreted within the quantum-like theory of conceptual representation developed in the thesis and manuscript.

The empirical strategy is human-aligned. Instead of computing all possible pairs and triplets among the 120 available concepts, the analyses are restricted to the pairs, triplets, and diagnostic designs that were actually used in the human studies. This is important because the computational model is being evaluated as a model of psychological judgments, not as an exercise in filling storage with elegant but irrelevant combinations.

The central question is whether representing concepts as subspaces, projectors, and density-like operators adds explanatory value beyond classical vector similarity. The benchmark is deliberately strong: cosine, angular distance, Euclidean distance, and dot product between saturated-contour centroids. If the quantum-like model only reproduced what a centroid cosine already explains, then the subspace machinery would be decorative algebra. Useful decorative algebra, perhaps, but still decorative.

The report compares these families:

1. Classical vector baselines, especially cosine between saturated-contour centroids.
2. Subspace/projector geometry, including overlap, containment, principal angles, Bures-like distances, and commutator-based incompatibility.
3. Operator/density metrics, including Hilbert–Schmidt similarity and trace-normalized containment between projectors or density-like objects.
4. Sequential QSM metrics, using projection sequences as state-dependent similarity measures.
5. Contextualized diagnostic metrics, where a context acts as a coordinate frame or Lüders-style filter.
6. Perplexity-inhibited metrics, where shared properties of a competing pair are removed before comparing the initial concept with each target.

The interpretive criterion is simple: a metric family is theoretically relevant when it predicts the human effect it was designed to capture, and especially when it does so better than classical centroid similarity.

2 Methodological pipeline and theoretical commitments

2.1 Phase 1: container semantic space

The analysis assumes a common semantic container space (H), operationalized as a 300-dimensional LSA/SVD space estimated from a large Spanish news corpus. This container is not interpreted as a psychological space by itself. It is the representational substrate in which vectors, subspaces, projectors, and density-like objects can all be expressed. This follows the manuscript’s proposal that concepts and contexts can be represented as subspaces inside a shared Hilbert-like container space.

The first controlled simplification is that the container is real-valued rather than complex-valued. This is an arbitrary but defensible decision: it preserves the geometry needed for projection, containment, angles, and density-like comparisons, while avoiding phase parameters that would be impossible to estimate from the present data without inventing them with suspicious confidence.

2.2 Phase 2: human-aligned empirical targets

The human data define the target phenomena: ipsative asymmetry, salience in two forms (ipsative forced choice and single-concept Likert salience), planned salience/similarity stimulus conditions, Likert similarity, order asymmetry, triangular structure, and diagnosticity. The computational analyses are therefore not exhaustive over the concept set. They are restricted to the same conceptual pairs, triplets, and diagnostic configurations observed in the human tasks.

This decision matters because the goal is not to discover any relation in the semantic space; the goal is to test whether the formal objects generated by the model reproduce the specific psychological comparisons measured in humans.

2.3 Phase 3A: saturated contours

For each concept, a saturated contour was built from all corpus occurrences that matched the target. A contour is a cloud of contextual document vectors, not yet a concept subspace. Methodologically, this distinguishes the empirical distribution of a word or concept in language from the formal object that will represent its conceptual structure.

The key decision is to use the contour centroid as the strongest classical baseline. The centroid is a useful classical summary because it collapses a concept’s contextual variability into one vector. If explicit similarity ratings are well predicted by this centroid, that suggests that some judgments are approximately average-proximity judgments. If asymmetry or diagnosticity are not well predicted by the centroid, that is exactly where subspace and operator structure become theoretically interesting.

2.4 Phase 3B: dimensionality and local semantic regions

Conceptual subspaces were estimated from saturated contours by selecting dimensionality and, where appropriate, local semantic regions. The main arbitrary decisions are the dimensionality rule and the clustering model. These were not treated as single hidden commitments. Instead, the analysis keeps multiple variants: Bayesian GMM versus GMM-BIC for local regions, and several dimensionality rules such as Horn/Wishart, permutation parallel analysis, Gavish-Donoho, and profile likelihood.

This is not methodological indecision wearing a lab coat. The point is sensitivity analysis. If a result only appears under one fragile variant, it should be interpreted cautiously. If it appears across families of variants, it is more likely to reflect a stable property of the representation.

2.5 Phase 3C: formal conceptual objects

From each contour and each dimensionality/local-region decision, the pipeline builds several formal objects:

• (S_A): an orthonormal basis for concept (A).
• (P_A = S_A S_A^T): the projector onto the conceptual subspace.
• (_A = P_A / Tr(P_A)): a normalized density-like representation of the subspace.
• (_{freq}): a frequency-weighted mixture of local semantic-region densities.
• (_{fit}): a fitted mixture intended to approximate the global structure using local regions.
• (P_{Lowdin}): a Löwdin-orthogonalized representation of concatenated local regions.

This is where the model becomes genuinely different from a vector model. A vector says “where the concept points on average.” A subspace says “which directions are relevant to the concept.” A density-like object says “how semantic mass is distributed across relevant directions.” Psychological similarity can then be tested as overlap, containment, distinguishability, contextual filtering, or order-dependent projection.

2.6 Phase 4: human-aligned metric evaluation

Phase 4 evaluates whether these formal objects predict human judgments. The important design decision is to evaluate families of metrics, not one cherished formula. The original QSM based on sequential projections is included, but it is not treated as the whole model. The thesis and manuscript motivate a wider algebra: projectors, containment, density-like overlap, contextualized states, incompatibility, and residual states after perplejity-like inhibition.

The results are interpreted at two levels:

1. Local hypothesis level: which metric best predicts each human effect?
2. Theoretical level: what does that success or failure imply about the psychological operation involved?

This is the distinction that prevents the notebook from becoming a leaderboard with Greek letters.

2.7 Planned salience and similarity conditions from the thesis annex

The thesis annex does not only list country pairs. It organizes the asymmetry/salience stimuli into a small factorial structure: concepts can be high or low in planned salience, and pairs can be high or low in planned similarity. This creates cells such as low–low / low similarity, low–low / high similarity, high–low / low similarity, high–low / high similarity, high–high / low similarity, and high–high / high similarity. In the rendered experimental files, these same pairs may appear in either order, so the analysis needs to distinguish the planned conceptual condition from the actual presentation order.

This distinction matters because it gives the notebook an additional layer of theory-guided analysis:

1. Manipulation check for salience. If the annex labels are meaningful, single-concept Likert salience should be higher for concepts labelled high-salience than for those labelled low-salience.
2. Ipsative salience check. In high–low and low–high pair presentations, participants should preferentially choose the high-salience concept. In high–high and low–low pairs, choice should be closer to chance.
3. Similarity manipulation check. Pairs labelled high similarity should receive higher Likert similarity ratings and higher computational similarity values than low-similarity pairs.
4. Asymmetry moderation. Directional containment should matter most when the pair has an unequal salience structure. Equal-salience pairs are less diagnostic for asymmetry.
5. Dimensionality interpretation. If Likert salience is concept-level rather than pairwise, dimensionality and corpus frequency become legitimate predictors of salience. This is not the same mechanism as ipsative salience: one concerns global representational availability, the other concerns directional comparison inside a pair.
6. Cross-contrast moderation. The salience/similarity cells should also qualify other contrasts: Likert order effects, explicit similarity ratings, and the strength of computational-human coupling inside each condition.
7. Diagnostic context as priming-like manipulation. The thesis does not define a separate priming task in the Phase 2 instruments. The closest experimental analogue is diagnosticity: a context/distractor is inserted into the comparison set and should activate, inhibit, or reweight diagnostic features. For this reason, the notebook treats diagnostic context as a priming-like contextual manipulation and analyzes whether context-target similarity predicts human choices and ratings.

The notebook therefore adds a condition-level block without changing the previous result tables. The condition analyses are treated as theory-guided diagnostics, not as a replacement for the main H1–H6 analyses.

2.8 Arbitrary decisions and how they are controlled

The following decisions are arbitrary in the technical sense that alternatives are possible:

• The container dimensionality is fixed at 300.
• The model uses real-valued LSA coordinates.
• Concept contours are based on corpus occurrence retrieval.
• Subspace dimensionality depends on statistical selection rules.
• Local semantic regions depend on clustering assumptions.
• Density-like objects are normalized projectors or mixtures, not empirically estimated quantum density matrices.
• Distances are reversed when the dependent human variable is similarity.
• Directional metrics are reoriented to match the human item order.
• Diagnostic perplexity uses a soft intersection/residual approximation rather than an exact psychological process model.

The notebook controls these decisions in three ways: by including classical baselines, by comparing multiple quantum-like metric families, and by reporting representation/variant sensitivity.

3 Packages and paths

required_packages <- c(
  "tidyverse", "vroom", "broom", "knitr", "scales", "stringr", "forcats", "fs"
)

missing_packages <- required_packages[!vapply(required_packages, requireNamespace, logical(1), quietly = TRUE)]

if (length(missing_packages) > 0) {
  if (isTRUE(params$install_missing)) {
    install.packages(missing_packages)
  } else {
    stop(
      "Missing packages: ", paste(missing_packages, collapse = ", "),
      "\nInstall them or render with -P install_missing:true. R wants snacks before working."
    )
  }
}

library(tidyverse)
library(vroom)
library(broom)
library(knitr)
library(scales)
library(stringr)
library(forcats)
library(fs)

project_root <- normalizePath(getwd(), mustWork = TRUE)
data_dir <- file.path(project_root, params$data_dir)
empirical_dir <- file.path(project_root, "Empirical_data")

clean_paths <- function(paths) {
  paths <- unlist(paths, use.names = FALSE)
  paths <- paths[!is.na(paths) & nzchar(paths)]
  unique(paths)
}

first_existing <- function(paths, type = c("file", "dir"), required = TRUE, label = "path") {
  type <- match.arg(type)
  paths <- clean_paths(paths)
  exists_fun <- if (type == "file") file.exists else dir.exists
  hit <- paths[exists_fun(paths)]
  if (length(hit) > 0) return(normalizePath(hit[[1]], mustWork = TRUE))
  if (required) {
    stop(
      "Could not find ", label, ". Tried:\n",
      paste(paths, collapse = "\n"),
      "\n\nCheck folder names or pass the explicit path with a Quarto parameter, e.g. -P phase4_dir:/your/path."
    )
  }
  NA_character_
}

find_parent_by_file <- function(roots, filename, max_depth = 5) {
  roots <- clean_paths(roots)
  roots <- roots[dir.exists(roots)]
  if (length(roots) == 0) return(character())

  hits <- character()
  for (r in roots) {
    files <- list.files(
      r,
      pattern = paste0("^", gsub("\\.", "\\\\.", filename), "$"),
      recursive = TRUE,
      full.names = TRUE,
      all.files = FALSE
    )
    if (length(files) > 0) {
      root_norm <- normalizePath(r, mustWork = FALSE)
      file_norm <- normalizePath(files, mustWork = FALSE)
      rel <- sub(paste0("^", root_norm, "/?"), "", file_norm)
      depth <- stringr::str_count(rel, .Platform$file.sep)
      files <- files[depth <= max_depth]
      hits <- c(hits, dirname(files))
    }
  }
  unique(hits)
}

phase4_candidates <- c(
  params$phase4_dir,
  file.path(data_dir, "quantum_metrics_human_aligned"),
  file.path(data_dir, "phase4_quantum_metrics_human_aligned"),
  file.path(project_root, "quantum_metrics_human_aligned"),
  file.path(project_root, "phase4_quantum_metrics_human_aligned"),
  find_parent_by_file(c(data_dir, project_root), "phase4_quantum_metrics_summary.json", max_depth = 4)
)

phase4_dir <- first_existing(phase4_candidates, type = "dir", label = "Phase 4 metrics directory")

dimensionality_candidates <- c(
  params$dimensionality_dir,
  file.path(data_dir, "dimensionality_decisions"),
  file.path(data_dir, "phase3b_dimensionality_decisions"),
  file.path(data_dir, "phase3b_dimensionality_decisions_bayesian_gmm_rank_safe_gmm30"),
  file.path(project_root, "dimensionality_decisions"),
  file.path(project_root, "phase3b_dimensionality_decisions"),
  find_parent_by_file(c(data_dir, project_root), "global_dimensionality_wide.csv", max_depth = 6)
)

dimensionality_dir <- first_existing(
  dimensionality_candidates,
  type = "dir",
  required = FALSE,
  label = "Phase 3B dimensionality directory"
)

phase2_candidates <- c(
  params$phase2_dir,
  file.path(empirical_dir, "tidy_outputs"),
  file.path(empirical_dir, "phase2_tidy_outputs"),
  file.path(data_dir, "phase2_tidy_outputs"),
  file.path(project_root, "phase2_tidy_outputs"),
  find_parent_by_file(c(empirical_dir, data_dir, project_root), "items_catalog_phase2.csv", max_depth = 5)
)

phase2_dir <- first_existing(phase2_candidates, type = "dir", required = FALSE, label = "Phase 2 tidy outputs directory")

stimuli_candidates <- c(
  params$stimuli_dir,
  file.path(data_dir, "stimuli", "human_stimuli_design"),
  file.path(data_dir, "stimuli", "phase4_human_stimuli_design"),
  file.path(data_dir, "human_stimuli_design"),
  file.path(data_dir, "phase4_human_stimuli_design"),
  file.path(project_root, "stimuli", "human_stimuli_design"),
  file.path(project_root, "stimuli", "phase4_human_stimuli_design"),
  file.path(project_root, "human_stimuli_design"),
  file.path(project_root, "phase4_human_stimuli_design"),
  find_parent_by_file(c(data_dir, project_root), "phase4_human_pairwise_design_model_ready.csv", max_depth = 6)
)

stimuli_dir <- first_existing(stimuli_candidates, type = "dir", label = "human stimuli design directory")

output_dir <- file.path(project_root, params$output_dir)
fs::dir_create(output_dir)
fs::dir_create(file.path(output_dir, "tables"))
fs::dir_create(file.path(output_dir, "figures"))
fs::dir_create(file.path(output_dir, "data"))

paths <- list(
  project_root = project_root,
  data_dir = data_dir,
  empirical_dir = empirical_dir,
  phase4_dir = phase4_dir,
  dimensionality_dir = dimensionality_dir,
  phase2_dir = phase2_dir,
  stimuli_dir = stimuli_dir,
  output_dir = output_dir
)

paths

$project_root
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel"

$data_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Computational_data"

$empirical_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Empirical_data"

$phase4_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Computational_data/quantum_metrics_human_aligned"

$dimensionality_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Computational_data/dimensionality_decisions"

$phase2_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Empirical_data/tidy_outputs"

$stimuli_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Computational_data/stimuli/human_stimuli_design"

$output_dir
[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Computational_data/phase4_R_analysis_outputs_v12"

4 Helper functions

read_csv_fast <- function(path, col_select = NULL, required = TRUE) {
  if (!file.exists(path)) {
    if (required) stop("File not found: ", path)
    return(tibble())
  }
  if (file.info(path)$size <= 1) return(tibble())
  if (!is.null(col_select)) {
    vroom::vroom(path, delim = ",", show_col_types = FALSE, progress = FALSE, col_select = all_of(col_select))
  } else {
    vroom::vroom(path, delim = ",", show_col_types = FALSE, progress = FALSE)
  }
}

canonical_pair <- function(a, b) {
  paste(pmin(as.character(a), as.character(b)), pmax(as.character(a), as.character(b)), sep = "__")
}

apa_num <- function(x, digits = 2) {
  ifelse(is.na(x), "", sprintf(paste0("%0.", digits, "f"), x))
}

apa_p <- function(p) {
  case_when(
    is.na(p) ~ "",
    p < .001 ~ "< .001",
    TRUE ~ sub("^0", "", sprintf("%.3f", p))
  )
}

apa_r <- function(x, digits = 2) {
  out <- sprintf(paste0("%0.", digits, "f"), x)
  out <- str_replace(out, "^-0\\.", "−.")
  out <- str_replace(out, "^0\\.", ".")
  out
}

apa_table <- function(data, caption = NULL, digits = 3) {
  knitr::kable(
    data,
    format = "html",
    caption = caption,
    digits = digits,
    align = "l",
    booktabs = TRUE
  )
}

write_table <- function(data, filename) {
  readr::write_csv(data, file.path(output_dir, "tables", filename))
}

save_plot <- function(plot, filename, width = 8, height = 5) {
  ggplot2::ggsave(
    filename = file.path(output_dir, "figures", filename),
    plot = plot,
    width = width,
    height = height,
    dpi = 300
  )
}

theme_apa7 <- function(base_size = 11) {
  # This is no longer a strict APA plot theme. Tables remain APA-like, but plots are
  # optimized for readability in an analytical notebook: clearer grids, larger labels,
  # and a colorblind-friendly palette where possible.
  ggplot2::theme_minimal(base_size = base_size, base_family = "sans") +
    theme(
      panel.grid.minor = element_blank(),
      panel.grid.major.x = element_line(linewidth = .25, color = "grey84"),
      panel.grid.major.y = element_blank(),
      axis.line.x = element_line(linewidth = .35, color = "grey35"),
      axis.ticks.x = element_line(color = "grey35"),
      plot.title = element_text(face = "bold", size = base_size + 2, margin = margin(b = 5)),
      plot.subtitle = element_text(size = base_size, color = "grey25", margin = margin(b = 8)),
      plot.caption = element_text(size = base_size - 2, hjust = 0, color = "grey35"),
      axis.title = element_text(size = base_size, face = "bold"),
      axis.text = element_text(size = base_size - 1, color = "grey20"),
      legend.position = "bottom",
      legend.title = element_blank(),
      legend.text = element_text(size = base_size - 1),
      strip.background = element_rect(fill = "grey95", color = NA),
      strip.text = element_text(face = "bold"),
      plot.margin = margin(10, 16, 10, 10)
    )
}

report_palette <- c(
  "#0072B2", "#D55E00", "#009E73", "#CC79A7",
  "#E69F00", "#56B4E9", "#999999", "#F0E442"
)

safe_cor <- function(data, x = "metric_value", y = "human_value", method = "spearman") {
  d <- data %>%
    filter(!is.na(.data[[x]]), !is.na(.data[[y]])) %>%
    filter(is.finite(.data[[x]]), is.finite(.data[[y]]))

  if (nrow(d) < 3 || n_distinct(d[[x]]) < 2 || n_distinct(d[[y]]) < 2) {
    return(tibble(n = nrow(d), estimate = NA_real_, p.value = NA_real_))
  }

  ct <- suppressWarnings(cor.test(d[[x]], d[[y]], method = method, exact = FALSE))
  tibble(
    n = nrow(d),
    estimate = unname(ct$estimate),
    p.value = ct$p.value
  )
}

cor_by_group <- function(data, group_cols, x = "metric_value", y = "human_value", method = "spearman") {
  # Different Phase 4 tables do not all carry the same descriptor columns
  # (for instance, H3 order-averaged metrics do not need metric_direction).
  # Use the requested grouping variables when present, and silently add the
  # missing ones back as NA after the correlation step. This keeps downstream
  # tables stable without forcing every intermediate tibble to pretend it has
  # every column in the universe. Very considerate of us.
  group_cols <- unique(group_cols)
  present_group_cols <- intersect(group_cols, names(data))
  missing_group_cols <- setdiff(group_cols, names(data))

  if (!x %in% names(data)) stop("Column '", x, "' not found in data passed to cor_by_group().")
  if (!y %in% names(data)) stop("Column '", y, "' not found in data passed to cor_by_group().")

  out <- data %>%
    filter(!is.na(.data[[x]]), !is.na(.data[[y]]))

  if (length(present_group_cols) > 0) {
    out <- out %>%
      group_by(across(all_of(present_group_cols))) %>%
      group_modify(~ safe_cor(.x, x = x, y = y, method = method)) %>%
      ungroup()
  } else {
    out <- safe_cor(out, x = x, y = y, method = method)
  }

  if (length(missing_group_cols) > 0) {
    for (cc in missing_group_cols) out[[cc]] <- NA_character_
  }

  out %>%
    mutate(
      p_fdr = p.adjust(p.value, method = "BH"),
      abs_estimate = abs(estimate)
    ) %>%
    arrange(desc(abs_estimate), p.value)
}

is_asymmetry_metric <- function(metric_name) {
  str_detect(metric_name, regex("asymmetry|a_minus_b|first_minus_second|second_minus_first", ignore_case = TRUE))
}

is_distance_metric <- function(metric_name) {
  str_detect(metric_name, regex("distance|bures|angle|geodesic|frobenius|commutator", ignore_case = TRUE))
}

metric_family_from_source <- function(metric_source) {
  case_when(
    metric_source == "classical_baselines" ~ "Classical vector baseline",
    metric_source == "pairwise_subspace_metrics" ~ "Subspace/projector geometry",
    metric_source == "pairwise_operator_density_metrics" ~ "Operator/density geometry",
    metric_source == "pairwise_qsm_state_metrics" ~ "Sequential QSM",
    metric_source == "triplet_distance_violations" ~ "Triplet distance geometry",
    metric_source == "triplet_mti_violations" ~ "Triplet similarity geometry",
    str_detect(metric_source, "diagnostic_context") ~ "Contextualized diagnostic",
    str_detect(metric_source, "diagnostic_perplexity") ~ "Perplexity-inhibited diagnostic",
    TRUE ~ metric_source
  )
}

metric_short_label <- function(metric_name) {
  case_when(
    str_detect(metric_name, "containment_asymmetry") ~ "Containment asymmetry",
    str_detect(metric_name, "qsm_asymmetry") ~ "QSM asymmetry",
    str_detect(metric_name, "qsm_p_b_given_a") ~ "QSM p(B|A)",
    str_detect(metric_name, "qsm_p_a_given_b") ~ "QSM p(A|B)",
    str_detect(metric_name, "density_fidelity") ~ "Density fidelity",
    str_detect(metric_name, "density_bures") ~ "Bures distance, reversed",
    str_detect(metric_name, "trace_distance") ~ "Trace distance, reversed",
    str_detect(metric_name, "cosine_hilbert_schmidt") ~ "Hilbert-Schmidt cosine",
    str_detect(metric_name, "symmetric_projector_overlap") ~ "Projector overlap",
    str_detect(metric_name, "symmetric_trace_normalized_overlap") ~ "Trace-normalized overlap",
    str_detect(metric_name, "projector_chordal") ~ "Chordal distance, reversed",
    str_detect(metric_name, "mean_cosine_sq") ~ "Mean cos² principal angles",
    str_detect(metric_name, "mean_cosine") ~ "Mean principal cosine",
    str_detect(metric_name, "classical_.*cosine") ~ "Centroid cosine",
    str_detect(metric_name, "classical_.*angular_distance") ~ "Angular distance, reversed",
    str_detect(metric_name, "classical_.*euclidean_distance") ~ "Euclidean distance, reversed",
    str_detect(metric_name, "contextualized_vector_cosine") ~ "Contextualized vector cosine",
    str_detect(metric_name, "density_hs_inner") ~ "Contextual density HS inner",
    str_detect(metric_name, "perplexity_density_fidelity") ~ "Perplexity density fidelity",
    TRUE ~ str_replace_all(metric_name, "_", " ")
  )
}

variant_short <- function(x) {
  x <- coalesce(as.character(x), "")
  x <- str_replace_all(x, "clust-", "")
  x <- str_replace_all(x, "__g-", " | g=")
  x <- str_replace_all(x, "__l-", " | l=")
  x
}

metric_is_classical <- function(metric_source) metric_source == "classical_baselines"

similarity_orient_value <- function(metric_name, value) {
  ifelse(is_distance_metric(metric_name), -as.numeric(value), as.numeric(value))
}

orient_asymmetry_to_human_order <- function(metric_name, value, direction_sign) {
  ifelse(is_asymmetry_metric(metric_name) & !is.na(direction_sign), as.numeric(value) * direction_sign, as.numeric(value))
}

interpret_corr_strength <- function(r) {
  ar <- abs(r)
  case_when(
    is.na(ar) ~ "not estimable",
    ar >= .80 ~ "very strong",
    ar >= .60 ~ "strong",
    ar >= .40 ~ "moderate",
    ar >= .20 ~ "weak-to-moderate",
    TRUE ~ "weak"
  )
}

normalize_salience_target <- function(x) {
  x <- as.character(x)
  x <- str_to_lower(x)
  x <- str_replace_all(x, "á", "a")
  x <- str_replace_all(x, "é", "e")
  x <- str_replace_all(x, "í", "i")
  x <- str_replace_all(x, "ó", "o")
  x <- str_replace_all(x, "ú", "u")
  x <- str_replace_all(x, "ü", "u")
  x <- str_replace_all(x, "ñ", "n")
  x <- recode(
    x,
    "eeuu" = "estados_unidos",
    "uk" = "reino_unido",
    "mejico" = "mexico",
    "espana" = "espana",
    .default = x
  )
  x
}

z_score <- function(x) as.numeric(scale(x))

plot_ranked_correlations <- function(rank_df, title, subtitle = NULL, n = 10, filename = NULL) {
  d <- rank_df %>%
    filter(!is.na(estimate)) %>%
    slice_head(n = n) %>%
    mutate(
      label = paste0(metric_short_label(metric_name), "\n", str_wrap(metric_family_from_source(metric_source), 28)),
      label = fct_reorder(label, abs_estimate),
      significant = if_else(!is.na(p_fdr) & p_fdr < .05, "FDR < .05", "FDR ≥ .05")
    )

  p <- ggplot(d, aes(x = label, y = estimate, fill = significant)) +
    geom_hline(yintercept = 0, linewidth = .35) +
    geom_col(width = .72) +
    coord_flip() +
    scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
    scale_fill_manual(values = report_palette) +
    labs(title = title, subtitle = subtitle, x = NULL, y = "Spearman rho") +
    theme_apa7()

  if (!is.null(filename)) save_plot(p, filename, width = 8.5, height = max(4.5, .38 * n + 1.5))
  p
}

plot_metric_scatter <- function(data, rank_row, title, y_label, filename = NULL) {
  if (nrow(rank_row) == 0) return(NULL)
  d <- data %>% filter(metric_id == rank_row$metric_id[[1]])
  if (nrow(d) == 0) return(NULL)

  p <- ggplot(d, aes(x = metric_value, y = human_value)) +
    geom_point(size = 2.2, alpha = .80) +
    geom_smooth(method = "lm", se = TRUE, linewidth = .75) +
    labs(
      title = title,
      subtitle = paste0(
        metric_short_label(rank_row$metric_name[[1]]),
        "; rho = ", apa_r(rank_row$estimate[[1]]),
        ", p ", apa_p(rank_row$p.value[[1]])
      ),
      x = "Computational metric value",
      y = y_label
    ) +
    theme_apa7()

  if (!is.null(filename)) save_plot(p, filename)
  p
}

best_by_family <- function(rank_df) {
  rank_df %>%
    mutate(metric_family = metric_family_from_source(metric_source)) %>%
    group_by(metric_family) %>%
    slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
    ungroup() %>%
    arrange(desc(abs_estimate))
}

compare_quantum_vs_cosine <- function(rank_df) {
  d <- rank_df %>%
    mutate(
      comparison_family = case_when(
        metric_source == "classical_baselines" & str_detect(metric_name, "cosine") ~ "Best classical cosine",
        metric_source == "classical_baselines" ~ "Other classical baseline",
        TRUE ~ "Best quantum-like metric"
      )
    ) %>%
    filter(comparison_family %in% c("Best classical cosine", "Best quantum-like metric")) %>%
    group_by(comparison_family) %>%
    slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
    ungroup() %>%
    arrange(comparison_family)
  d
}

plot_family_comparison <- function(best_df, title, filename = NULL) {
  d <- best_df %>%
    mutate(
      metric_family = fct_reorder(metric_family, abs_estimate),
      label = paste0(metric_family, "\n", metric_short_label(metric_name))
    )
  p <- ggplot(d, aes(x = fct_reorder(label, abs_estimate), y = estimate)) +
    geom_hline(yintercept = 0, linewidth = .35) +
    geom_col(width = .72) +
    coord_flip() +
    scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
    labs(title = title, x = NULL, y = "Best Spearman rho within family") +
    theme_apa7()
  if (!is.null(filename)) save_plot(p, filename, width = 8.5, height = max(4.5, .55 * nrow(d) + 1.5))
  p
}

5 Load data

phase4_files <- list(
  summary = file.path(phase4_dir, "phase4_quantum_metrics_summary.json"),
  subspace = file.path(phase4_dir, "pairwise_subspace_metrics.csv"),
  operator_density = file.path(phase4_dir, "pairwise_operator_density_metrics.csv"),
  qsm_state = file.path(phase4_dir, "pairwise_qsm_state_metrics.csv"),
  pairwise_long = file.path(phase4_dir, "pairwise_metrics_long_for_human_merge.csv"),
  pairwise_human_prejoined = file.path(phase4_dir, "pairwise_metrics_with_human_behavior.csv"),
  classical = file.path(phase4_dir, "classical_baselines.csv"),
  triplet_distance = file.path(phase4_dir, "triplet_distance_violations.csv"),
  triplet_mti = file.path(phase4_dir, "triplet_mti_violations.csv"),
  diagnostic_context = file.path(phase4_dir, "diagnostic_contextualized_similarity.csv"),
  diagnostic_perplexity = file.path(phase4_dir, "diagnostic_perplexity_metrics.csv"),
  diagnostic_choice = file.path(phase4_dir, "diagnostic_choice_predictions.csv"),
  diagnostic_design_normalized = file.path(phase4_dir, "diagnostic_design_normalized.csv"),
  representation_alignment = file.path(phase4_dir, "representation_alignment.csv"),
  variant_sensitivity = file.path(phase4_dir, "variant_sensitivity.csv")
)

stimuli_files <- list(
  pairwise_design = file.path(stimuli_dir, "phase4_human_pairwise_design_model_ready.csv"),
  triplet_design = file.path(stimuli_dir, "phase4_human_triplet_design_model_ready.csv"),
  diagnostic_design = file.path(stimuli_dir, "phase4_diagnostic_design_model_ready.csv")
)

phase2_files <- list(
  saliency_2 = first_existing(
    c(
      file.path(phase2_dir, "analysis_ready_default_sources", "saliency_2.csv"),
      file.path(phase2_dir, "saliency_2.csv"),
      file.path(dirname(phase2_dir), "audit_outputs", "analysis_ready_default", "saliency_2.csv"),
      file.path(dirname(phase2_dir), "audit_outputs", "normalized_with_participant_id", "saliency_2.csv"),
      file.path(project_root, "saliency_2.csv"),
      file.path(find_parent_by_file(c(empirical_dir, data_dir, project_root), "saliency_2.csv", max_depth = 7), "saliency_2.csv")
    ),
    type = "file",
    required = FALSE,
    label = "single-concept Likert salience data, saliency_2.csv"
  )
)

dimensionality_files <- list(
  global = first_existing(
    c(
      file.path(dimensionality_dir, "global_dimensionality_wide.csv"),
      file.path(data_dir, "dimensionality_decisions", "global_dimensionality_wide.csv"),
      file.path(project_root, "global_dimensionality_wide.csv"),
      file.path(find_parent_by_file(c(data_dir, project_root), "global_dimensionality_wide.csv", max_depth = 7), "global_dimensionality_wide.csv")
    ),
    type = "file",
    required = FALSE,
    label = "global dimensionality decisions"
  ),
  local = first_existing(
    c(
      file.path(dimensionality_dir, "local_dimensionality_wide.csv"),
      file.path(data_dir, "dimensionality_decisions", "local_dimensionality_wide.csv"),
      file.path(project_root, "local_dimensionality_wide.csv"),
      file.path(find_parent_by_file(c(data_dir, project_root), "local_dimensionality_wide.csv", max_depth = 7), "local_dimensionality_wide.csv")
    ),
    type = "file",
    required = FALSE,
    label = "local dimensionality decisions"
  )
)

pair_design_raw <- read_csv_fast(stimuli_files$pairwise_design)
triplet_design <- read_csv_fast(stimuli_files$triplet_design)
diagnostic_design <- read_csv_fast(stimuli_files$diagnostic_design)
saliency_2_raw <- read_csv_fast(phase2_files$saliency_2, required = FALSE)
global_dimensionality_raw <- read_csv_fast(dimensionality_files$global, required = FALSE)
local_dimensionality_raw <- read_csv_fast(dimensionality_files$local, required = FALSE)

subspace_raw <- read_csv_fast(phase4_files$subspace)
operator_raw <- read_csv_fast(phase4_files$operator_density)
qsm_raw <- read_csv_fast(phase4_files$qsm_state)
classical_raw <- read_csv_fast(phase4_files$classical)
triplet_distance_raw <- read_csv_fast(phase4_files$triplet_distance)
triplet_mti_raw <- read_csv_fast(phase4_files$triplet_mti)
diag_context_raw <- read_csv_fast(phase4_files$diagnostic_context)
diag_perplexity_raw <- read_csv_fast(phase4_files$diagnostic_perplexity)
diag_choice_raw <- read_csv_fast(phase4_files$diagnostic_choice)
representation_alignment <- read_csv_fast(phase4_files$representation_alignment)
variant_sensitivity <- read_csv_fast(phase4_files$variant_sensitivity)

pairwise_long_raw <- if (isTRUE(params$read_pairwise_long) && file.exists(phase4_files$pairwise_long)) {
  read_csv_fast(phase4_files$pairwise_long)
} else {
  NULL
}

overview <- tibble(
  data_object = c(
    "pair_design_raw", "triplet_design", "diagnostic_design", "subspace_raw", "operator_raw", "qsm_raw",
    "classical_raw", "triplet_distance_raw", "triplet_mti_raw", "diag_context_raw", "diag_perplexity_raw",
    "diag_choice_raw", "representation_alignment", "variant_sensitivity"
  ),
  rows = c(
    nrow(pair_design_raw), nrow(triplet_design), nrow(diagnostic_design), nrow(subspace_raw), nrow(operator_raw), nrow(qsm_raw),
    nrow(classical_raw), nrow(triplet_distance_raw), nrow(triplet_mti_raw), nrow(diag_context_raw), nrow(diag_perplexity_raw),
    nrow(diag_choice_raw), nrow(representation_alignment), nrow(variant_sensitivity)
  ),
  columns = c(
    ncol(pair_design_raw), ncol(triplet_design), ncol(diagnostic_design), ncol(subspace_raw), ncol(operator_raw), ncol(qsm_raw),
    ncol(classical_raw), ncol(triplet_distance_raw), ncol(triplet_mti_raw), ncol(diag_context_raw), ncol(diag_perplexity_raw),
    ncol(diag_choice_raw), ncol(representation_alignment), ncol(variant_sensitivity)
  )
)

apa_table(overview, caption = "Table 1. Imported data objects.")

Table 1. Imported data objects.

data_object	rows	columns
pair_design_raw	350	34
triplet_design	66	17
diagnostic_design	220	15
subspace_raw	113288	38
operator_raw	451248	25
qsm_raw	171360	17
classical_raw	7140	11
triplet_distance_raw	3168	12
triplet_mti_raw	3168	13
diag_context_raw	3520	26
diag_perplexity_raw	1760	36
diag_choice_raw	9856	13
representation_alignment	7616	18
variant_sensitivity	26712	16

write_table(overview, "table_01_imported_data_objects.csv")

6 Prepare human-aligned analysis tables

pair_behavior <- pair_design_raw %>%
  rename(
    human_target_a = target_a,
    human_target_b = target_b
  ) %>%
  mutate(
    pair_id = if_else(is.na(pair_id), canonical_pair(human_target_a, human_target_b), pair_id),
    human_first = as.character(human_target_a),
    human_second = as.character(human_target_b),
    context = as.character(context),
    human_value = as.numeric(human_value),
    human_n = as.numeric(human_n)
  ) %>%
  filter(both_available %in% c(TRUE, "TRUE", 1, "1"), !is.na(human_value))

human_pair_ids <- pair_behavior %>% distinct(pair_id)

subspace_metric_cols <- c(
  "principal_overlap_trace", "principal_overlap_nuclear", "mean_cosine", "mean_cosine_sq", "min_cosine", "max_cosine",
  "mean_angle_deg", "max_angle_deg", "min_angle_deg", "containment_a_to_b", "containment_b_to_a",
  "containment_asymmetry_a_minus_b", "symmetric_projector_overlap", "projector_chordal_distance",
  "projector_chordal_distance_normalized", "grassmann_geodesic_min_dim", "projector_commutator_fro",
  "projector_commutator_fro_normalized", "density_fidelity_from_projectors", "density_bures_from_projectors",
  "qsm_neutral_a_to_b", "qsm_neutral_b_to_a", "qsm_neutral_asymmetry_a_minus_b"
)

operator_metric_cols <- c(
  "trace_inner", "frobenius_distance", "frobenius_distance_sq", "cosine_hilbert_schmidt",
  "a_in_b_trace_normalized", "b_in_a_trace_normalized", "containment_asymmetry_a_minus_b",
  "symmetric_trace_normalized_overlap", "frobenius_distance_trace_normalized"
)

qsm_metric_cols <- c("qsm_p_b_given_a", "qsm_p_a_given_b", "qsm_asymmetry_a_to_b_minus_b_to_a")

make_subspace_long <- function(df) {
  df %>%
    semi_join(human_pair_ids, by = "pair_id") %>%
    rename(model_target_a = target_a, model_target_b = target_b) %>%
    pivot_longer(cols = any_of(subspace_metric_cols), names_to = "metric_name", values_to = "value") %>%
    mutate(
      metric_source = "pairwise_subspace_metrics",
      object = basis_object,
      state_vector_source = NA_character_,
      state_type = NA_character_
    )
}

make_operator_long <- function(df) {
  df %>%
    semi_join(human_pair_ids, by = "pair_id") %>%
    rename(model_target_a = target_a, model_target_b = target_b, basis_object = object) %>%
    pivot_longer(cols = any_of(operator_metric_cols), names_to = "metric_name", values_to = "value") %>%
    mutate(
      metric_source = "pairwise_operator_density_metrics",
      object = basis_object,
      state_vector_source = NA_character_,
      state_type = NA_character_
    )
}

make_qsm_long <- function(df) {
  df %>%
    semi_join(human_pair_ids, by = "pair_id") %>%
    rename(model_target_a = target_a, model_target_b = target_b) %>%
    pivot_longer(cols = any_of(qsm_metric_cols), names_to = "metric_name", values_to = "value") %>%
    mutate(
      metric_source = "pairwise_qsm_state_metrics",
      object = basis_object
    )
}

make_classical_long <- function(df) {
  df %>%
    semi_join(human_pair_ids, by = "pair_id") %>%
    rename(model_target_a = target_a, model_target_b = target_b) %>%
    pivot_longer(
      cols = any_of(c("cosine", "angular_distance", "euclidean_distance", "dot_product")),
      names_to = "baseline_metric",
      values_to = "value"
    ) %>%
    mutate(
      metric_name = paste0("classical_", vector_source, "_", baseline_metric),
      metric_source = "classical_baselines",
      variant = "classical",
      cluster_method = NA_character_,
      global_k_method = NA_character_,
      local_k_method = NA_character_,
      basis_object = NA_character_,
      object = vector_source,
      state_vector_source = vector_source,
      state_type = "vector"
    )
}

pairwise_metric_values <- bind_rows(
  make_subspace_long(subspace_raw),
  make_operator_long(operator_raw),
  make_qsm_long(qsm_raw),
  make_classical_long(classical_raw)
) %>%
  mutate(
    value = as.numeric(value),
    metric_family = metric_family_from_source(metric_source),
    metric_short = metric_short_label(metric_name),
    variant_label = if_else(metric_source == "classical_baselines", "classical", variant_short(variant)),
    metric_id = paste(
      metric_source, metric_name, coalesce(variant, ""), coalesce(basis_object, ""),
      coalesce(state_vector_source, ""), coalesce(state_type, ""), sep = " | "
    )
  )

join_metrics_to_behavior <- function(human_df, metrics_df = pairwise_metric_values) {
  metrics_df %>%
    inner_join(human_df, by = "pair_id") %>%
    mutate(
      direction_sign = case_when(
        model_target_a == human_first & model_target_b == human_second ~ 1,
        model_target_a == human_second & model_target_b == human_first ~ -1,
        TRUE ~ NA_real_
      ),
      metric_value_directional = orient_asymmetry_to_human_order(metric_name, value, direction_sign),
      metric_value = similarity_orient_value(metric_name, metric_value_directional),
      metric_direction = case_when(
        is_asymmetry_metric(metric_name) ~ "directional_asymmetry",
        is_distance_metric(metric_name) ~ "distance_reversed_to_similarity",
        TRUE ~ "similarity_or_overlap"
      )
    )
}

pairwise_all_human <- join_metrics_to_behavior(pair_behavior)
write_csv(pairwise_all_human, file.path(output_dir, "data", "pairwise_all_human_aligned_long_v7.csv"))

pairwise_source_summary <- pairwise_all_human %>%
  count(hypothesis, metric_family, metric_source, sort = TRUE)

apa_table(
  pairwise_source_summary,
  caption = "Table 2. Human-aligned pairwise metric rows by hypothesis and metric family."
)

Table 2. Human-aligned pairwise metric rows by hypothesis and metric family.

hypothesis	metric_family	metric_source	n
H3_likert_order_asymmetry_H4_triangle_network	Operator/density geometry	pairwise_operator_density_metrics	103680
H3_likert_order_asymmetry_H4_triangle_network	Subspace/projector geometry	pairwise_subspace_metrics	66240
H6_diagnosticity_choice_full	Operator/density geometry	pairwise_operator_density_metrics	38016
H6_diagnosticity_rating	Operator/density geometry	pairwise_operator_density_metrics	25344
H6_diagnosticity_choice_full	Subspace/projector geometry	pairwise_subspace_metrics	24288
H1_asymmetry_ipsative	Operator/density geometry	pairwise_operator_density_metrics	17280
H2_salience	Operator/density geometry	pairwise_operator_density_metrics	17280
H6_diagnosticity_rating	Subspace/projector geometry	pairwise_subspace_metrics	16192
H3_likert_order_asymmetry_H4_triangle_network	Sequential QSM	pairwise_qsm_state_metrics	12960
H1_asymmetry_ipsative	Subspace/projector geometry	pairwise_subspace_metrics	11040
H2_salience	Subspace/projector geometry	pairwise_subspace_metrics	11040
H6_diagnosticity_choice_full	Sequential QSM	pairwise_qsm_state_metrics	4752
H6_diagnosticity_rating	Sequential QSM	pairwise_qsm_state_metrics	3168
H1_asymmetry_ipsative	Sequential QSM	pairwise_qsm_state_metrics	2160
H2_salience	Sequential QSM	pairwise_qsm_state_metrics	2160
H3_likert_order_asymmetry_H4_triangle_network	Classical vector baseline	classical_baselines	720
H6_diagnosticity_choice_full	Classical vector baseline	classical_baselines	264
H6_diagnosticity_rating	Classical vector baseline	classical_baselines	176
H1_asymmetry_ipsative	Classical vector baseline	classical_baselines	120
H2_salience	Classical vector baseline	classical_baselines	120

write_table(pairwise_source_summary, "table_02_pairwise_rows_by_hypothesis_and_metric_family.csv")

7 Compute all hypothesis-level rankings

# H1 and H2 use directional asymmetry metrics as primary, but cosine baselines are kept for systematic comparison.
h1_human <- pair_behavior %>% filter(hypothesis == "H1_asymmetry_ipsative")
h2_human <- pair_behavior %>% filter(hypothesis == "H2_salience")

h1_all <- join_metrics_to_behavior(h1_human)
h2_all <- join_metrics_to_behavior(h2_human)

rank_group_cols <- c(
  "metric_id", "metric_source", "metric_family", "metric_name", "metric_short", "variant", "variant_label", "cluster_method",
  "global_k_method", "local_k_method", "basis_object", "object", "state_vector_source", "state_type", "metric_direction"
)

h1_rank_all <- cor_by_group(h1_all, rank_group_cols) %>% mutate(analysis_block = "H1 ipsative asymmetry")
h1_rank_directional <- h1_rank_all %>% filter(is_asymmetry_metric(metric_name))
h1_rank_baselines <- h1_rank_all %>% filter(metric_source == "classical_baselines")

h2_rank_all <- cor_by_group(h2_all, rank_group_cols) %>% mutate(analysis_block = "H2 salience")
h2_rank_directional <- h2_rank_all %>% filter(is_asymmetry_metric(metric_name))
h2_rank_baselines <- h2_rank_all %>% filter(metric_source == "classical_baselines")

# H2b: single-concept Likert salience.
# This is concept-level rather than pairwise. Therefore, the relevant predictors are not pairwise cosines,
# but properties of each concept representation: frequency, global dimensionality, and local richness.
salience_metadata_cols <- c(
  "ID", "source_file", "source_row", "raw_ID", "participant_id",
  "attempt_index_within_source", "n_rows_for_participant_in_source"
)

salience_likert_long <- if (nrow(saliency_2_raw) > 0) {
  saliency_2_raw %>%
    select(-any_of(salience_metadata_cols), -ends_with("_rt")) %>%
    pivot_longer(everything(), names_to = "target_raw", values_to = "salience_likert") %>%
    mutate(
      target_id = normalize_salience_target(target_raw),
      salience_likert = as.numeric(salience_likert)
    ) %>%
    filter(!is.na(salience_likert), salience_likert >= 1, salience_likert <= 9)
} else {
  tibble(target_raw = character(), target_id = character(), salience_likert = numeric())
}

salience_likert_summary <- salience_likert_long %>%
  group_by(target_id) %>%
  summarise(
    mean_salience_likert = mean(salience_likert, na.rm = TRUE),
    sd_salience_likert = sd(salience_likert, na.rm = TRUE),
    n_salience_likert = n(),
    se_salience_likert = sd_salience_likert / sqrt(n_salience_likert),
    .groups = "drop"
  )

local_dimensionality_summary <- if (nrow(local_dimensionality_raw) > 0) {
  local_dimensionality_raw %>%
    mutate(
      is_estimable_local = !is.na(rank_effective) & rank_effective >= 1,
      across(any_of(c("gavish_donoho", "horn_wishart", "permutation_pa", "profile_likelihood", "var80", "var90", "var95")), as.numeric)
    ) %>%
    group_by(target_id, cluster_method) %>%
    summarise(
      n_local_candidates = n(),
      n_estimable_local_clusters = sum(is_estimable_local, na.rm = TRUE),
      mean_local_gavish_donoho = mean(gavish_donoho[is_estimable_local], na.rm = TRUE),
      mean_local_horn_wishart = mean(horn_wishart[is_estimable_local], na.rm = TRUE),
      mean_local_permutation_pa = mean(permutation_pa[is_estimable_local], na.rm = TRUE),
      sum_local_gavish_donoho = sum(gavish_donoho[is_estimable_local], na.rm = TRUE),
      sum_local_horn_wishart = sum(horn_wishart[is_estimable_local], na.rm = TRUE),
      sum_local_permutation_pa = sum(permutation_pa[is_estimable_local], na.rm = TRUE),
      .groups = "drop"
    ) %>%
    pivot_wider(
      names_from = cluster_method,
      values_from = c(
        n_local_candidates, n_estimable_local_clusters,
        mean_local_gavish_donoho, mean_local_horn_wishart, mean_local_permutation_pa,
        sum_local_gavish_donoho, sum_local_horn_wishart, sum_local_permutation_pa
      ),
      names_sep = "__"
    )
} else {
  tibble(target_id = character())
}

salience_likert_dimensionality <- salience_likert_summary %>%
  inner_join(global_dimensionality_raw, by = "target_id") %>%
  left_join(local_dimensionality_summary, by = "target_id") %>%
  mutate(
    log10_n_occurrences = log10(n_occurrences),
    salience_z = z_score(mean_salience_likert),
    log10_n_occurrences_z = z_score(log10_n_occurrences)
  )

salience_predictor_cols <- c(
  "log10_n_occurrences", "n_occurrences", "rank_effective", "broken_stick", "gavish_donoho",
  "horn_wishart", "permutation_pa", "marchenko_pastur", "profile_likelihood",
  "individual_var_ge_0.005", "var80", "var90", "var95", "var99",
  "n_estimable_local_clusters__bayesian_gmm", "n_estimable_local_clusters__gmm_bic",
  "mean_local_gavish_donoho__bayesian_gmm", "mean_local_gavish_donoho__gmm_bic",
  "sum_local_gavish_donoho__bayesian_gmm", "sum_local_gavish_donoho__gmm_bic",
  "mean_local_horn_wishart__bayesian_gmm", "mean_local_horn_wishart__gmm_bic",
  "sum_local_horn_wishart__bayesian_gmm", "sum_local_horn_wishart__gmm_bic"
)

salience_predictor_labels <- c(
  log10_n_occurrences = "Log frequency",
  n_occurrences = "Raw frequency",
  rank_effective = "Effective rank",
  broken_stick = "Broken-stick dimensionality",
  gavish_donoho = "Gavish-Donoho dimensionality",
  horn_wishart = "Horn/Wishart dimensionality",
  permutation_pa = "Permutation PA dimensionality",
  marchenko_pastur = "Marchenko-Pastur dimensionality",
  profile_likelihood = "Profile-likelihood dimensionality",
  individual_var_ge_0.005 = "Individual variance ≥ .005",
  var80 = "Dimensions for 80% variance",
  var90 = "Dimensions for 90% variance",
  var95 = "Dimensions for 95% variance",
  var99 = "Dimensions for 99% variance",
  `n_estimable_local_clusters__bayesian_gmm` = "Estimable local clusters, Bayesian GMM",
  `n_estimable_local_clusters__gmm_bic` = "Estimable local clusters, GMM-BIC",
  `mean_local_gavish_donoho__bayesian_gmm` = "Mean local Gavish, Bayesian GMM",
  `mean_local_gavish_donoho__gmm_bic` = "Mean local Gavish, GMM-BIC",
  `sum_local_gavish_donoho__bayesian_gmm` = "Total local Gavish, Bayesian GMM",
  `sum_local_gavish_donoho__gmm_bic` = "Total local Gavish, GMM-BIC",
  `mean_local_horn_wishart__bayesian_gmm` = "Mean local Horn, Bayesian GMM",
  `mean_local_horn_wishart__gmm_bic` = "Mean local Horn, GMM-BIC",
  `sum_local_horn_wishart__bayesian_gmm` = "Total local Horn, Bayesian GMM",
  `sum_local_horn_wishart__gmm_bic` = "Total local Horn, GMM-BIC"
)

h2_likert_predictor_long <- salience_likert_dimensionality %>%
  pivot_longer(
    cols = any_of(salience_predictor_cols),
    names_to = "metric_name",
    values_to = "metric_value"
  ) %>%
  mutate(
    metric_value = as.numeric(metric_value),
    human_value = mean_salience_likert,
    metric_source = "concept_level_dimensionality",
    metric_family = case_when(
      metric_name %in% c("log10_n_occurrences", "n_occurrences") ~ "Corpus frequency baseline",
      str_detect(metric_name, "local|clusters") ~ "Local representational richness",
      TRUE ~ "Global representational dimensionality"
    ),
    metric_short = recode(metric_name, !!!salience_predictor_labels, .default = metric_name),
    variant = NA_character_,
    variant_label = NA_character_,
    cluster_method = NA_character_,
    global_k_method = NA_character_,
    local_k_method = NA_character_,
    basis_object = NA_character_,
    object = "concept-level representation",
    state_vector_source = NA_character_,
    state_type = NA_character_,
    metric_direction = "concept_level_predictor",
    metric_id = paste(metric_source, metric_name, sep = " | ")
  ) %>%
  filter(!is.na(metric_value), is.finite(metric_value), !is.na(human_value))

h2_likert_rank <- cor_by_group(h2_likert_predictor_long, rank_group_cols) %>%
  mutate(analysis_block = "H2b Likert salience")

run_frequency_adjusted_salience_model <- function(predictor_name) {
  d <- salience_likert_dimensionality %>%
    select(target_id, mean_salience_likert, log10_n_occurrences, all_of(predictor_name)) %>%
    rename(predictor = all_of(predictor_name)) %>%
    mutate(
      predictor = as.numeric(predictor),
      salience_z = z_score(mean_salience_likert),
      predictor_z = z_score(predictor),
      log_frequency_z = z_score(log10_n_occurrences)
    ) %>%
    filter(if_all(all_of(c("salience_z", "predictor_z", "log_frequency_z")), ~ !is.na(.x) & is.finite(.x)))

  if (nrow(d) < 6 || n_distinct(d$predictor_z) < 2) {
    return(tibble(
      metric_name = predictor_name,
      n = nrow(d),
      beta_predictor = NA_real_,
      p_predictor = NA_real_,
      beta_log_frequency = NA_real_,
      p_log_frequency = NA_real_,
      r_squared = NA_real_
    ))
  }

  fit <- lm(salience_z ~ predictor_z + log_frequency_z, data = d)
  td <- broom::tidy(fit)
  gl <- broom::glance(fit)
  tibble(
    metric_name = predictor_name,
    n = nrow(d),
    beta_predictor = td$estimate[td$term == "predictor_z"],
    p_predictor = td$p.value[td$term == "predictor_z"],
    beta_log_frequency = td$estimate[td$term == "log_frequency_z"],
    p_log_frequency = td$p.value[td$term == "log_frequency_z"],
    r_squared = gl$r.squared
  )
}

h2_likert_frequency_adjusted <- map_dfr(
  setdiff(intersect(salience_predictor_cols, names(salience_likert_dimensionality)), c("log10_n_occurrences", "n_occurrences")),
  run_frequency_adjusted_salience_model
) %>%
  mutate(
    metric_short = recode(metric_name, !!!salience_predictor_labels, .default = metric_name),
    p_fdr_predictor = p.adjust(p_predictor, method = "BH"),
    abs_beta_predictor = abs(beta_predictor)
  ) %>%
  arrange(p_predictor, desc(abs_beta_predictor))


# H2c: planned salience/similarity condition structure from the thesis annex.
# The annex condition table is entered explicitly because the exported response files do not carry
# this full design metadata. The order here is the theoretical/planned order, not necessarily the
# actual on-screen presentation order in every task file.
annex_salience_conditions <- tibble::tribble(
  ~planned_concept_1, ~planned_concept_2, ~planned_concept_1_es, ~planned_concept_2_es, ~planned_salience_1, ~planned_salience_2, ~planned_similarity, ~annex_condition, ~condition_source,
  "ghana", "luxemburgo", "Ghana", "Luxemburgo", "low", "low", "low", "low_low__low_similarity", "thesis_annex",
  "islas_feroe", "singapur", "Islas Feroe", "Singapur", "low", "low", "low", "low_low__low_similarity", "thesis_annex",
  "burkina_faso", "guayana_francesa", "Burkina Faso", "Guayana Francesa", "low", "low", "low", "low_low__low_similarity", "thesis_annex",
  "mongolia", "bulgaria", "Mongolia", "Bulgaria", "low", "low", "low", "low_low__low_similarity", "thesis_annex",
  "oman", "belice", "Omán", "Belice", "low", "low", "low", "low_low__low_similarity", "thesis_annex",

  "eslovenia", "eslovaquia", "Eslovenia", "Eslovaquia", "low", "low", "high", "low_low__high_similarity", "thesis_annex",
  "zambia", "zimbabue", "Zambia", "Zimbabue", "low", "low", "high", "low_low__high_similarity", "thesis_annex",
  "laos", "camboya", "Laos", "Camboya", "low", "low", "high", "low_low__high_similarity", "thesis_annex",
  "oman", "yemen", "Omán", "Yemen", "low", "low", "high", "low_low__high_similarity", "thesis_annex",
  "turkmenistan", "uzbekistan", "Turkmenistán", "Uzbekistán", "low", "low", "high", "low_low__high_similarity", "thesis_annex",

  "francia", "bolivia", "Francia", "Bolivia", "high", "low", "low", "high_low__low_similarity", "thesis_annex",
  "estados_unidos", "belice", "Estados Unidos", "Belice", "high", "low", "low", "high_low__low_similarity", "thesis_annex",
  "china", "luxemburgo", "China", "Luxemburgo", "high", "low", "low", "high_low__low_similarity", "thesis_annex",
  "mexico", "laos", "México", "Laos", "high", "low", "low", "high_low__low_similarity", "thesis_annex",
  "rusia", "burkina_faso", "Rusia", "Burkina Faso", "high", "low", "low", "high_low__low_similarity", "thesis_annex",

  "francia", "belgica", "Francia", "Bélgica", "high", "low", "high", "high_low__high_similarity", "thesis_annex",
  "espana", "andorra", "España", "Andorra", "high", "low", "high", "high_low__high_similarity", "thesis_annex",
  "china", "singapur", "China", "Singapur", "high", "low", "high", "high_low__high_similarity", "thesis_annex",
  "rusia", "bielorrusia", "Rusia", "Bielorrusia", "high", "low", "high", "high_low__high_similarity", "thesis_annex",
  "argentina", "paraguay", "Argentina", "Paraguay", "high", "low", "high", "high_low__high_similarity", "thesis_annex",

  "francia", "brasil", "Francia", "Brasil", "high", "high", "low", "high_high__low_similarity", "thesis_annex",
  "alemania", "canada", "Alemania", "Canadá", "high", "high", "low", "high_high__low_similarity", "thesis_annex",
  "italia", "japon", "Italia", "Japón", "high", "high", "low", "high_high__low_similarity", "thesis_annex",
  "marruecos", "argentina", "Marruecos", "Argentina", "high", "high", "low", "high_high__low_similarity", "thesis_annex",
  "india", "mexico", "India", "México", "high", "high", "low", "high_high__low_similarity", "thesis_annex",

  "italia", "espana", "Italia", "España", "high", "high", "high", "high_high__high_similarity", "thesis_annex",
  "reino_unido", "estados_unidos", "Reino Unido", "Estados Unidos", "high", "high", "high", "high_high__high_similarity", "thesis_annex",
  "suecia", "noruega", "Suecia", "Noruega", "high", "high", "high", "high_high__high_similarity", "thesis_annex",
  "brasil", "portugal", "Brasil", "Portugal", "high", "high", "high", "high_high__high_similarity", "thesis_annex",
  "mexico", "colombia", "México", "Colombia", "high", "high", "high", "high_high__high_similarity", "thesis_annex_not_observed_in_current_human_pair_file",
  "ecuador", "peru", "Ecuador", "Perú", "high", "high", "high", "high_high__high_similarity", "observed_human_file_replacement_or_extra"
) %>%
  mutate(
    pair_id = canonical_pair(planned_concept_1, planned_concept_2),
    planned_salience_pair = paste(planned_salience_1, planned_salience_2, sep = "_"),
    planned_similarity = factor(planned_similarity, levels = c("low", "high")),
    planned_salience_pair = factor(planned_salience_pair, levels = c("low_low", "high_low", "high_high")),
    annex_condition = factor(
      annex_condition,
      levels = c(
        "low_low__low_similarity", "low_low__high_similarity",
        "high_low__low_similarity", "high_low__high_similarity",
        "high_high__low_similarity", "high_high__high_similarity"
      )
    )
  )

annex_condition_audit <- annex_salience_conditions %>%
  left_join(
    pair_behavior %>% distinct(pair_id) %>% mutate(observed_in_human_pair_design = TRUE),
    by = "pair_id"
  ) %>%
  mutate(observed_in_human_pair_design = coalesce(observed_in_human_pair_design, FALSE))

pair_behavior_with_conditions <- pair_behavior %>%
  left_join(annex_salience_conditions, by = "pair_id") %>%
  mutate(
    human_first_planned_salience = case_when(
      human_first == planned_concept_1 ~ planned_salience_1,
      human_first == planned_concept_2 ~ planned_salience_2,
      TRUE ~ NA_character_
    ),
    human_second_planned_salience = case_when(
      human_second == planned_concept_1 ~ planned_salience_1,
      human_second == planned_concept_2 ~ planned_salience_2,
      TRUE ~ NA_character_
    ),
    presentation_salience_pattern = if_else(
      !is.na(human_first_planned_salience) & !is.na(human_second_planned_salience),
      paste(human_first_planned_salience, human_second_planned_salience, sep = "_"),
      NA_character_
    ),
    presentation_salience_pattern = factor(
      presentation_salience_pattern,
      levels = c("low_low", "low_high", "high_low", "high_high")
    ),
    salience_contrast_type = case_when(
      presentation_salience_pattern %in% c("high_low", "low_high") ~ "mixed_salience",
      presentation_salience_pattern == "high_high" ~ "both_high",
      presentation_salience_pattern == "low_low" ~ "both_low",
      TRUE ~ NA_character_
    ),
    prop_choose_high_salience = case_when(
      hypothesis == "H2_salience" & presentation_salience_pattern == "high_low" ~ human_value,
      hypothesis == "H2_salience" & presentation_salience_pattern == "low_high" ~ 1 - human_value,
      TRUE ~ NA_real_
    ),
    distance_from_chance = abs(human_value - .5)
  )

annex_concept_salience_labels <- annex_salience_conditions %>%
  select(pair_id, planned_concept_1, planned_concept_2, planned_salience_1, planned_salience_2) %>%
  pivot_longer(
    cols = c(planned_concept_1, planned_concept_2),
    names_to = "concept_position",
    values_to = "target_id"
  ) %>%
  mutate(
    planned_salience_label = if_else(concept_position == "planned_concept_1", planned_salience_1, planned_salience_2)
  ) %>%
  distinct(target_id, planned_salience_label) %>%
  group_by(target_id) %>%
  summarise(
    n_high_labels = sum(planned_salience_label == "high"),
    n_low_labels = sum(planned_salience_label == "low"),
    planned_salience_label = case_when(
      n_high_labels > 0 & n_low_labels == 0 ~ "high",
      n_low_labels > 0 & n_high_labels == 0 ~ "low",
      n_high_labels > 0 & n_low_labels > 0 ~ "mixed_or_inconsistent",
      TRUE ~ NA_character_
    ),
    .groups = "drop"
  )

group_difference <- function(data, value_col, group_col, high_label = "high", low_label = "low") {
  d <- data %>%
    select(value = all_of(value_col), group = all_of(group_col)) %>%
    filter(!is.na(value), is.finite(value), group %in% c(high_label, low_label)) %>%
    mutate(group = as.character(group))

  if (nrow(d) < 4 || n_distinct(d$group) < 2) {
    return(tibble(
      outcome = value_col,
      n_high = sum(d$group == high_label),
      n_low = sum(d$group == low_label),
      mean_high = mean(d$value[d$group == high_label], na.rm = TRUE),
      mean_low = mean(d$value[d$group == low_label], na.rm = TRUE),
      difference_high_minus_low = NA_real_,
      p.value = NA_real_
    ))
  }

  tt <- suppressWarnings(t.test(value ~ group, data = d))
  tibble(
    outcome = value_col,
    n_high = sum(d$group == high_label),
    n_low = sum(d$group == low_label),
    mean_high = mean(d$value[d$group == high_label], na.rm = TRUE),
    mean_low = mean(d$value[d$group == low_label], na.rm = TRUE),
    difference_high_minus_low = mean_high - mean_low,
    p.value = tt$p.value
  )
}

h2c_human_condition_summary <- pair_behavior_with_conditions %>%
  filter(hypothesis %in% c("H1_asymmetry_ipsative", "H2_salience", "H3_likert_order_asymmetry_H4_triangle_network")) %>%
  filter(!is.na(annex_condition)) %>%
  group_by(hypothesis, annex_condition, presentation_salience_pattern, planned_similarity) %>%
  summarise(
    n_items = n_distinct(pair_id),
    mean_human_value = mean(human_value, na.rm = TRUE),
    mean_abs_deviation_from_chance = mean(distance_from_chance, na.rm = TRUE),
    mean_prop_choose_high_salience = mean(prop_choose_high_salience, na.rm = TRUE),
    .groups = "drop"
  )

h2c_likert_condition_dimensionality <- salience_likert_dimensionality %>%
  inner_join(annex_concept_salience_labels, by = "target_id") %>%
  filter(planned_salience_label %in% c("high", "low"))

h2c_concept_condition_summary <- h2c_likert_condition_dimensionality %>%
  group_by(planned_salience_label) %>%
  summarise(
    n_concepts = n(),
    mean_likert_salience = mean(mean_salience_likert, na.rm = TRUE),
    mean_log10_frequency = mean(log10_n_occurrences, na.rm = TRUE),
    mean_effective_rank = mean(rank_effective, na.rm = TRUE),
    mean_horn_dimensionality = mean(horn_wishart, na.rm = TRUE),
    mean_gavish_dimensionality = mean(gavish_donoho, na.rm = TRUE),
    mean_permutation_dimensionality = mean(permutation_pa, na.rm = TRUE),
    .groups = "drop"
  )

h2c_concept_condition_tests <- map_dfr(
  intersect(c("mean_salience_likert", "log10_n_occurrences", "rank_effective", "horn_wishart", "gavish_donoho", "permutation_pa", "profile_likelihood"), names(h2c_likert_condition_dimensionality)),
  ~ group_difference(h2c_likert_condition_dimensionality, .x, "planned_salience_label")
) %>%
  mutate(
    p_fdr = p.adjust(p.value, method = "BH"),
    outcome_label = recode(outcome, !!!salience_predictor_labels, mean_salience_likert = "Mean Likert salience", log10_n_occurrences = "Log frequency", .default = outcome)
  ) %>%
  arrange(p.value)

h2c_similarity_condition_human <- pair_behavior %>%
  filter(hypothesis == "H3_likert_order_asymmetry_H4_triangle_network", response_type == "rating_1_9") %>%
  group_by(pair_id) %>%
  summarise(
    human_value = mean(human_value, na.rm = TRUE),
    human_sd = sd(human_value, na.rm = TRUE),
    human_n = sum(human_n, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  inner_join(annex_salience_conditions, by = "pair_id")

h2c_similarity_condition_summary <- h2c_similarity_condition_human %>%
  group_by(planned_similarity, planned_salience_pair) %>%
  summarise(
    n_pairs = n_distinct(pair_id),
    mean_human_similarity = mean(human_value, na.rm = TRUE),
    sd_human_similarity = sd(human_value, na.rm = TRUE),
    .groups = "drop"
  )

h2c_similarity_condition_lm <- if (nrow(h2c_similarity_condition_human) >= 6) {
  broom::tidy(lm(human_value ~ planned_similarity + planned_salience_pair, data = h2c_similarity_condition_human))
} else {
  tibble(term = character(), estimate = numeric(), std.error = numeric(), statistic = numeric(), p.value = numeric())
}

h2c_pairwise_condition_metric_tests <- pairwise_metric_values %>%
  inner_join(annex_salience_conditions %>% select(pair_id, planned_similarity, annex_condition, planned_salience_pair), by = "pair_id") %>%
  filter(!is_asymmetry_metric(metric_name)) %>%
  mutate(metric_value = similarity_orient_value(metric_name, value)) %>%
  filter(!is.na(metric_value), is.finite(metric_value)) %>%
  group_by(metric_id, metric_source, metric_family, metric_name, metric_short, variant, variant_label, basis_object, object, state_vector_source, state_type) %>%
  group_modify(~ group_difference(.x, "metric_value", "planned_similarity")) %>%
  ungroup() %>%
  mutate(
    p_fdr = p.adjust(p.value, method = "BH"),
    abs_difference = abs(difference_high_minus_low)
  ) %>%
  arrange(desc(abs_difference), p.value)

# H3a: symmetric pairwise similarity, order-averaged by pair.
h3_similarity_human <- pair_behavior %>%
  filter(hypothesis == "H3_likert_order_asymmetry_H4_triangle_network", response_type == "rating_1_9") %>%
  group_by(pair_id) %>%
  summarise(
    human_value = mean(human_value, na.rm = TRUE),
    human_sd = sd(human_value, na.rm = TRUE),
    human_n = sum(human_n, na.rm = TRUE),
    human_first = first(human_first),
    human_second = first(human_second),
    hypothesis = "H3_rating_similarity_order_averaged",
    response_type = "rating_1_9_order_averaged",
    .groups = "drop"
  )

h3_similarity_metrics <- pairwise_metric_values %>%
  filter(!is_asymmetry_metric(metric_name)) %>%
  distinct(metric_id, pair_id, .keep_all = TRUE) %>%
  inner_join(h3_similarity_human, by = "pair_id") %>%
  mutate(
    metric_value = similarity_orient_value(metric_name, value),
    metric_direction = if_else(is_distance_metric(metric_name), "distance_reversed_to_similarity", "similarity_or_overlap")
  )

h3_rating_rank <- cor_by_group(h3_similarity_metrics, rank_group_cols) %>%
  mutate(analysis_block = "H3 Likert similarity")

# H3b: human order asymmetry, compared only with directional asymmetry metrics.
h3_order_human <- pair_behavior %>%
  filter(hypothesis == "H3_likert_order_asymmetry_H4_triangle_network", response_type == "rating_1_9") %>%
  mutate(
    order_label = case_when(
      str_detect(coalesce(direction_version, ""), "direct|a_direct") ~ "direct",
      str_detect(coalesce(direction_version, ""), "reverse|b_reverse") ~ "reverse",
      TRUE ~ as.character(direction_version)
    )
  ) %>%
  filter(order_label %in% c("direct", "reverse")) %>%
  group_by(pair_id) %>%
  summarise(
    direct_mean = mean(human_value[order_label == "direct"], na.rm = TRUE),
    reverse_mean = mean(human_value[order_label == "reverse"], na.rm = TRUE),
    human_first = first(human_first),
    human_second = first(human_second),
    n_orders = n_distinct(order_label),
    .groups = "drop"
  ) %>%
  filter(n_orders == 2, is.finite(direct_mean), is.finite(reverse_mean)) %>%
  mutate(
    human_order_delta = direct_mean - reverse_mean,
    human_value = human_order_delta,
    hypothesis = "H3_order_asymmetry"
  )

h3_order_metrics <- join_metrics_to_behavior(h3_order_human, pairwise_metric_values) %>%
  filter(is_asymmetry_metric(metric_name)) %>%
  distinct(metric_id, pair_id, .keep_all = TRUE)

h3_order_rank <- cor_by_group(h3_order_metrics, rank_group_cols, y = "human_order_delta") %>%
  mutate(analysis_block = "H3 order asymmetry")

h3_order_test <- broom::tidy(t.test(h3_order_human$human_order_delta, mu = 0)) %>%
  transmute(
    n = nrow(h3_order_human),
    mean_delta = mean(h3_order_human$human_order_delta, na.rm = TRUE),
    median_abs_delta = median(abs(h3_order_human$human_order_delta), na.rm = TRUE),
    statistic,
    df = parameter,
    p.value
  )

# H4: triplet residuals from order-averaged human ratings.
h3_pair_similarity <- h3_similarity_human %>%
  left_join(
    pair_behavior %>%
      filter(hypothesis == "H3_likert_order_asymmetry_H4_triangle_network", response_type == "rating_1_9") %>%
      group_by(pair_id) %>%
      summarise(
        scale_min = suppressWarnings(min(human_scale_min, na.rm = TRUE)),
        scale_max = suppressWarnings(max(human_scale_max, na.rm = TRUE)),
        .groups = "drop"
      ),
    by = "pair_id"
  ) %>%
  mutate(
    scale_min = if_else(is.finite(scale_min), scale_min, 1),
    scale_max = if_else(is.finite(scale_max), scale_max, 9),
    human_similarity = (human_value - scale_min) / (scale_max - scale_min),
    human_distance = 1 - human_similarity
  )

human_triplets <- triplet_design %>%
  left_join(h3_pair_similarity %>% select(pair_id, sim_endpoint = human_similarity, d_endpoint = human_distance),
            by = c("endpoint_pair_id" = "pair_id")) %>%
  left_join(h3_pair_similarity %>% select(pair_id, sim_leg_1 = human_similarity, d_leg_1 = human_distance),
            by = c("leg_pair_1_id" = "pair_id")) %>%
  left_join(h3_pair_similarity %>% select(pair_id, sim_leg_2 = human_similarity, d_leg_2 = human_distance),
            by = c("leg_pair_2_id" = "pair_id")) %>%
  mutate(
    human_triangle_residual = d_endpoint - (d_leg_1 + d_leg_2),
    human_triangle_violation = human_triangle_residual > 0,
    human_mti_residual = sim_endpoint - (sim_leg_1 * sim_leg_2),
    human_mti_lower_than_product = human_mti_residual < 0,
    human_mti_higher_than_product = human_mti_residual > 0
  )

human_triplet_summary <- human_triplets %>%
  summarise(
    n_contrasts = n(),
    n_unordered_triplets = n_distinct(triplet_unordered_id),
    additive_violations = sum(human_triangle_violation, na.rm = TRUE),
    mti_lower_than_product = sum(human_mti_lower_than_product, na.rm = TRUE),
    mean_triangle_residual = mean(human_triangle_residual, na.rm = TRUE),
    mean_mti_residual = mean(human_mti_residual, na.rm = TRUE)
  )

triplet_distance_human <- triplet_distance_raw %>%
  inner_join(human_triplets %>% select(triplet_id, human_triangle_residual, human_triangle_violation), by = "triplet_id")

h4_distance_rank <- cor_by_group(
  triplet_distance_human,
  group_cols = c("variant", "basis_object", "distance_metric"),
  x = "triangle_residual_ac_minus_ab_bc",
  y = "human_triangle_residual"
) %>%
  mutate(
    analysis_block = "H4 additive triangle",
    metric_source = "triplet_distance_violations",
    metric_family = "Triplet distance geometry",
    metric_name = distance_metric,
    metric_short = metric_short_label(distance_metric),
    variant_label = variant_short(variant)
  )

triplet_mti_human <- triplet_mti_raw %>%
  inner_join(
    human_triplets %>% select(triplet_id, human_mti_residual, human_mti_lower_than_product, human_mti_higher_than_product),
    by = "triplet_id"
  )

h4_mti_rank <- cor_by_group(
  triplet_mti_human,
  group_cols = c("variant", "basis_object", "similarity_metric"),
  x = "mti_residual_sac_minus_sab_sbc",
  y = "human_mti_residual"
) %>%
  mutate(
    analysis_block = "H4 multiplicative triangle",
    metric_source = "triplet_mti_violations",
    metric_family = "Triplet similarity geometry",
    metric_name = similarity_metric,
    metric_short = metric_short_label(similarity_metric),
    variant_label = variant_short(variant)
  )

mti_classification <- triplet_mti_human %>%
  group_by(variant, basis_object, similarity_metric) %>%
  summarise(
    n = n(),
    true_positive = sum(mti_lower_than_product & human_mti_lower_than_product, na.rm = TRUE),
    false_positive = sum(mti_lower_than_product & !human_mti_lower_than_product, na.rm = TRUE),
    false_negative = sum(!mti_lower_than_product & human_mti_lower_than_product, na.rm = TRUE),
    true_negative = sum(!mti_lower_than_product & !human_mti_lower_than_product, na.rm = TRUE),
    accuracy = mean(mti_lower_than_product == human_mti_lower_than_product, na.rm = TRUE),
    precision = true_positive / pmax(true_positive + false_positive, 1),
    recall = true_positive / pmax(true_positive + false_negative, 1),
    f1 = if_else(precision + recall > 0, 2 * precision * recall / (precision + recall), 0),
    .groups = "drop"
  ) %>%
  arrange(desc(f1), desc(accuracy))

# H6 static pairwise metrics.
h6_static <- pair_behavior %>% filter(str_detect(hypothesis, "H6_diagnosticity"))
h6_static_metrics <- join_metrics_to_behavior(h6_static, pairwise_metric_values)

h6_static_rank <- cor_by_group(
  h6_static_metrics,
  group_cols = c("hypothesis", rank_group_cols),
  x = "metric_value",
  y = "human_value"
) %>%
  group_by(hypothesis) %>%
  mutate(p_fdr_within_hypothesis = p.adjust(p.value, method = "BH")) %>%
  ungroup() %>%
  mutate(analysis_block = paste("H6 static", hypothesis))

# H6 contextualized metrics.
diag_human_rows <- pair_behavior %>%
  filter(str_detect(hypothesis, "H6_diagnosticity")) %>%
  transmute(
    hypothesis,
    response_type,
    task_family,
    initial = human_first,
    target = human_second,
    context,
    human_value,
    human_n,
    item_id,
    pair_id
  ) %>%
  filter(!is.na(context), !is.na(initial), !is.na(target))

context_metric_cols <- c(
  "contextualized_vector_cosine", "contextualized_vector_dot",
  "density_hs_inner", "density_hs_cosine", "density_fidelity",
  "density_bures_distance", "density_trace_distance", "density_frobenius_distance"
)

h6_context_long <- diag_context_raw %>%
  pivot_longer(cols = any_of(context_metric_cols), names_to = "metric_name", values_to = "value") %>%
  filter(!is.na(value), status == "ok") %>%
  mutate(
    metric_value = similarity_orient_value(metric_name, value),
    metric_source = "diagnostic_contextualized_similarity",
    metric_family = case_when(
      metric_family == "contextualized_vector" ~ "Contextualized vector",
      metric_family == "luders_contextualized_density" ~ "Lüders contextualized density",
      TRUE ~ as.character(metric_family)
    ),
    metric_short = metric_short_label(metric_name),
    metric_id = paste(metric_family, metric_name, variant, basis_object, density_object, state_vector_source, sep = " | "),
    variant_label = variant_short(variant)
  ) %>%
  inner_join(diag_human_rows, by = c("initial", "context", "target"))

h6_context_rank <- cor_by_group(
  h6_context_long,
  group_cols = c(
    "hypothesis", "metric_id", "metric_source", "metric_family", "metric_name", "metric_short", "variant",
    "variant_label", "cluster_method", "global_k_method", "local_k_method", "basis_object", "density_object", "state_vector_source"
  ),
  x = "metric_value",
  y = "human_value"
) %>%
  group_by(hypothesis) %>%
  mutate(p_fdr_within_hypothesis = p.adjust(p.value, method = "BH")) %>%
  ungroup() %>%
  mutate(analysis_block = paste("H6 contextualized", hypothesis))

# H6 perplexity-inhibited metrics.
perplexity_metric_cols <- c(
  "baseline_projector_containment_initial_to_target",
  "perplexity_residual_density_to_target_containment",
  "perplexity_residual_projector_to_target_containment",
  "delta_residual_density_containment_minus_baseline",
  "delta_residual_projector_containment_minus_baseline",
  "perplexity_density_hs_inner",
  "perplexity_density_hs_cosine",
  "perplexity_density_frobenius_distance",
  "perplexity_density_fidelity",
  "perplexity_density_bures_distance",
  "perplexity_density_trace_distance"
)

h6_perplexity_long <- diag_perplexity_raw %>%
  mutate(context = str_remove(condition, "^ctx-")) %>%
  pivot_longer(cols = any_of(perplexity_metric_cols), names_to = "metric_name", values_to = "value") %>%
  filter(!is.na(value)) %>%
  mutate(
    metric_value = similarity_orient_value(metric_name, value),
    metric_source = "diagnostic_perplexity_metrics",
    metric_family = "Perplexity-inhibited diagnostic",
    metric_short = metric_short_label(metric_name),
    metric_id = paste(metric_family, metric_name, variant, basis_object, density_object, sep = " | "),
    variant_label = variant_short(variant)
  ) %>%
  inner_join(diag_human_rows, by = c("initial", "context", "target"))

h6_perplexity_rank <- cor_by_group(
  h6_perplexity_long,
  group_cols = c(
    "hypothesis", "metric_id", "metric_source", "metric_family", "metric_name", "metric_short", "variant",
    "variant_label", "cluster_method", "global_k_method", "local_k_method", "basis_object", "density_object"
  ),
  x = "metric_value",
  y = "human_value"
) %>%
  group_by(hypothesis) %>%
  mutate(p_fdr_within_hypothesis = p.adjust(p.value, method = "BH")) %>%
  ungroup() %>%
  mutate(analysis_block = paste("H6 perplexity", hypothesis))

# Diagnostic choice predictions: compare predicted pairwise winner with the human winner.
# The prediction table contains pairwise target choices; the human option values come from
# H6 choice-full rows, where human_value is the proportion selecting each option.
human_option_values <- pair_behavior %>%
  filter(hypothesis == "H6_diagnosticity_choice_full") %>%
  transmute(
    initial = human_first,
    context,
    target = human_second,
    human_value
  ) %>%
  group_by(initial, context, target) %>%
  summarise(human_value = mean(human_value, na.rm = TRUE), .groups = "drop")

h6_choice_prediction_human <- diag_choice_raw %>%
  mutate(
    context = str_remove(condition, "^ctx-"),
    diagnostic_choice_set = case_when(
      str_detect(trial_id, "choice_candidates_only") ~ "choice_candidates_only",
      str_detect(trial_id, "choice_full_with_context") ~ "choice_full_with_context",
      TRUE ~ "unknown"
    ),
    hypothesis = "H6_diagnosticity_choice_full"
  ) %>%
  left_join(
    human_option_values %>% rename(target_a = target, human_value_a = human_value),
    by = c("initial", "context", "target_a")
  ) %>%
  left_join(
    human_option_values %>% rename(target_b = target, human_value_b = human_value),
    by = c("initial", "context", "target_b")
  ) %>%
  filter(!is.na(human_value_a), !is.na(human_value_b)) %>%
  mutate(
    human_preferred_choice = if_else(human_value_a >= human_value_b, target_a, target_b),
    correct = predicted_choice == human_preferred_choice,
    metric_source = source_table,
    metric_short = metric_short_label(metric),
    metric_family_label = case_when(
      metric_family == "contextualized_vector" ~ "Contextualized vector",
      metric_family == "luders_contextualized_density" ~ "Lüders contextualized density",
      metric_family == "perplexity" ~ "Perplexity-inhibited diagnostic",
      TRUE ~ as.character(metric_family)
    )
  )

h6_choice_accuracy <- h6_choice_prediction_human %>%
  group_by(hypothesis, diagnostic_choice_set, metric_family_label, metric, variant) %>%
  summarise(
    n = n(),
    accuracy = mean(correct, na.rm = TRUE),
    mean_abs_preference = mean(abs(preference_score_a_minus_b), na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(desc(accuracy), desc(mean_abs_preference))

# Representation alignment and variant sensitivity.
alignment_summary <- representation_alignment %>%
  group_by(object_a, object_b) %>%
  summarise(
    n = n(),
    mean_hs_cosine = mean(cosine_hilbert_schmidt, na.rm = TRUE),
    sd_hs_cosine = sd(cosine_hilbert_schmidt, na.rm = TRUE),
    mean_trace_overlap = mean(symmetric_trace_normalized_overlap, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(desc(mean_hs_cosine))

parse_variant <- function(x, field) {
  m <- str_match(x, "clust-(.*?)__g-(.*?)__l-(.*)$")
  case_when(
    field == "cluster" ~ m[, 2],
    field == "global" ~ m[, 3],
    field == "local" ~ m[, 4],
    TRUE ~ NA_character_
  )
}

variant_sensitivity_labeled <- variant_sensitivity %>%
  mutate(
    cluster_a = parse_variant(variant_a, "cluster"),
    cluster_b = parse_variant(variant_b, "cluster"),
    global_a = parse_variant(variant_a, "global"),
    global_b = parse_variant(variant_b, "global"),
    local_a = parse_variant(variant_a, "local"),
    local_b = parse_variant(variant_b, "local"),
    changed_cluster = cluster_a != cluster_b,
    changed_global = global_a != global_b,
    changed_local = local_a != local_b,
    comparison_type = case_when(
      changed_cluster & !changed_global & !changed_local ~ "Clustering only",
      !changed_cluster & (changed_global | changed_local) ~ "Dimensionality only",
      changed_cluster & (changed_global | changed_local) ~ "Both clustering and dimensionality",
      TRUE ~ "No detected change"
    )
  )

variant_sensitivity_summary <- variant_sensitivity_labeled %>%
  group_by(object, comparison_type) %>%
  summarise(
    n = n(),
    mean_hs_cosine = mean(cosine_hilbert_schmidt, na.rm = TRUE),
    sd_hs_cosine = sd(cosine_hilbert_schmidt, na.rm = TRUE),
    mean_frobenius_distance = mean(frobenius_distance, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(object, comparison_type)

# Combined summaries.
rank_for_summary <- bind_rows(
  h1_rank_directional,
  h2_rank_directional,
  h2_likert_rank,
  h3_rating_rank,
  h3_order_rank,
  h4_distance_rank %>% rename(metric_id = distance_metric),
  h4_mti_rank %>% rename(metric_id = similarity_metric),
  h6_static_rank,
  h6_context_rank,
  h6_perplexity_rank
)

best_predictor_by_block <- bind_rows(
  h1_rank_directional %>% slice_head(n = 1),
  h2_rank_directional %>% slice_head(n = 1),
  h2_likert_rank %>% slice_head(n = 1),
  h3_rating_rank %>% slice_head(n = 1),
  h3_order_rank %>% slice_head(n = 1),
  h4_distance_rank %>% slice_head(n = 1),
  h4_mti_rank %>% slice_head(n = 1),
  h6_static_rank %>% group_by(hypothesis) %>% slice_head(n = 1) %>% ungroup(),
  h6_context_rank %>% group_by(hypothesis) %>% slice_head(n = 1) %>% ungroup(),
  h6_perplexity_rank %>% group_by(hypothesis) %>% slice_head(n = 1) %>% ungroup()
) %>%
  mutate(
    metric_family = coalesce(metric_family, metric_family_from_source(metric_source)),
    display_block = coalesce(analysis_block, hypothesis),
    display_metric = metric_short_label(metric_name)
  )

cosine_comparisons <- bind_rows(
  compare_quantum_vs_cosine(h1_rank_all) %>% mutate(analysis_block = "H1 ipsative asymmetry"),
  compare_quantum_vs_cosine(h2_rank_all) %>% mutate(analysis_block = "H2 salience"),
  compare_quantum_vs_cosine(h3_rating_rank) %>% mutate(analysis_block = "H3 Likert similarity"),
  compare_quantum_vs_cosine(h6_static_rank %>% filter(hypothesis == "H6_diagnosticity_choice_full")) %>% mutate(analysis_block = "H6 choice full"),
  compare_quantum_vs_cosine(h6_static_rank %>% filter(hypothesis == "H6_diagnosticity_rating")) %>% mutate(analysis_block = "H6 rating")
)

# Export full tables.
write_table(h1_rank_all, "h1_all_metric_rankings.csv")
write_table(h1_rank_directional, "h1_directional_metric_rankings.csv")
write_table(h2_rank_all, "h2_all_metric_rankings.csv")
write_table(h2_rank_directional, "h2_directional_metric_rankings.csv")
write_table(h2_likert_rank, "h2b_likert_salience_dimensionality_correlations.csv")
write_table(h2_likert_frequency_adjusted, "h2b_likert_salience_frequency_adjusted_models.csv")
write_table(h3_rating_rank, "h3_rating_similarity_metric_rankings.csv")
write_table(h3_order_rank, "h3_order_asymmetry_metric_rankings.csv")
write_table(h3_order_test, "h3_human_order_asymmetry_test.csv")
write_table(human_triplets, "h4_human_triplet_residuals.csv")
write_table(human_triplet_summary, "h4_human_triplet_summary.csv")
write_table(h4_distance_rank, "h4_additive_triangle_metric_rankings.csv")
write_table(h4_mti_rank, "h4_mti_metric_rankings.csv")
write_table(mti_classification, "h4_mti_classification_performance.csv")
write_table(h6_static_rank, "h6_static_pairwise_metric_rankings.csv")
write_table(h6_context_rank, "h6_contextualized_metric_rankings.csv")
write_table(h6_perplexity_rank, "h6_perplexity_metric_rankings.csv")
write_table(h6_choice_accuracy, "h6_diagnostic_choice_prediction_accuracy.csv")
write_table(alignment_summary, "representation_alignment_summary.csv")
write_table(variant_sensitivity_summary, "variant_sensitivity_summary.csv")
write_table(best_predictor_by_block, "best_predictor_by_analysis_block.csv")
write_table(cosine_comparisons, "cosine_vs_quantum_comparisons.csv")

8 Executive summary

The executive summary should be read as a bridge between statistical performance and theoretical interpretation. A high correlation is not enough by itself; the relevant question is whether the winning metric corresponds to the psychological operation hypothesized for that task. For example, if centroid cosine wins in Likert similarity, that supports an average-vector account of explicit similarity. If containment asymmetry wins in ipsative tasks, that supports the subspace account of directional conceptual inclusion. The same number, in the wrong theoretical family, would mean something quite different.

summary_table <- best_predictor_by_block %>%
  transmute(
    `Analysis block` = display_block,
    `Best metric family` = metric_family,
    `Best metric` = display_metric,
    `Object / representation` = coalesce(basis_object, object, density_object, state_type, ""),
    `Variant` = str_trunc(coalesce(variant_label, variant_short(variant), ""), 50),
    n,
    `Spearman rho` = apa_r(estimate),
    p = apa_p(p.value),
    q = apa_p(coalesce(p_fdr_within_hypothesis, p_fdr))
  )

apa_table(summary_table, caption = "Table 3. Best computational predictor by analysis block.")

Table 3. Best computational predictor by analysis block.

Analysis block	Best metric family	Best metric	Object / representation	Variant	n	Spearman rho	p	q
H1 ipsative asymmetry	Subspace/projector geometry	Containment asymmetry	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	30	.90	< .001	< .001
H2 salience	Subspace/projector geometry	Containment asymmetry	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	30	−.90	< .001	< .001
H2b Likert salience	Corpus frequency baseline	log10 n occurrences	concept-level representation		44	.89	< .001	< .001
H3 Likert similarity	Classical vector baseline	Angular distance, reversed	contour_centroid	classical	89	.51	< .001	< .001
H3 order asymmetry	Operator/density geometry	Containment asymmetry	P_concat_direct	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.32	.002	.029
H4 additive triangle	Triplet distance geometry	Bures distance, reversed	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.49	< .001	< .001
H4 multiplicative triangle	Triplet similarity geometry	Density fidelity	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	66	.55	< .001	< .001
H6 static H6_diagnosticity_choice_full	Operator/density geometry	frobenius distance	rho_fit_global_density	gmm_bic | g=profile_likelihood | l=profile_like...	66	.40	< .001	.235
H6 static H6_diagnosticity_rating	Operator/density geometry	Containment asymmetry	rho_freq_density	gmm_bic | g=gavish_donoho | l=gavish_donoho	44	−.69	< .001	< .001
H6 contextualized H6_diagnosticity_choice_full	Lüders contextualized density	Contextual density HS inner	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	212	.36	< .001	< .001
H6 perplexity H6_diagnosticity_choice_full	Perplexity-inhibited diagnostic	perplexity residual projector to target containment	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	212	−.26	< .001	.007

write_table(summary_table, "table_03_executive_best_predictor_by_block_apa.csv")

The strongest pattern in the report is the contrast between general similarity, directional conceptual structure, and concept-level representational availability. Likert similarity is where the classical contour-centroid cosine is difficult to beat. Ipsative asymmetry and ipsative salience are different: there, containment asymmetry between subspaces is the dominant predictor. Single-concept Likert salience is different again: it is tested against frequency and dimensionality because the dependent variable refers to a concept considered on its own. Apparently, the mind did not ask permission before becoming asymmetric, scalar, and frequency-sensitive all at once.

cosine_table <- cosine_comparisons %>%
  transmute(
    `Analysis block` = analysis_block,
    `Comparison family` = comparison_family,
    `Metric` = metric_short_label(metric_name),
    `Metric source` = metric_source,
    `Representation` = coalesce(basis_object, object, state_type, state_vector_source, ""),
    n,
    `Spearman rho` = apa_r(estimate),
    `|rho|` = apa_num(abs_estimate, 2),
    p = apa_p(p.value),
    q = apa_p(p_fdr)
  )

apa_table(cosine_table, caption = "Table 4. Systematic comparison between the best quantum-like metric and the best classical cosine baseline.")

Table 4. Systematic comparison between the best quantum-like metric and the best classical cosine baseline.

Analysis block	Comparison family	Metric	Metric source	Representation	n	Spearman rho	|rho|	p	q
H1 ipsative asymmetry	Best classical cosine	Centroid cosine	classical_baselines	contour_centroid	30	−.01	0.01	.971	.975
H1 ipsative asymmetry	Best quantum-like metric	Containment asymmetry	pairwise_subspace_metrics	S_lowdin	30	.90	0.90	< .001	< .001
H2 salience	Best classical cosine	Centroid cosine	classical_baselines	contour_centroid	30	.10	0.10	.586	.658
H2 salience	Best quantum-like metric	Containment asymmetry	pairwise_subspace_metrics	S_lowdin	30	−.90	0.90	< .001	< .001
H3 Likert similarity	Best classical cosine	Centroid cosine	classical_baselines	contour_centroid	89	.51	0.51	< .001	< .001
H3 Likert similarity	Best quantum-like metric	a in b trace normalized	pairwise_operator_density_metrics	rho_freq_density	89	.45	0.45	< .001	< .001
H6 choice full	Best classical cosine	Centroid cosine	classical_baselines	contour_centroid	66	.28	0.28	.024	.420
H6 choice full	Best quantum-like metric	frobenius distance	pairwise_operator_density_metrics	rho_fit_global_density	66	.40	0.40	< .001	.071
H6 rating	Best classical cosine	Centroid cosine	classical_baselines	contour_centroid	44	.24	0.24	.119	.723
H6 rating	Best quantum-like metric	Containment asymmetry	pairwise_operator_density_metrics	rho_freq_density	44	−.69	0.69	< .001	< .001

write_table(cosine_table, "table_04_cosine_vs_quantum_apa.csv")

cosine_plot <- cosine_comparisons %>%
  mutate(
    analysis_block = fct_inorder(analysis_block),
    comparison_family = fct_relevel(comparison_family, "Best classical cosine", "Best quantum-like metric")
  ) %>%
  ggplot(aes(x = analysis_block, y = estimate, fill = comparison_family)) +
  geom_hline(yintercept = 0, linewidth = .35) +
  geom_col(position = position_dodge(width = .72), width = .62) +
  coord_flip() +
  scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
  scale_fill_manual(values = report_palette) +
  labs(
    title = "Quantum-like metrics versus classical cosine",
    subtitle = "Best Spearman correlation within each family and analysis block.",
    x = NULL,
    y = "Spearman rho"
  ) +
  theme_apa7()

cosine_plot

save_plot(cosine_plot, "executive_cosine_vs_quantum_comparison.png", width = 8.5, height = 5.2)

9 Metric families and interpretive map

This map translates each computational family into a psychological interpretation. The notebook uses it repeatedly because the same statistical index, Spearman correlation, is applied to very different formal objects. Without this map, the analysis risks becoming a contest between filenames. A correlation produced by centroid cosine means something different from a correlation produced by projector containment, even if both are numerically similar.

metric_map <- tibble(
  `Metric family` = c(
    "Classical vector baseline",
    "Subspace/projector geometry",
    "Operator/density geometry",
    "Sequential QSM",
    "Contextualized diagnostic",
    "Perplexity-inhibited diagnostic"
  ),
  `Main object` = c(
    "Contour centroid vector",
    "Bases and projectors S, P",
    "Projectors and density-like matrices",
    "State plus ordered projections",
    "Contextual basis or Lüders-filtered density",
    "Residual state after removing confusing shared structure"
  ),
  `Psychological interpretation` = c(
    "Average semantic proximity; strong baseline for explicit similarity ratings.",
    "Conceptual inclusion, overlap, distance, incompatibility, and subspace geometry.",
    "State-like similarity and distinguishability between global/local conceptual structures.",
    "Order-sensitive similarity through sequential projection.",
    "How similarity changes when concepts are compared inside a context.",
    "How choices shift after inhibiting properties shared by a plausible competing pair."
  ),
  `Expected strongest domain` = c(
    "Likert similarity",
    "Asymmetry, salience, triplet structure",
    "Similarity and diagnostic ratings",
    "Asymmetry and order effects",
    "Diagnosticity with explicit context",
    "Diagnostic grouping/perplexity tasks"
  )
)

apa_table(metric_map, caption = "Table 5. Conceptual interpretation of computational metric families.")

Table 5. Conceptual interpretation of computational metric families.

Metric family	Main object	Psychological interpretation	Expected strongest domain
Classical vector baseline	Contour centroid vector	Average semantic proximity; strong baseline for explicit similarity ratings.	Likert similarity
Subspace/projector geometry	Bases and projectors S, P	Conceptual inclusion, overlap, distance, incompatibility, and subspace geometry.	Asymmetry, salience, triplet structure
Operator/density geometry	Projectors and density-like matrices	State-like similarity and distinguishability between global/local conceptual structures.	Similarity and diagnostic ratings
Sequential QSM	State plus ordered projections	Order-sensitive similarity through sequential projection.	Asymmetry and order effects
Contextualized diagnostic	Contextual basis or Lüders-filtered density	How similarity changes when concepts are compared inside a context.	Diagnosticity with explicit context
Perplexity-inhibited diagnostic	Residual state after removing confusing shared structure	How choices shift after inhibiting properties shared by a plausible competing pair.	Diagnostic grouping/perplexity tasks

write_table(metric_map, "table_05_metric_family_interpretive_map.csv")

10 H1: ipsative asymmetry

10.1 Theoretical rationale

Ipsative asymmetry is the clearest test of whether similarity is more than symmetric proximity. In a classical cosine model, (sim(A,B)=sim(B,A)), so asymmetry has to be added externally. In the subspace model, asymmetry can emerge naturally from directional containment: concept (A) can be largely contained in concept (B) even when (B) is not equally contained in (A).

Psychologically, this corresponds to the idea that one concept may be treated as more specific, narrower, or more dependent on features that are also present in the other concept. The prediction is therefore not that two concepts are simply close, but that one conceptual region is included in the other to a greater degree. This is why H1 is interpreted primarily through containment asymmetry and only secondarily through sequential QSM.

10.2 Methodological choices for H1

Directional metrics are reoriented to match the human item order. This is essential: the computational files store pairs canonically, while the human task has a first and second item. Without reorientation, a good asymmetry metric would look unstable merely because the row order changed. Classical cosine baselines are included as a negative control: they can predict overall similarity, but they should not be able to predict direction unless direction is indirectly encoded by some confound.

H1 tests whether directional computational structure predicts forced-choice asymmetry. The primary theoretical metric is containment asymmetry: whether the first concept is more contained in the second than the second is contained in the first.

h1_top_directional <- h1_rank_directional %>% slice_head(n = params$top_n_metrics)
h1_family_best <- best_by_family(h1_rank_all)
h1_cosine_comp <- compare_quantum_vs_cosine(h1_rank_all)

apa_table(
  h1_top_directional %>%
    transmute(
      Metric = metric_short,
      Family = metric_family,
      Variant = str_trunc(variant_label, 50),
      Object = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 6. H1 top directional quantum-like predictors of ipsative asymmetry."
)

Table 6. H1 top directional quantum-like predictors of ipsative asymmetry.

Metric	Family	Variant	Object	n	Spearman rho	p	q
Containment asymmetry	Subspace/projector geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	.90	< .001	< .001
qsm neutral asymmetry a minus b	Subspace/projector geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	.90	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	P_concat_direct	30	.90	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	P_lowdin	30	.90	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	P_concat_direct	30	.86	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	P_lowdin	30	.86	< .001	< .001
Containment asymmetry	Subspace/projector geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	.86	< .001	< .001
qsm neutral asymmetry a minus b	Subspace/projector geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	.86	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	projector_mixture_freq	30	.83	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	projector_mixture_fit_global	30	.83	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=permutation_pa | l=permutation_pa	P_concat_direct	30	.79	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=permutation_pa | l=permutation_pa	P_lowdin	30	.79	< .001	< .001

apa_table(
  h1_cosine_comp %>%
    transmute(
      `Comparison family` = comparison_family,
      Metric = metric_short,
      Family = metric_family,
      Representation = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 7. H1 comparison against the classical cosine baseline."
)

Table 7. H1 comparison against the classical cosine baseline.

Comparison family	Metric	Family	Representation	n	Spearman rho	p	q
Best classical cosine	Centroid cosine	Classical vector baseline	contour_centroid	30	−.01	.971	.975
Best quantum-like metric	Containment asymmetry	Subspace/projector geometry	S_lowdin	30	.90	< .001	< .001

plot_ranked_correlations(
  h1_top_directional,
  title = "H1: directional predictors of ipsative asymmetry",
  subtitle = "Containment asymmetry should dominate if human asymmetry reflects conceptual inclusion.",
  n = params$top_n_plots,
  filename = "h1_top_directional_metric_correlations_v7.png"
)

h1_primary <- h1_top_directional %>% slice_head(n = 1)
plot_metric_scatter(
  h1_all,
  h1_primary,
  title = "H1 primary metric: containment asymmetry",
  y_label = "Human forced-choice proportion for first concept",
  filename = "h1_primary_metric_scatter_v7.png"
)

h1_best <- h1_top_directional %>% slice_head(n = 1)
h1_cos <- h1_cosine_comp %>% filter(comparison_family == "Best classical cosine") %>% slice_head(n = 1)
cat(
  "**Interpretation.** The best H1 predictor is ", h1_best$metric_short[[1]],
  " from the ", h1_best$metric_family[[1]], " family, with rho = ", apa_r(h1_best$estimate[[1]]),
  " (p ", apa_p(h1_best$p.value[[1]]), "). ",
  "This is ", interpret_corr_strength(h1_best$estimate[[1]]),
  ". The best classical cosine baseline reaches rho = ", apa_r(h1_cos$estimate[[1]]),
  ". Thus, H1 is mainly a directional subspace result rather than a simple vector-similarity result.\n"
)

Interpretation. The best H1 predictor is Containment asymmetry from the Subspace/projector geometry family, with rho = .90 (p < .001 ). This is very strong . The best classical cosine baseline reaches rho = −.01 . Thus, H1 is mainly a directional subspace result rather than a simple vector-similarity result.

11 H2: salience

11.1 Theoretical rationale

Salience is expected to modulate asymmetry. In Tversky-like accounts, a more salient or prototypical concept can dominate the comparison, making the less salient concept appear more similar to the salient one than the reverse. In the present subspace model, this can be reinterpreted geometrically: the more salient concept may behave as a broader or more diagnostic region of semantic structure, so the less salient concept is more contained in it than vice versa.

This means H2 should not merely correlate with similarity. It should correlate with the reverse of containment asymmetry if salience is functioning as the broad/prototypical pole of the relation. A strong negative association between H2 and the H1 containment metric is therefore theoretically coherent rather than inconvenient.

11.2 Methodological choices for H2

The same directional metrics used for H1 are tested here. This keeps the interpretation clean: H1 and H2 are not two unrelated analyses but two views of the same directional geometry. The relevant question is whether the salience data invert the asymmetry data, and whether this inversion is better captured by subspace containment than by centroid cosine.

H2 tests salience. The expected relation is theoretically close to H1, but usually with the opposite sign: if one concept functions as a broader or more salient reference, the containment asymmetry can reverse relative to ipsative choice.

h2_top_directional <- h2_rank_directional %>% slice_head(n = params$top_n_metrics)
h2_family_best <- best_by_family(h2_rank_all)
h2_cosine_comp <- compare_quantum_vs_cosine(h2_rank_all)

apa_table(
  h2_top_directional %>%
    transmute(
      Metric = metric_short,
      Family = metric_family,
      Variant = str_trunc(variant_label, 50),
      Object = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 8. H2 top directional predictors of salience."
)

Table 8. H2 top directional predictors of salience.

Metric	Family	Variant	Object	n	Spearman rho	p	q
Containment asymmetry	Subspace/projector geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	−.90	< .001	< .001
qsm neutral asymmetry a minus b	Subspace/projector geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	−.90	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	P_concat_direct	30	−.89	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	P_lowdin	30	−.89	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	P_concat_direct	30	−.88	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	P_lowdin	30	−.88	< .001	< .001
Containment asymmetry	Subspace/projector geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	−.88	< .001	< .001
qsm neutral asymmetry a minus b	Subspace/projector geometry	gmm_bic | g=gavish_donoho | l=gavish_donoho	S_lowdin	30	−.88	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	projector_mixture_freq	30	−.80	< .001	< .001
Containment asymmetry	Operator/density geometry	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	projector_mixture_fit_global	30	−.79	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=permutation_pa | l=permutation_pa	P_concat_direct	30	−.79	< .001	< .001
Containment asymmetry	Operator/density geometry	gmm_bic | g=permutation_pa | l=permutation_pa	P_lowdin	30	−.79	< .001	< .001

h1_h2_human <- pair_behavior %>%
  filter(hypothesis %in% c("H1_asymmetry_ipsative", "H2_salience")) %>%
  select(hypothesis, pair_id, human_value) %>%
  pivot_wider(names_from = hypothesis, values_from = human_value) %>%
  filter(!is.na(H1_asymmetry_ipsative), !is.na(H2_salience))

h1_h2_link <- safe_cor(h1_h2_human, x = "H1_asymmetry_ipsative", y = "H2_salience")

apa_table(
  h1_h2_link %>%
    transmute(
      Comparison = "H1 human asymmetry vs H2 human salience",
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value)
    ),
  caption = "Table 9. Association between human ipsative asymmetry and human salience."
)

Table 9. Association between human ipsative asymmetry and human salience.

Comparison	n	Spearman rho	p
H1 human asymmetry vs H2 human salience	30	−.95	< .001

apa_table(
  h2_cosine_comp %>%
    transmute(
      `Comparison family` = comparison_family,
      Metric = metric_short,
      Family = metric_family,
      Representation = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 10. H2 comparison against the classical cosine baseline."
)

Table 10. H2 comparison against the classical cosine baseline.

Comparison family	Metric	Family	Representation	n	Spearman rho	p	q
Best classical cosine	Centroid cosine	Classical vector baseline	contour_centroid	30	.10	.586	.658
Best quantum-like metric	Containment asymmetry	Subspace/projector geometry	S_lowdin	30	−.90	< .001	< .001

plot_ranked_correlations(
  h2_top_directional,
  title = "H2: directional predictors of salience",
  subtitle = "Negative associations indicate that salience reverses the H1 containment direction.",
  n = params$top_n_plots,
  filename = "h2_top_directional_metric_correlations_v7.png"
)

h2_primary <- h2_top_directional %>% slice_head(n = 1)
plot_metric_scatter(
  h2_all,
  h2_primary,
  title = "H2 primary metric: salience and containment",
  y_label = "Human salience score",
  filename = "h2_primary_metric_scatter_v7.png"
)

h2_best <- h2_top_directional %>% slice_head(n = 1)
h2_cos <- h2_cosine_comp %>% filter(comparison_family == "Best classical cosine") %>% slice_head(n = 1)
cat(
  "**Interpretation.** The best H2 predictor is ", h2_best$metric_short[[1]],
  " with rho = ", apa_r(h2_best$estimate[[1]]), " (p ", apa_p(h2_best$p.value[[1]]), "). ",
  "The sign is informative: salience behaves as the reverse side of the directional containment relation. ",
  "The best classical cosine baseline reaches rho = ", apa_r(h2_cos$estimate[[1]]),
  ", so the salience result is again not reducible to simple centroid similarity.\n"
)

Interpretation. The best H2 predictor is Containment asymmetry with rho = −.90 (p < .001 ). The sign is informative: salience behaves as the reverse side of the directional containment relation. The best classical cosine baseline reaches rho = .10 , so the salience result is again not reducible to simple centroid similarity.

11.3 H2b: single-concept Likert salience and representational dimensionality

The previous H2 analysis concerns ipsative salience: participants choose which member of a pair feels more salient. The dataset also contains a second salience measure: single-concept Likert salience ratings. This is a different psychological object. It is not directional and it is not pairwise. It asks whether a concept, considered on its own, appears cognitively salient or prominent.

Because this task is concept-level, pairwise cosine is not the right baseline. A more natural predictor is representational richness: how many dimensions are needed to describe the saturated contour of a concept, how many occurrences it has in the corpus, and how many local semantic regions can be estimated. In the theory, a concept with a richer semantic contour should occupy a broader, more differentiated subspace in the container. If participants’ Likert salience tracks this richness, then dimensionality should predict ratings. If frequency alone explains the effect, then the result is less specifically quantum-like and more about linguistic exposure. Annoyingly reasonable, but important.

The arbitrary decisions here are explicit. First, the analysis treats saliency_2.csv as a single-concept Likert task and averages ratings by target. Second, the predictor set includes several dimensionality criteria rather than pretending that one rule is metaphysically ordained. Third, log corpus frequency is included as a baseline and as a covariate, because dimensionality and occurrence frequency are naturally entangled in corpus data. The statistical question is therefore twofold: (a) does dimensionality correlate with Likert salience? and (b) does it add anything beyond raw linguistic frequency?

h2_likert_top <- h2_likert_rank %>% slice_head(n = params$top_n_metrics)

apa_table(
  h2_likert_top %>%
    transmute(
      Predictor = metric_short,
      Family = metric_family,
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 11. H2b concept-level predictors of single-concept Likert salience."
)

Table 11. H2b concept-level predictors of single-concept Likert salience.

Predictor	Family	n	Spearman rho	p	q
Log frequency	Corpus frequency baseline	44	.89	< .001	< .001
Raw frequency	Corpus frequency baseline	44	.89	< .001	< .001
Total local Gavish, GMM-BIC	Local representational richness	44	.89	< .001	< .001
Marchenko-Pastur dimensionality	Global representational dimensionality	44	.89	< .001	< .001
Total local Gavish, Bayesian GMM	Local representational richness	44	.89	< .001	< .001
Total local Horn, GMM-BIC	Local representational richness	44	.88	< .001	< .001
Mean local Gavish, Bayesian GMM	Local representational richness	44	.88	< .001	< .001
Gavish-Donoho dimensionality	Global representational dimensionality	44	.87	< .001	< .001
Estimable local clusters, GMM-BIC	Local representational richness	44	.87	< .001	< .001
Dimensions for 95% variance	Global representational dimensionality	44	.87	< .001	< .001
Dimensions for 90% variance	Global representational dimensionality	44	.87	< .001	< .001
Dimensions for 80% variance	Global representational dimensionality	44	.86	< .001	< .001

apa_table(
  h2_likert_frequency_adjusted %>%
    slice_head(n = params$top_n_metrics) %>%
    transmute(
      Predictor = metric_short,
      n,
      `beta predictor` = apa_r(beta_predictor),
      `p predictor` = apa_p(p_predictor),
      `q predictor` = apa_p(p_fdr_predictor),
      `beta log frequency` = apa_r(beta_log_frequency),
      `p log frequency` = apa_p(p_log_frequency),
      `R2` = apa_num(r_squared, 2)
    ),
  caption = "Table 12. H2b dimensionality predictors of Likert salience adjusted for log corpus frequency."
)

Table 12. H2b dimensionality predictors of Likert salience adjusted for log corpus frequency.

Predictor	n	beta predictor	p predictor	q predictor	beta log frequency	p log frequency	R2
Mean local Gavish, GMM-BIC	44	−.21	.068	.623	1.03	< .001	0.78
Estimable local clusters, GMM-BIC	44	.32	.089	.623	.58	.003	0.78
Marchenko-Pastur dimensionality	44	.87	.105	.623	.01	.979	0.78
Individual variance ≥ .005	44	−.15	.149	.623	.77	< .001	0.78
Mean local Gavish, Bayesian GMM	44	.27	.159	.623	.63	.002	0.77
Gavish-Donoho dimensionality	44	.24	.170	.623	.66	< .001	0.77
Mean local Horn, GMM-BIC	44	−.11	.242	.686	.93	< .001	0.77
Profile-likelihood dimensionality	44	−.10	.249	.686	.82	< .001	0.77
Total local Horn, GMM-BIC	44	.25	.304	.743	.63	.012	0.77
Mean local Horn, Bayesian GMM	44	.09	.412	.907	.81	< .001	0.77
Broken-stick dimensionality	44	.12	.475	.949	.77	< .001	0.77
Effective rank	44	−.05	.622	.951	.91	< .001	0.76

write_table(salience_likert_summary, "h2b_likert_salience_by_target.csv")
write_table(h2_likert_rank, "h2b_likert_salience_dimensionality_correlations.csv")
write_table(h2_likert_frequency_adjusted, "h2b_likert_salience_frequency_adjusted_models.csv")

h2b_rank_plot <- h2_likert_rank %>%
  filter(!is.na(estimate)) %>%
  slice_head(n = params$top_n_plots) %>%
  mutate(
    label = fct_reorder(str_wrap(metric_short, 32), abs_estimate),
    significant = if_else(!is.na(p_fdr) & p_fdr < .05, "FDR < .05", "FDR ≥ .05")
  ) %>%
  ggplot(aes(x = label, y = estimate, fill = metric_family)) +
  geom_hline(yintercept = 0, linewidth = .35) +
  geom_col(width = .72) +
  coord_flip() +
  scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
  scale_fill_manual(values = c(
    "Corpus frequency baseline" = "#D55E00",
    "Global representational dimensionality" = "#0072B2",
    "Local representational richness" = "#009E73"
  )) +
  labs(
    title = "H2b: single-concept Likert salience",
    subtitle = "Concept-level salience is compared with frequency and representational dimensionality.",
    x = NULL,
    y = "Spearman rho"
  ) +
  theme_apa7()

h2b_rank_plot

save_plot(h2b_rank_plot, "h2b_likert_salience_dimensionality_correlations_v8.png", width = 9, height = 6)

h2b_best_predictor <- h2_likert_rank %>% slice_head(n = 1)
h2b_best_data <- h2_likert_predictor_long %>% filter(metric_id == h2b_best_predictor$metric_id[[1]])

h2b_best_scatter <- h2b_best_data %>%
  ggplot(aes(x = metric_value, y = human_value)) +
  geom_point(size = 2.4, alpha = .80) +
  geom_smooth(method = "lm", se = TRUE, linewidth = .75) +
  labs(
    title = "Best concept-level predictor of Likert salience",
    subtitle = paste0(h2b_best_predictor$metric_short[[1]], "; rho = ", apa_r(h2b_best_predictor$estimate[[1]]), ", p ", apa_p(h2b_best_predictor$p.value[[1]])),
    x = h2b_best_predictor$metric_short[[1]],
    y = "Mean Likert salience"
  ) +
  theme_apa7()

h2b_best_scatter

save_plot(h2b_best_scatter, "h2b_likert_salience_best_predictor_scatter_v8.png", width = 7.5, height = 5)

h2b_freq_scatter <- salience_likert_dimensionality %>%
  ggplot(aes(x = log10_n_occurrences, y = mean_salience_likert)) +
  geom_point(size = 2.4, alpha = .80) +
  geom_smooth(method = "lm", se = TRUE, linewidth = .75) +
  labs(
    title = "Frequency baseline for Likert salience",
    subtitle = "This checks whether rated salience mostly reflects how often a concept occurs in the corpus.",
    x = "Log10 corpus occurrences",
    y = "Mean Likert salience"
  ) +
  theme_apa7()

h2b_freq_scatter

save_plot(h2b_freq_scatter, "h2b_likert_salience_frequency_scatter_v8.png", width = 7.5, height = 5)

h2b_best <- h2_likert_rank %>% slice_head(n = 1)
h2b_freq <- h2_likert_rank %>% filter(metric_name == "log10_n_occurrences") %>% slice_head(n = 1)
h2b_adjusted_best <- h2_likert_frequency_adjusted %>% slice_head(n = 1)
cat(
  "**Interpretation.** The strongest concept-level predictor of Likert salience is ", h2b_best$metric_short[[1]],
  " with rho = ", apa_r(h2b_best$estimate[[1]]), " (p ", apa_p(h2b_best$p.value[[1]]), "). ",
  "The log-frequency baseline reaches rho = ", apa_r(h2b_freq$estimate[[1]]), ". ",
  "The frequency-adjusted models test whether dimensionality has predictive value over and above exposure. ",
  "The strongest adjusted predictor is ", h2b_adjusted_best$metric_short[[1]],
  " with beta = ", apa_r(h2b_adjusted_best$beta_predictor[[1]]),
  " (p ", apa_p(h2b_adjusted_best$p_predictor[[1]]), "). ",
  "If the unadjusted dimensionality correlations are strong but the adjusted effects weaken, the interpretation should be cautious: Likert salience is tracking representational richness, but much of that richness may be coupled to corpus prevalence. That is still theoretically informative, because it separates ipsative salience as directional containment from Likert salience as global availability/richness.\n"
)

Interpretation. The strongest concept-level predictor of Likert salience is Log frequency with rho = .89 (p < .001 ). The log-frequency baseline reaches rho = .89 . The frequency-adjusted models test whether dimensionality has predictive value over and above exposure. The strongest adjusted predictor is Mean local Gavish, GMM-BIC with beta = −.21 (p .068 ). If the unadjusted dimensionality correlations are strong but the adjusted effects weaken, the interpretation should be cautious: Likert salience is tracking representational richness, but much of that richness may be coupled to corpus prevalence. That is still theoretically informative, because it separates ipsative salience as directional containment from Likert salience as global availability/richness.

11.4 H2c: planned salience/similarity condition structure from the thesis annex

The annex design adds an important layer that is easy to miss if we only look at hypothesis-level correlations. The asymmetry/salience country pairs were not arbitrary: they were prepared to cross planned salience and planned similarity. This means the same human and computational results can be read not only pair by pair, but also by experimental condition.

This gives four useful analyses:

1. Annex audit. Check whether each planned pair is present in the current human-aligned dataset. This is especially important because one pair differs between the thesis listing and the empirical response file: the thesis list includes Mexico–Colombia, while the current salience/asymmetry files include Ecuador–Peru. The notebook keeps both entries and flags their source.
2. Concept-level salience manipulation check. Concepts labelled high-salience in the annex should receive higher single-concept Likert salience ratings than low-salience concepts. If dimensionality also differs by planned salience, then dimensionality may be part of the computational signature of salience.
3. Pair-level salience choice check. In mixed high–low pairs, ipsative salience should select the high-salience concept. In low–low and high–high pairs, the task should be less strongly determined by the planned salience manipulation.
4. Similarity manipulation check. Pairs labelled high-similarity should show higher human Likert similarity and higher computational similarity than low-similarity pairs.

The theoretical point is that salience is probably not a single thing. Ipsative salience is a directional comparison between two concepts. Likert salience is a concept-level availability/richness judgment. Planned salience cells let us test how these two levels relate without pretending they are the same psychological operation, a small mercy for everyone involved.

apa_table(
  annex_condition_audit %>%
    transmute(
      `Concept 1` = planned_concept_1_es,
      `Concept 2` = planned_concept_2_es,
      `Planned salience` = paste(planned_salience_1, planned_salience_2, sep = "--"),
      `Planned similarity` = as.character(planned_similarity),
      `Annex condition` = as.character(annex_condition),
      `Observed in human pair file` = observed_in_human_pair_design,
      Source = condition_source
    ),
  caption = "Table H2c-1. Audit of planned salience/similarity conditions from the thesis annex."
)

Table H2c-1. Audit of planned salience/similarity conditions from the thesis annex.

Concept 1	Concept 2	Planned salience	Planned similarity	Annex condition	Observed in human pair file	Source
Ghana	Luxemburgo	low--low	low	low_low__low_similarity	TRUE	thesis_annex
Islas Feroe	Singapur	low--low	low	low_low__low_similarity	TRUE	thesis_annex
Burkina Faso	Guayana Francesa	low--low	low	low_low__low_similarity	TRUE	thesis_annex
Mongolia	Bulgaria	low--low	low	low_low__low_similarity	TRUE	thesis_annex
Omán	Belice	low--low	low	low_low__low_similarity	TRUE	thesis_annex
Eslovenia	Eslovaquia	low--low	high	low_low__high_similarity	TRUE	thesis_annex
Zambia	Zimbabue	low--low	high	low_low__high_similarity	TRUE	thesis_annex
Laos	Camboya	low--low	high	low_low__high_similarity	TRUE	thesis_annex
Omán	Yemen	low--low	high	low_low__high_similarity	TRUE	thesis_annex
Turkmenistán	Uzbekistán	low--low	high	low_low__high_similarity	TRUE	thesis_annex
Francia	Bolivia	high--low	low	high_low__low_similarity	TRUE	thesis_annex
Estados Unidos	Belice	high--low	low	high_low__low_similarity	TRUE	thesis_annex
China	Luxemburgo	high--low	low	high_low__low_similarity	TRUE	thesis_annex
México	Laos	high--low	low	high_low__low_similarity	TRUE	thesis_annex
Rusia	Burkina Faso	high--low	low	high_low__low_similarity	TRUE	thesis_annex
Francia	Bélgica	high--low	high	high_low__high_similarity	TRUE	thesis_annex
España	Andorra	high--low	high	high_low__high_similarity	TRUE	thesis_annex
China	Singapur	high--low	high	high_low__high_similarity	TRUE	thesis_annex
Rusia	Bielorrusia	high--low	high	high_low__high_similarity	TRUE	thesis_annex
Argentina	Paraguay	high--low	high	high_low__high_similarity	TRUE	thesis_annex
Francia	Brasil	high--high	low	high_high__low_similarity	TRUE	thesis_annex
Alemania	Canadá	high--high	low	high_high__low_similarity	TRUE	thesis_annex
Italia	Japón	high--high	low	high_high__low_similarity	TRUE	thesis_annex
Marruecos	Argentina	high--high	low	high_high__low_similarity	TRUE	thesis_annex
India	México	high--high	low	high_high__low_similarity	TRUE	thesis_annex
Italia	España	high--high	high	high_high__high_similarity	TRUE	thesis_annex
Reino Unido	Estados Unidos	high--high	high	high_high__high_similarity	TRUE	thesis_annex
Suecia	Noruega	high--high	high	high_high__high_similarity	TRUE	thesis_annex
Brasil	Portugal	high--high	high	high_high__high_similarity	TRUE	thesis_annex
México	Colombia	high--high	high	high_high__high_similarity	FALSE	thesis_annex_not_observed_in_current_human_pair_file
Ecuador	Perú	high--high	high	high_high__high_similarity	TRUE	observed_human_file_replacement_or_extra

apa_table(
  h2c_human_condition_summary %>%
    transmute(
      Hypothesis = hypothesis,
      `Annex condition` = as.character(annex_condition),
      `Presentation salience` = as.character(presentation_salience_pattern),
      `Planned similarity` = as.character(planned_similarity),
      `n items` = n_items,
      `Mean human value` = apa_num(mean_human_value, 3),
      `Mean |deviation from .5|` = apa_num(mean_abs_deviation_from_chance, 3),
      `Mean P(choose high salience)` = apa_num(mean_prop_choose_high_salience, 3)
    ),
  caption = "Table H2c-2. Human responses summarized by planned annex condition."
)

Table H2c-2. Human responses summarized by planned annex condition.

Hypothesis	Annex condition	Presentation salience	Planned similarity	n items	Mean human value	Mean |deviation from .5|	Mean P(choose high salience)
H1_asymmetry_ipsative	low_low__low_similarity	low_low	low	5	0.698	0.198
H1_asymmetry_ipsative	low_low__high_similarity	low_low	high	5	0.575	0.075
H1_asymmetry_ipsative	high_low__low_similarity	low_high	low	2	0.904	0.404
H1_asymmetry_ipsative	high_low__low_similarity	high_low	low	3	0.118	0.382
H1_asymmetry_ipsative	high_low__high_similarity	low_high	high	2	0.957	0.457
H1_asymmetry_ipsative	high_low__high_similarity	high_low	high	3	0.162	0.338
H1_asymmetry_ipsative	high_high__low_similarity	high_high	low	5	0.378	0.122
H1_asymmetry_ipsative	high_high__high_similarity	high_high	high	5	0.620	0.120
H2_salience	low_low__low_similarity	low_low	low	5	0.266	0.234
H2_salience	low_low__high_similarity	low_low	high	5	0.442	0.103
H2_salience	high_low__low_similarity	low_high	low	2	0.030	0.470	0.970
H2_salience	high_low__low_similarity	high_low	low	3	0.963	0.463	0.963
H2_salience	high_low__high_similarity	low_high	high	2	0.020	0.480	0.980
H2_salience	high_low__high_similarity	high_low	high	3	0.905	0.405	0.905
H2_salience	high_high__low_similarity	high_high	low	5	0.683	0.189
H2_salience	high_high__high_similarity	high_high	high	5	0.392	0.154
H3_likert_order_asymmetry_H4_triangle_network	low_low__low_similarity	low_low	low	5	3.672	3.172
H3_likert_order_asymmetry_H4_triangle_network	low_low__high_similarity	low_low	high	5	6.114	5.614
H3_likert_order_asymmetry_H4_triangle_network	high_low__low_similarity	low_high	low	5	3.043	2.543
H3_likert_order_asymmetry_H4_triangle_network	high_low__low_similarity	high_low	low	5	2.986	2.486
H3_likert_order_asymmetry_H4_triangle_network	high_low__high_similarity	low_high	high	5	6.950	6.450
H3_likert_order_asymmetry_H4_triangle_network	high_low__high_similarity	high_low	high	5	6.826	6.326
H3_likert_order_asymmetry_H4_triangle_network	high_high__low_similarity	high_high	low	5	3.788	3.288
H3_likert_order_asymmetry_H4_triangle_network	high_high__high_similarity	high_high	high	5	7.027	6.527

write_table(annex_condition_audit, "h2c_annex_condition_audit.csv")
write_table(h2c_human_condition_summary, "h2c_human_condition_summary.csv")

apa_table(
  h2c_concept_condition_summary %>%
    transmute(
      `Planned concept salience` = planned_salience_label,
      `n concepts` = n_concepts,
      `Mean Likert salience` = apa_num(mean_likert_salience, 2),
      `Mean log frequency` = apa_num(mean_log10_frequency, 2),
      `Mean effective rank` = apa_num(mean_effective_rank, 2),
      `Mean Horn dimensionality` = apa_num(mean_horn_dimensionality, 2),
      `Mean Gavish dimensionality` = apa_num(mean_gavish_dimensionality, 2),
      `Mean permutation PA dimensionality` = apa_num(mean_permutation_dimensionality, 2)
    ),
  caption = "Table H2c-3. Concept-level salience, frequency, and dimensionality by planned salience label."
)

Table H2c-3. Concept-level salience, frequency, and dimensionality by planned salience label.

Planned concept salience	n concepts	Mean Likert salience	Mean log frequency	Mean effective rank	Mean Horn dimensionality	Mean Gavish dimensionality	Mean permutation PA dimensionality
high	20	6.22	3.90	300.00	65.00	41.50	62.20
low	24	3.18	2.58	229.88	43.75	21.92	35.12

apa_table(
  h2c_concept_condition_tests %>%
    transmute(
      Outcome = outcome_label,
      `n high` = n_high,
      `n low` = n_low,
      `Mean high` = apa_num(mean_high, 2),
      `Mean low` = apa_num(mean_low, 2),
      `High − low` = apa_num(difference_high_minus_low, 2),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table H2c-4. Planned high-vs-low salience differences in ratings and representational richness."
)

Table H2c-4. Planned high-vs-low salience differences in ratings and representational richness.

Outcome	n high	n low	Mean high	Mean low	High − low	p	q
Log frequency	20	24	3.90	2.58	1.31	< .001	< .001
Mean Likert salience	20	24	6.22	3.18	3.03	< .001	< .001
Gavish-Donoho dimensionality	20	24	41.50	21.92	19.58	< .001	< .001
Permutation PA dimensionality	20	24	62.20	35.12	27.08	< .001	< .001
Horn/Wishart dimensionality	20	24	65.00	43.75	21.25	< .001	< .001
Profile-likelihood dimensionality	20	24	84.25	118.04	-33.79	< .001	< .001
Effective rank	20	24	300.00	229.88	70.12	.001	.001

write_table(h2c_concept_condition_summary, "h2c_concept_condition_summary.csv")
write_table(h2c_concept_condition_tests, "h2c_concept_condition_tests.csv")

apa_table(
  h2c_similarity_condition_summary %>%
    transmute(
      `Planned similarity` = as.character(planned_similarity),
      `Planned salience pair` = as.character(planned_salience_pair),
      `n pairs` = n_pairs,
      `Mean human similarity` = apa_num(mean_human_similarity, 2),
      `SD human similarity` = apa_num(sd_human_similarity, 2)
    ),
  caption = "Table H2c-5. Human Likert similarity by planned similarity and salience condition."
)

Table H2c-5. Human Likert similarity by planned similarity and salience condition.

Planned similarity	Planned salience pair	n pairs	Mean human similarity	SD human similarity
low	low_low	5	3.67	0.68
low	high_low	5	3.01	0.31
low	high_high	5	3.79	1.09
high	low_low	5	6.11	0.61
high	high_low	5	6.89	0.50
high	high_high	5	7.15	0.59

apa_table(
  h2c_similarity_condition_lm %>%
    transmute(
      Term = term,
      Estimate = apa_num(estimate, 3),
      SE = apa_num(std.error, 3),
      statistic = apa_num(statistic, 2),
      p = apa_p(p.value)
    ),
  caption = "Table H2c-6. Linear model predicting human Likert similarity from planned annex conditions."
)

Table H2c-6. Linear model predicting human Likert similarity from planned annex conditions.

Term	Estimate	SE	statistic	p
(Intercept)	3.281	0.263	12.45	< .001
planned_similarityhigh	3.224	0.263	12.24	< .001
planned_salience_pairhigh_low	0.058	0.323	0.18	.859
planned_salience_pairhigh_high	0.573	0.323	1.78	.087

apa_table(
  h2c_pairwise_condition_metric_tests %>%
    slice_head(n = params$top_n_metrics) %>%
    transmute(
      Metric = metric_short,
      Family = metric_family,
      Object = coalesce(basis_object, object, state_type, ""),
      `Mean high similarity` = apa_num(mean_high, 3),
      `Mean low similarity` = apa_num(mean_low, 3),
      `High − low` = apa_num(difference_high_minus_low, 3),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table H2c-7. Computational metrics that best separate planned high- vs low-similarity pairs."
)

Table H2c-7. Computational metrics that best separate planned high- vs low-similarity pairs.

Metric	Family	Object	Mean high similarity	Mean low similarity	High − low	p	q
frobenius distance sq	Operator/density geometry	P_concat_direct	-40.489	-95.634	55.145	.088	.785
frobenius distance sq	Operator/density geometry	P_lowdin	-40.489	-95.634	55.145	.088	.785
frobenius distance sq	Operator/density geometry	P_lowdin	-31.667	-83.611	51.944	.053	.785
frobenius distance sq	Operator/density geometry	P_concat_direct	-31.667	-83.611	51.944	.053	.785
principal overlap nuclear	Subspace/projector geometry	S_lowdin	244.396	204.169	40.228	.278	.799
frobenius distance sq	Operator/density geometry	P_concat_direct	-63.982	-104.087	40.105	.255	.799
frobenius distance sq	Operator/density geometry	P_lowdin	-63.982	-104.087	40.105	.255	.799
trace inner	Operator/density geometry	P_concat_direct	242.300	202.728	39.572	.299	.799
trace inner	Operator/density geometry	P_lowdin	242.300	202.728	39.572	.299	.799
principal overlap trace	Subspace/projector geometry	S_lowdin	242.300	202.728	39.572	.299	.799
principal overlap nuclear	Subspace/projector geometry	S_lowdin	215.812	177.644	38.167	.399	.799
trace inner	Operator/density geometry	P_concat_direct	213.989	176.550	37.439	.415	.799

write_table(h2c_similarity_condition_summary, "h2c_similarity_condition_summary.csv")
write_table(h2c_similarity_condition_lm, "h2c_similarity_condition_lm.csv")
write_table(h2c_pairwise_condition_metric_tests, "h2c_pairwise_condition_metric_tests.csv")

h2c_condition_plot <- pair_behavior_with_conditions %>%
  filter(hypothesis %in% c("H1_asymmetry_ipsative", "H2_salience"), !is.na(presentation_salience_pattern)) %>%
  mutate(
    hypothesis_label = recode(
      hypothesis,
      H1_asymmetry_ipsative = "H1 ipsative asymmetry",
      H2_salience = "H2 ipsative salience"
    )
  ) %>%
  ggplot(aes(x = presentation_salience_pattern, y = human_value, fill = planned_similarity)) +
  geom_hline(yintercept = .5, linewidth = .35, linetype = "dashed") +
  geom_boxplot(width = .65, alpha = .75, outlier.shape = NA) +
  geom_jitter(aes(color = planned_similarity), width = .08, height = 0, size = 2, alpha = .80, show.legend = FALSE) +
  facet_wrap(~ hypothesis_label, ncol = 1) +
  scale_fill_manual(values = c("low" = "#E69F00", "high" = "#0072B2")) +
  scale_color_manual(values = c("low" = "#E69F00", "high" = "#0072B2")) +
  scale_y_continuous(limits = c(0, 1), breaks = seq(0, 1, .25)) +
  labs(
    title = "Ipsative responses by planned salience condition",
    subtitle = "The dashed line marks chance-level choice. Presentation order is separated from the annex condition.",
    x = "Presentation salience pattern",
    y = "Proportion choosing first option"
  ) +
  theme_apa7()

h2c_condition_plot

save_plot(h2c_condition_plot, "h2c_ipsative_responses_by_salience_condition_v9.png", width = 8.5, height = 7)

h2c_concept_plot <- h2c_likert_condition_dimensionality %>%
  pivot_longer(
    cols = any_of(c("mean_salience_likert", "log10_n_occurrences", "horn_wishart", "gavish_donoho", "permutation_pa")),
    names_to = "outcome",
    values_to = "value"
  ) %>%
  mutate(outcome = recode(outcome, !!!salience_predictor_labels, mean_salience_likert = "Mean Likert salience", log10_n_occurrences = "Log frequency", .default = outcome)) %>%
  ggplot(aes(x = planned_salience_label, y = value, fill = planned_salience_label)) +
  geom_boxplot(width = .55, alpha = .70, outlier.shape = NA) +
  geom_jitter(width = .08, size = 1.9, alpha = .75) +
  facet_wrap(~ outcome, scales = "free_y", ncol = 2) +
  scale_fill_manual(values = c("low" = "#999999", "high" = "#0072B2")) +
  labs(
    title = "Concept-level planned salience, ratings, and dimensionality",
    subtitle = "This evaluates whether high-salience concepts are also richer or more frequent in the corpus-derived representation.",
    x = "Planned concept salience",
    y = NULL
  ) +
  theme_apa7() +
  theme(legend.position = "none")

h2c_concept_plot

save_plot(h2c_concept_plot, "h2c_concept_salience_dimensionality_by_planned_label_v9.png", width = 9, height = 7)

h2c_best_similarity_metric <- h2c_pairwise_condition_metric_tests %>% slice_head(n = 1)
h2c_best_similarity_data <- pairwise_metric_values %>%
  inner_join(annex_salience_conditions %>% select(pair_id, planned_similarity, planned_salience_pair), by = "pair_id") %>%
  filter(metric_id == h2c_best_similarity_metric$metric_id[[1]]) %>%
  mutate(metric_value = similarity_orient_value(metric_name, value))

h2c_similarity_metric_plot <- h2c_best_similarity_data %>%
  ggplot(aes(x = planned_similarity, y = metric_value, fill = planned_similarity)) +
  geom_boxplot(width = .55, alpha = .75, outlier.shape = NA) +
  geom_jitter(width = .08, size = 2, alpha = .75) +
  scale_fill_manual(values = c("low" = "#E69F00", "high" = "#0072B2")) +
  labs(
    title = "Best computational separator of planned similarity",
    subtitle = paste0(h2c_best_similarity_metric$metric_short[[1]], "; high − low = ", apa_num(h2c_best_similarity_metric$difference_high_minus_low[[1]], 3)),
    x = "Planned similarity condition",
    y = "Computational similarity metric"
  ) +
  theme_apa7() +
  theme(legend.position = "none")

h2c_similarity_metric_plot

save_plot(h2c_similarity_metric_plot, "h2c_best_computational_similarity_condition_separator_v9.png", width = 7.5, height = 5)

h2c_salience_rating_diff <- h2c_concept_condition_tests %>% filter(outcome == "mean_salience_likert") %>% slice_head(n = 1)
h2c_frequency_diff <- h2c_concept_condition_tests %>% filter(outcome == "log10_n_occurrences") %>% slice_head(n = 1)
h2c_best_condition_metric <- h2c_pairwise_condition_metric_tests %>% slice_head(n = 1)
cat(
  "**Interpretation.** The annex condition structure lets us separate salience as an experimental manipulation from salience as an estimated psychological variable. ",
  "High-salience concepts differ from low-salience concepts in mean Likert salience by ", apa_num(h2c_salience_rating_diff$difference_high_minus_low[[1]], 2),
  " points (p ", apa_p(h2c_salience_rating_diff$p.value[[1]]), "). ",
  "The corresponding high-minus-low log-frequency difference is ", apa_num(h2c_frequency_diff$difference_high_minus_low[[1]], 2),
  " (p ", apa_p(h2c_frequency_diff$p.value[[1]]), "). ",
  "This matters because any dimensionality effect has to be read against frequency: rich concepts may be rich because they are semantically differentiated, but also because they appear more often in the corpus. ",
  "For planned similarity, the best computational separator is ", h2c_best_condition_metric$metric_short[[1]],
  " from the ", h2c_best_condition_metric$metric_family[[1]], " family, with high-minus-low difference = ",
  apa_num(h2c_best_condition_metric$difference_high_minus_low[[1]], 3), ". ",
  "Substantively, these condition analyses should be treated as manipulation checks and moderation analyses: they tell us whether the stimuli behaved as designed, and whether the quantum-like metrics are tracking the intended salience/similarity structure rather than merely fitting item-level noise. Which would be embarrassing, though hardly unprecedented in human affairs.\n"
)

Interpretation. The annex condition structure lets us separate salience as an experimental manipulation from salience as an estimated psychological variable. High-salience concepts differ from low-salience concepts in mean Likert salience by 3.03 points (p < .001 ). The corresponding high-minus-low log-frequency difference is 1.31 (p < .001 ). This matters because any dimensionality effect has to be read against frequency: rich concepts may be rich because they are semantically differentiated, but also because they appear more often in the corpus. For planned similarity, the best computational separator is frobenius distance sq from the Operator/density geometry family, with high-minus-low difference = 55.145 . Substantively, these condition analyses should be treated as manipulation checks and moderation analyses: they tell us whether the stimuli behaved as designed, and whether the quantum-like metrics are tracking the intended salience/similarity structure rather than merely fitting item-level noise. Which would be embarrassing, though hardly unprecedented in human affairs.

11.5 H2d: salience/similarity conditions as moderators of other contrasts

The planned salience cells should not only be used as a manipulation check for salience itself. They can also qualify the other contrasts built from the same country pairs. The theoretical reason is simple: if salience changes the diagnostic weight of a concept, then it should affect forced-choice asymmetry, Likert order asymmetry, and even how strongly computational containment predicts human responses. If this moderation is absent, the salience manipulation may still predict salience choices but not the more general comparison process.

The analyses below are deliberately exploratory because several cells contain only five planned pairs. They should be read as condition diagnostics, not as final hypothesis tests polished for ceremonial sacrifice to Reviewer 2.

safe_condition_lm <- function(data, outcome_col, rhs, analysis_label) {
  d <- data %>%
    filter(!is.na(.data[[outcome_col]]), is.finite(.data[[outcome_col]]))

  formula_text <- paste(outcome_col, "~", rhs)
  vars <- setdiff(all.vars(as.formula(formula_text)), outcome_col)
  usable <- nrow(d) >= 6 && all(vapply(vars, function(v) v %in% names(d) && n_distinct(d[[v]][!is.na(d[[v]])]) >= 2, logical(1)))

  if (!usable) {
    return(tibble(
      analysis_block = analysis_label,
      term = "model_not_estimable",
      estimate = NA_real_,
      std.error = NA_real_,
      statistic = NA_real_,
      p.value = NA_real_,
      n = nrow(d),
      formula = formula_text
    ))
  }

  tryCatch(
    broom::tidy(lm(as.formula(formula_text), data = d)) %>%
      mutate(analysis_block = analysis_label, n = nrow(d), formula = formula_text) %>%
      select(analysis_block, term, estimate, std.error, statistic, p.value, n, formula),
    error = function(e) tibble(
      analysis_block = analysis_label,
      term = paste0("model_error: ", e$message),
      estimate = NA_real_,
      std.error = NA_real_,
      statistic = NA_real_,
      p.value = NA_real_,
      n = nrow(d),
      formula = formula_text
    )
  )
}

h1_condition_data <- pair_behavior_with_conditions %>%
  filter(hypothesis == "H1_asymmetry_ipsative", !is.na(presentation_salience_pattern), !is.na(planned_similarity))

h2_condition_data <- pair_behavior_with_conditions %>%
  filter(hypothesis == "H2_salience", !is.na(presentation_salience_pattern), !is.na(planned_similarity))

h3_similarity_condition_data <- h3_similarity_human %>%
  inner_join(
    annex_salience_conditions %>% select(pair_id, planned_salience_pair, planned_similarity, annex_condition),
    by = "pair_id"
  ) %>%
  filter(!is.na(planned_salience_pair), !is.na(planned_similarity))

h3_order_condition_data <- h3_order_human %>%
  inner_join(
    annex_salience_conditions %>% select(pair_id, planned_salience_pair, planned_similarity, annex_condition),
    by = "pair_id"
  ) %>%
  filter(!is.na(planned_salience_pair), !is.na(planned_similarity))

h2d_condition_moderation_models <- bind_rows(
  safe_condition_lm(h1_condition_data, "human_value", "presentation_salience_pattern * planned_similarity", "H1 ipsative asymmetry by planned salience/similarity"),
  safe_condition_lm(h2_condition_data, "human_value", "presentation_salience_pattern * planned_similarity", "H2 ipsative salience by planned salience/similarity"),
  safe_condition_lm(h3_similarity_condition_data, "human_value", "planned_salience_pair * planned_similarity", "H3 Likert similarity by planned salience/similarity"),
  safe_condition_lm(h3_order_condition_data, "human_order_delta", "planned_salience_pair * planned_similarity", "H3 Likert order asymmetry by planned salience/similarity")
) %>%
  mutate(p_fdr = p.adjust(p.value, method = "BH"))

apa_table(
  h2d_condition_moderation_models %>%
    filter(term != "(Intercept)") %>%
    transmute(
      Analysis = analysis_block,
      Term = term,
      n,
      Estimate = apa_num(estimate, 3),
      SE = apa_num(std.error, 3),
      statistic = apa_num(statistic, 2),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table H2d-1. Planned salience/similarity conditions as moderators of human contrasts."
)

Table H2d-1. Planned salience/similarity conditions as moderators of human contrasts.

Analysis	Term	n	Estimate	SE	statistic	p	q
H1 ipsative asymmetry by planned salience/similarity	presentation_salience_patternlow_high	30	0.206	0.081	2.54	.019	.048
H1 ipsative asymmetry by planned salience/similarity	presentation_salience_patternhigh_low	30	-0.580	0.071	-8.18	< .001	< .001
H1 ipsative asymmetry by planned salience/similarity	presentation_salience_patternhigh_high	30	-0.321	0.061	-5.22	< .001	< .001
H1 ipsative asymmetry by planned salience/similarity	planned_similarityhigh	30	-0.123	0.061	-2.01	.057	.123
H1 ipsative asymmetry by planned salience/similarity	presentation_salience_patternlow_high:planned_similarityhigh	30	0.177	0.115	1.54	.138	.201
H1 ipsative asymmetry by planned salience/similarity	presentation_salience_patternhigh_low:planned_similarityhigh	30	0.167	0.100	1.66	.110	.193
H1 ipsative asymmetry by planned salience/similarity	presentation_salience_patternhigh_high:planned_similarityhigh	30	0.366	0.087	4.22	< .001	.001
H2 ipsative salience by planned salience/similarity	presentation_salience_patternlow_high	30	-0.236	0.125	-1.88	.073	.143
H2 ipsative salience by planned salience/similarity	presentation_salience_patternhigh_low	30	0.697	0.110	6.36	< .001	< .001
H2 ipsative salience by planned salience/similarity	presentation_salience_patternhigh_high	30	0.417	0.095	4.39	< .001	< .001
H2 ipsative salience by planned salience/similarity	planned_similarityhigh	30	0.176	0.095	1.86	.077	.143
H2 ipsative salience by planned salience/similarity	presentation_salience_patternlow_high:planned_similarityhigh	30	-0.186	0.177	-1.05	.307	.358
H2 ipsative salience by planned salience/similarity	presentation_salience_patternhigh_low:planned_similarityhigh	30	-0.235	0.155	-1.52	.144	.201
H2 ipsative salience by planned salience/similarity	presentation_salience_patternhigh_high:planned_similarityhigh	30	-0.466	0.134	-3.48	.002	.006
H3 Likert similarity by planned salience/similarity	planned_salience_pairhigh_low	30	-0.658	0.426	-1.54	.136	.201
H3 Likert similarity by planned salience/similarity	planned_salience_pairhigh_high	30	0.115	0.426	0.27	.789	.789
H3 Likert similarity by planned salience/similarity	planned_similarityhigh	30	2.442	0.426	5.73	< .001	< .001
H3 Likert similarity by planned salience/similarity	planned_salience_pairhigh_low:planned_similarityhigh	30	1.432	0.603	2.37	.026	.061
H3 Likert similarity by planned salience/similarity	planned_salience_pairhigh_high:planned_similarityhigh	30	0.916	0.603	1.52	.142	.201
H3 Likert order asymmetry by planned salience/similarity	planned_salience_pairhigh_low	30	-0.054	0.112	-0.49	.631	.669
H3 Likert order asymmetry by planned salience/similarity	planned_salience_pairhigh_high	30	-0.052	0.112	-0.47	.645	.669
H3 Likert order asymmetry by planned salience/similarity	planned_similarityhigh	30	-0.138	0.112	-1.23	.230	.303
H3 Likert order asymmetry by planned salience/similarity	planned_salience_pairhigh_low:planned_similarityhigh	30	0.167	0.158	1.06	.302	.358
H3 Likert order asymmetry by planned salience/similarity	planned_salience_pairhigh_high:planned_similarityhigh	30	0.192	0.158	1.21	.238	.303

write_table(h2d_condition_moderation_models, "h2d_condition_moderation_models.csv")

h2d_h1_condition_metric_data <- join_metrics_to_behavior(h1_condition_data, pairwise_metric_values) %>%
  filter(is_asymmetry_metric(metric_name)) %>%
  mutate(
    analysis_block = "H1 ipsative asymmetry",
    condition_block = paste(as.character(presentation_salience_pattern), as.character(planned_similarity), sep = " | similarity=")
  )

h2d_h2_condition_metric_data <- join_metrics_to_behavior(h2_condition_data, pairwise_metric_values) %>%
  filter(is_asymmetry_metric(metric_name)) %>%
  mutate(
    analysis_block = "H2 ipsative salience",
    condition_block = paste(as.character(presentation_salience_pattern), as.character(planned_similarity), sep = " | similarity=")
  )

h2d_h3_order_condition_metric_data <- h3_order_metrics %>%
  inner_join(
    annex_salience_conditions %>% select(pair_id, planned_salience_pair, planned_similarity, annex_condition),
    by = "pair_id"
  ) %>%
  mutate(
    analysis_block = "H3 Likert order asymmetry",
    condition_block = paste(as.character(planned_salience_pair), as.character(planned_similarity), sep = " | similarity=")
  )

h2d_condition_metric_rank <- bind_rows(
  h2d_h1_condition_metric_data,
  h2d_h2_condition_metric_data,
  h2d_h3_order_condition_metric_data
) %>%
  filter(!is.na(condition_block)) %>%
  cor_by_group(
    group_cols = c("analysis_block", "condition_block", rank_group_cols),
    x = "metric_value",
    y = "human_value"
  )

h2d_best_metric_by_condition <- h2d_condition_metric_rank %>%
  filter(!is.na(estimate), n >= 3) %>%
  group_by(analysis_block, condition_block) %>%
  slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
  ungroup() %>%
  arrange(analysis_block, condition_block)

apa_table(
  h2d_best_metric_by_condition %>%
    transmute(
      Analysis = analysis_block,
      Condition = condition_block,
      Metric = metric_short,
      Family = metric_family,
      Object = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table H2d-2. Best directional computational-human association within each salience/similarity condition."
)

Table H2d-2. Best directional computational-human association within each salience/similarity condition.

Analysis	Condition	Metric	Family	Object	n	Spearman rho	p	q
H1 ipsative asymmetry	high_high | similarity=high	Containment asymmetry	Operator/density geometry	P_concat_direct	5	1.00	< .001	< .001
H1 ipsative asymmetry	high_high | similarity=low	Containment asymmetry	Operator/density geometry	rho_fit_global_density	5	.90	.037	.198
H1 ipsative asymmetry	high_low | similarity=high	Containment asymmetry	Operator/density geometry	P_global	3	1.00	< .001	< .001
H1 ipsative asymmetry	high_low | similarity=low	Containment asymmetry	Operator/density geometry	P_concat_direct	3	1.00	< .001	< .001
H1 ipsative asymmetry	low_low | similarity=high	Containment asymmetry	Operator/density geometry	P_concat_direct	5	.90	.037	.198
H1 ipsative asymmetry	low_low | similarity=low	Containment asymmetry	Operator/density geometry	P_concat_direct	5	1.00	< .001	< .001
H2 ipsative salience	high_high | similarity=high	Containment asymmetry	Operator/density geometry	P_concat_direct	5	−.90	.037	.198
H2 ipsative salience	high_high | similarity=low	Containment asymmetry	Operator/density geometry	P_concat_direct	5	−.90	.037	.198
H2 ipsative salience	high_low | similarity=high	Containment asymmetry	Operator/density geometry	P_global	3	-1.00	< .001	< .001
H2 ipsative salience	high_low | similarity=low	Containment asymmetry	Operator/density geometry	P_concat_direct	3	-1.00	< .001	< .001
H2 ipsative salience	low_low | similarity=high	Containment asymmetry	Operator/density geometry	P_concat_direct	5	−.90	.037	.198
H2 ipsative salience	low_low | similarity=low	QSM asymmetry	Sequential QSM	S_global	5	-1.00	< .001	< .001
H3 Likert order asymmetry	high_high | similarity=high	Containment asymmetry	Operator/density geometry	rho_fit_global_density	5	−.90	.037	.198
H3 Likert order asymmetry	high_high | similarity=low	QSM asymmetry	Sequential QSM	S_global	5	.90	.037	.198
H3 Likert order asymmetry	high_low | similarity=high	Containment asymmetry	Operator/density geometry	projector_mixture_freq	5	1.00	< .001	< .001
H3 Likert order asymmetry	high_low | similarity=low	Containment asymmetry	Operator/density geometry	rho_global_density	5	.90	.037	.198
H3 Likert order asymmetry	low_low | similarity=high	Containment asymmetry	Operator/density geometry	P_concat_direct	5	-1.00	< .001	< .001
H3 Likert order asymmetry	low_low | similarity=low	Containment asymmetry	Operator/density geometry	P_global	5	1.00	< .001	< .001

write_table(h2d_condition_metric_rank, "h2d_condition_metric_rankings.csv")
write_table(h2d_best_metric_by_condition, "h2d_best_metric_by_condition.csv")

h2d_order_term <- h2d_condition_moderation_models %>%
  filter(analysis_block == "H3 Likert order asymmetry by planned salience/similarity", term != "(Intercept)", !str_detect(term, "model_not_estimable|model_error")) %>%
  arrange(p.value) %>%
  slice_head(n = 1)

h2d_best_coupling <- h2d_best_metric_by_condition %>%
  filter(!is.na(estimate)) %>%
  arrange(desc(abs_estimate)) %>%
  slice_head(n = 1)

order_sentence <- if (nrow(h2d_order_term) > 0) {
  paste0("The most informative H3 order-asymmetry condition term is `", h2d_order_term$term[[1]], "` (p ", apa_p(h2d_order_term$p.value[[1]]), "). ")
} else {
  "The H3 order-asymmetry condition model was not estimable with enough variation in the available cells. "
}

coupling_sentence <- if (nrow(h2d_best_coupling) > 0) {
  paste0(
    "The strongest within-condition computational-human coupling is found for ", h2d_best_coupling$analysis_block[[1]],
    " in the condition ", h2d_best_coupling$condition_block[[1]], ", with ", h2d_best_coupling$metric_short[[1]],
    " from ", h2d_best_coupling$metric_family[[1]], " reaching rho = ", apa_r(h2d_best_coupling$estimate[[1]]), ". "
  )
} else {
  "No condition-specific computational coupling was estimable. "
}

cat(
  "**Interpretation.** These condition-level analyses ask whether the planned salience manipulation also changes the expression of other effects. ",
  order_sentence,
  "Because several cells contain only five pairs, these models are better treated as a design audit than as decisive inference. ",
  coupling_sentence,
  "If unequal-salience cells show stronger directional containment effects than equal-salience cells, that supports the thesis interpretation that salience changes the diagnostic weighting of conceptual regions rather than merely adding a generic response bias.\n"
)

Interpretation. These condition-level analyses ask whether the planned salience manipulation also changes the expression of other effects. The most informative H3 order-asymmetry condition term is planned_similarityhigh (p .230). Because several cells contain only five pairs, these models are better treated as a design audit than as decisive inference. The strongest within-condition computational-human coupling is found for H1 ipsative asymmetry in the condition high_low | similarity=high, with Containment asymmetry from Operator/density geometry reaching rho = 1.00. If unequal-salience cells show stronger directional containment effects than equal-salience cells, that supports the thesis interpretation that salience changes the diagnostic weighting of conceptual regions rather than merely adding a generic response bias.

12 H3: Likert similarity and order asymmetry

12.1 Theoretical rationale

Likert similarity is psychologically different from ipsative forced choice. A rating scale encourages participants to compress a conceptual relation into a single graded number. That kind of task can be well approximated by average semantic proximity, which is exactly what a contour centroid represents. Therefore, a strong centroid-cosine baseline in H3 is not a failure of the quantum-like model. It means that explicit scalar similarity may be closer to a classical average-proximity judgment.

The more demanding prediction concerns order asymmetry. If the same pair receives different ratings depending on order, then directional subspace metrics should help. If order effects are weak or absent in the human data, then no computational metric should be expected to produce a strong confirmatory result. A weak H3b is therefore informative: the measurement format may suppress the asymmetry that appears under ipsative choice.

H3 is separated into two analyses. H3a asks whether metrics predict order-averaged explicit similarity ratings. H3b asks whether metrics predict the much smaller order asymmetry in those ratings.

12.2 H3a: order-averaged Likert similarity

Here the two presentation orders are averaged, so the dependent variable is intentionally symmetric. The best computational account should therefore be a symmetric similarity or reversed distance. This is the place where the classical centroid baseline is allowed to shine. Annoying, perhaps, but methodologically healthy.

h3_rating_top <- h3_rating_rank %>% slice_head(n = params$top_n_metrics)
h3_rating_family_best <- best_by_family(h3_rating_rank)
h3_rating_cosine_comp <- compare_quantum_vs_cosine(h3_rating_rank)

apa_table(
  h3_rating_family_best %>%
    transmute(
      Family = metric_family,
      Metric = metric_short,
      Representation = coalesce(basis_object, object, state_type, state_vector_source, ""),
      Variant = str_trunc(coalesce(variant_label, ""), 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 13. H3a best predictor within each metric family."
)

Table 13. H3a best predictor within each metric family.

Family	Metric	Representation	Variant	n	Spearman rho	p	q
Classical vector baseline	Angular distance, reversed	contour_centroid	classical	89	.51	< .001	< .001
Operator/density geometry	a in b trace normalized	rho_freq_density	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.45	< .001	< .001
Subspace/projector geometry	principal overlap trace	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	89	.42	< .001	.001
Sequential QSM	QSM p(A|B)	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	89	.37	< .001	.008

apa_table(
  h3_rating_cosine_comp %>%
    transmute(
      `Comparison family` = comparison_family,
      Metric = metric_short,
      Family = metric_family,
      Representation = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 14. H3a direct comparison between quantum-like predictors and classical cosine."
)

Table 14. H3a direct comparison between quantum-like predictors and classical cosine.

Comparison family	Metric	Family	Representation	n	Spearman rho	p	q
Best classical cosine	Centroid cosine	Classical vector baseline	contour_centroid	89	.51	< .001	< .001
Best quantum-like metric	a in b trace normalized	Operator/density geometry	rho_freq_density	89	.45	< .001	< .001

plot_family_comparison(
  h3_rating_family_best,
  title = "H3a: best predictor by metric family",
  filename = "h3_rating_best_by_metric_family_v7.png"
)

h3_primary <- h3_rating_rank %>% slice_head(n = 1)
plot_metric_scatter(
  h3_similarity_metrics,
  h3_primary,
  title = "H3a primary metric for explicit similarity ratings",
  y_label = "Human order-averaged similarity rating",
  filename = "h3_rating_primary_metric_scatter_v7.png"
)

h3_best <- h3_rating_rank %>% slice_head(n = 1)
h3_cos <- h3_rating_cosine_comp %>% filter(comparison_family == "Best classical cosine") %>% slice_head(n = 1)
cat(
  "**Interpretation.** For explicit Likert similarity, the best overall metric is ", h3_best$metric_short[[1]],
  " (", h3_best$metric_family[[1]], "), rho = ", apa_r(h3_best$estimate[[1]]),
  ". The best classical cosine baseline gives rho = ", apa_r(h3_cos$estimate[[1]]),
  ". If cosine is competitive or superior here, this is theoretically useful rather than embarrassing: explicit scalar similarity is exactly where centroid-based vector semantics should perform well. The quantum-like model is expected to add more for directionality, context, and relational structure.\n"
)

Interpretation. For explicit Likert similarity, the best overall metric is Angular distance, reversed ( Classical vector baseline ), rho = .51 . The best classical cosine baseline gives rho = .51 . If cosine is competitive or superior here, this is theoretically useful rather than embarrassing: explicit scalar similarity is exactly where centroid-based vector semantics should perform well. The quantum-like model is expected to add more for directionality, context, and relational structure.

12.3 H3b: order asymmetry in Likert ratings

Here the dependent variable is the difference between orders. Because the human order effect is small, this block is treated as exploratory. A metric can correlate with the small residual order effect, but the interpretation should remain cautious unless the human asymmetry itself is reliable.

h3_order_top <- h3_order_rank %>% slice_head(n = params$top_n_metrics)

apa_table(
  h3_order_test %>%
    transmute(
      n,
      `Mean direct − reverse` = apa_num(mean_delta, 3),
      `Median |delta|` = apa_num(median_abs_delta, 3),
      t = apa_num(statistic, 2),
      df = apa_num(df, 1),
      p = apa_p(p.value)
    ),
  caption = "Table 15. Human order asymmetry in Likert ratings."
)

Table 15. Human order asymmetry in Likert ratings.

n	Mean direct − reverse	Median |delta|	t	df	p
89	-0.014	0.133	-0.81	88.0	.422

apa_table(
  h3_order_top %>%
    transmute(
      Metric = metric_short,
      Family = metric_family,
      Representation = coalesce(basis_object, object, state_type, ""),
      Variant = str_trunc(coalesce(variant_label, ""), 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 16. Exploratory predictors of H3 order asymmetry."
)

Table 16. Exploratory predictors of H3 order asymmetry.

Metric	Family	Representation	Variant	n	Spearman rho	p	q
Containment asymmetry	Operator/density geometry	P_concat_direct	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.32	.002	.029
Containment asymmetry	Operator/density geometry	P_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.32	.002	.029
Containment asymmetry	Subspace/projector geometry	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.32	.002	.029
qsm neutral asymmetry a minus b	Subspace/projector geometry	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.32	.002	.029
Containment asymmetry	Operator/density geometry	projector_mixture_freq	bayesian_gmm | g=horn_wishart | l=horn_wishart	89	.31	.003	.029
Containment asymmetry	Operator/density geometry	projector_mixture_fit_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	89	.31	.003	.029
Containment asymmetry	Operator/density geometry	P_concat_direct	gmm_bic | g=gavish_donoho | l=gavish_donoho	89	.31	.003	.029
Containment asymmetry	Operator/density geometry	P_lowdin	gmm_bic | g=gavish_donoho | l=gavish_donoho	89	.31	.003	.029
Containment asymmetry	Subspace/projector geometry	S_lowdin	gmm_bic | g=gavish_donoho | l=gavish_donoho	89	.31	.003	.029
qsm neutral asymmetry a minus b	Subspace/projector geometry	S_lowdin	gmm_bic | g=gavish_donoho | l=gavish_donoho	89	.31	.003	.029
Containment asymmetry	Operator/density geometry	P_concat_direct	bayesian_gmm | g=horn_wishart | l=horn_wishart	89	.31	.003	.029
Containment asymmetry	Operator/density geometry	P_lowdin	bayesian_gmm | g=horn_wishart | l=horn_wishart	89	.31	.003	.029

h3_order_best <- h3_order_top %>% slice_head(n = 1)
cat(
  "**Interpretation.** The human order effect is small: mean direct-minus-reverse delta = ",
  apa_num(h3_order_test$mean_delta[[1]], 3), " (p ", apa_p(h3_order_test$p.value[[1]]), "). ",
  "The best computational association with order asymmetry is ", h3_order_best$metric_short[[1]],
  ", rho = ", apa_r(h3_order_best$estimate[[1]]), ". Because the behavioral effect itself is weak, this block should be treated as exploratory rather than confirmatory.\n"
)

Interpretation. The human order effect is small: mean direct-minus-reverse delta = -0.014 (p .422 ). The best computational association with order asymmetry is Containment asymmetry , rho = .32 . Because the behavioral effect itself is weak, this block should be treated as exploratory rather than confirmatory.

13 H4: triangle and multiplicative triangle structure

13.1 Theoretical rationale

Triangle analyses test whether conceptual similarity behaves like a classical metric space. If human judgments violate additive or multiplicative triangle expectations, then a simple Euclidean interpretation is incomplete. The quantum-like model offers several alternatives: projector distances, Bures-like distances, and fidelity-like similarities between normalized conceptual structures.

The main theoretical distinction is between distance residuals and similarity-product residuals. Additive triangle residuals evaluate whether one conceptual distance exceeds the path through a third concept. Multiplicative residuals evaluate whether direct similarity is lower than expected from the product of two indirect similarities. The latter is especially relevant because it can reveal non-classical relational structure even when additive geometry looks well behaved.

13.2 Methodological choices for H4

The notebook uses only the triplets present in the human design and evaluates both continuous residuals and binary violation detection. This matters because a model can capture the rank ordering of residuals without correctly classifying the small number of actual violations. Treating these as separate outcomes prevents a base-rate accuracy mirage, that charming statistical swamp.

H4 evaluates whether the geometry of the computational model captures triplet structure. The key analyses are continuous residual correlations. Binary violations are also summarized, but they are less informative when violations are rare.

apa_table(human_triplet_summary, caption = "Table 17. Human triplet residual summary.")

Table 17. Human triplet residual summary.

n_contrasts	n_unordered_triplets	additive_violations	mti_lower_than_product	mean_triangle_residual	mean_mti_residual
66	22	0	7	-0.593	0.248

h4_distance_top <- h4_distance_rank %>% slice_head(n = params$top_n_metrics)
h4_mti_top <- h4_mti_rank %>% slice_head(n = params$top_n_metrics)

apa_table(
  h4_distance_top %>%
    transmute(
      Metric = metric_short,
      Object = basis_object,
      Variant = str_trunc(variant_label, 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 18. H4 additive triangle residual correlations."
)

Table 18. H4 additive triangle residual correlations.

Metric	Object	Variant	n	Spearman rho	p	q
Bures distance, reversed	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.49	< .001	< .001
Bures distance, reversed	S_global	gmm_bic | g=horn_wishart | l=horn_wishart	66	.49	< .001	< .001
Bures distance, reversed	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	66	.49	< .001	< .001
Bures distance, reversed	S_global	gmm_bic | g=profile_likelihood | l=profile_like...	66	.49	< .001	< .001
Chordal distance, reversed	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.45	< .001	< .001
Chordal distance, reversed	S_global	gmm_bic | g=horn_wishart | l=horn_wishart	66	.45	< .001	< .001
Chordal distance, reversed	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	66	.45	< .001	.001
Chordal distance, reversed	S_global	gmm_bic | g=profile_likelihood | l=profile_like...	66	.45	< .001	.001
Bures distance, reversed	S_global	bayesian_gmm | g=permutation_pa | l=permutation_pa	66	.42	< .001	.002
Bures distance, reversed	S_global	gmm_bic | g=permutation_pa | l=permutation_pa	66	.42	< .001	.002
Chordal distance, reversed	S_global	bayesian_gmm | g=permutation_pa | l=permutation_pa	66	.42	< .001	.002
Chordal distance, reversed	S_global	gmm_bic | g=permutation_pa | l=permutation_pa	66	.42	< .001	.002

apa_table(
  h4_mti_top %>%
    transmute(
      Metric = metric_short,
      Object = basis_object,
      Variant = str_trunc(variant_label, 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr)
    ),
  caption = "Table 19. H4 multiplicative triangle residual correlations."
)

Table 19. H4 multiplicative triangle residual correlations.

Metric	Object	Variant	n	Spearman rho	p	q
Density fidelity	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	66	.55	< .001	< .001
Density fidelity	S_global	gmm_bic | g=profile_likelihood | l=profile_like...	66	.55	< .001	< .001
Projector overlap	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	66	.52	< .001	< .001
Projector overlap	S_global	gmm_bic | g=profile_likelihood | l=profile_like...	66	.52	< .001	< .001
Density fidelity	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.51	< .001	< .001
Density fidelity	S_global	gmm_bic | g=horn_wishart | l=horn_wishart	66	.51	< .001	< .001
Projector overlap	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.44	< .001	.001
Projector overlap	S_global	gmm_bic | g=horn_wishart | l=horn_wishart	66	.44	< .001	.001
Density fidelity	S_lowdin	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.42	< .001	.002
Density fidelity	S_global	bayesian_gmm | g=permutation_pa | l=permutation_pa	66	.42	< .001	.002
Density fidelity	S_global	gmm_bic | g=permutation_pa | l=permutation_pa	66	.42	< .001	.002
Projector overlap	S_global	bayesian_gmm | g=permutation_pa | l=permutation_pa	66	.41	< .001	.002

apa_table(
  mti_classification %>%
    slice_head(n = params$top_n_metrics) %>%
    transmute(
      Metric = metric_short_label(similarity_metric),
      Object = basis_object,
      Variant = str_trunc(variant_short(variant), 50),
      n,
      Accuracy = apa_num(accuracy, 2),
      Precision = apa_num(precision, 2),
      Recall = apa_num(recall, 2),
      F1 = apa_num(f1, 2)
    ),
  caption = "Table 20. H4 MTI lower-than-product classification performance."
)

Table 20. H4 MTI lower-than-product classification performance.

Metric	Object	Variant	n	Accuracy	Precision	Recall	F1
Mean cos² principal angles	S_lowdin	bayesian_gmm | g=permutation_pa | l=permutation_pa	66	0.88	0.40	0.29	0.33
Mean cos² principal angles	S_global	bayesian_gmm | g=permutation_pa | l=permutation_pa	66	0.89	0.50	0.14	0.22
Mean cos² principal angles	S_global	gmm_bic | g=permutation_pa | l=permutation_pa	66	0.89	0.50	0.14	0.22
Mean cos² principal angles	S_lowdin	bayesian_gmm | g=profile_likelihood | l=profile...	66	0.86	0.25	0.14	0.18
Mean cos² principal angles	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.85	0.20	0.14	0.17
Mean cos² principal angles	S_lowdin	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	0.85	0.20	0.14	0.17
Mean cos² principal angles	S_lowdin	gmm_bic | g=gavish_donoho | l=gavish_donoho	66	0.73	0.08	0.14	0.10
Density fidelity	S_global	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.89	0.00	0.00	0.00
Mean cos² principal angles	S_global	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.89	0.00	0.00	0.00
Projector overlap	S_global	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.89	0.00	0.00	0.00
Density fidelity	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.89	0.00	0.00	0.00
Projector overlap	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.89	0.00	0.00	0.00

plot_ranked_correlations(
  h4_distance_top,
  title = "H4 additive triangle: residual correlations",
  subtitle = "Continuous residuals are more informative than rare binary violations.",
  n = params$top_n_plots,
  filename = "h4_additive_triangle_top_correlations_v7.png"
)

plot_ranked_correlations(
  h4_mti_top,
  title = "H4 multiplicative triangle: residual correlations",
  subtitle = "Positive correlation means computational MTI residuals track human MTI residuals.",
  n = params$top_n_plots,
  filename = "h4_mti_top_correlations_v7.png"
)

h4_dist_primary <- h4_distance_top %>% slice_head(n = 1)
h4_dist_primary_data <- triplet_distance_human %>%
  filter(variant == h4_dist_primary$variant[[1]], basis_object == h4_dist_primary$basis_object[[1]], distance_metric == h4_dist_primary$distance_metric[[1]])

h4_dist_scatter <- ggplot(h4_dist_primary_data, aes(x = triangle_residual_ac_minus_ab_bc, y = human_triangle_residual)) +
  geom_point(size = 2.2, alpha = .80) +
  geom_smooth(method = "lm", se = TRUE, linewidth = .75) +
  labs(
    title = "H4 additive triangle: primary residual metric",
    subtitle = paste0(h4_dist_primary$metric_short[[1]], "; rho = ", apa_r(h4_dist_primary$estimate[[1]])),
    x = "Computational triangle residual",
    y = "Human triangle residual"
  ) +
  theme_apa7()

h4_dist_scatter

save_plot(h4_dist_scatter, "h4_additive_primary_residual_scatter_v7.png")

h4_d_best <- h4_distance_top %>% slice_head(n = 1)
h4_m_best <- h4_mti_top %>% slice_head(n = 1)
cat(
  "**Interpretation.** Additive triangle structure is best captured by ", h4_d_best$metric_short[[1]],
  " with rho = ", apa_r(h4_d_best$estimate[[1]]), ". Multiplicative triangle structure is best captured by ",
  h4_m_best$metric_short[[1]], " with rho = ", apa_r(h4_m_best$estimate[[1]]), ". ",
  "The classification table should be read cautiously because lower-than-product violations are sparse; residual correlations are the more stable evidence.\n"
)

Interpretation. Additive triangle structure is best captured by Bures distance, reversed with rho = .49 . Multiplicative triangle structure is best captured by Density fidelity with rho = .55 . The classification table should be read cautiously because lower-than-product violations are sparse; residual correlations are the more stable evidence.

14 H6: diagnosticity

14.1 Theoretical rationale

Diagnosticity is the hardest block because the relevant comparison is not just between two isolated concepts. The human task introduces a context or competing alternative that changes which features are useful for judgment. In the thesis, three computational routes are relevant: sequential projection, contextualized similarity, and perplexity-inhibited similarity.

The static pairwise analyses ask whether diagnosticity can be approximated without explicit context. The contextualized analyses test whether the context acts as a coordinate frame or Lüders-style filter. The perplexity analyses test whether a plausible competing pair activates shared properties that should be removed before comparing the initial concept with each target. These mechanisms are not interchangeable. If one succeeds and another fails, the theoretical interpretation changes.

H6 is analyzed three ways: static pairwise metrics, contextualized metrics, and perplexity-inhibited metrics. The static analysis asks whether diagnostic judgments can be approximated without explicit context. The contextualized and perplexity analyses test mechanisms closer to the thesis model.

14.2 H6a: static pairwise diagnostic metrics

Static pairwise metrics deliberately ignore the explicit context. They are useful as a baseline: if they perform well, diagnosticity may partly reduce to pre-existing pairwise structure. If they perform poorly relative to contextualized metrics, then the context mechanism is doing real explanatory work.

h6_static_top <- h6_static_rank %>%
  group_by(hypothesis) %>%
  slice_max(order_by = abs_estimate, n = params$top_n_metrics, with_ties = FALSE) %>%
  ungroup()

h6_static_family_best <- h6_static_rank %>%
  mutate(metric_family = metric_family_from_source(metric_source)) %>%
  group_by(hypothesis, metric_family) %>%
  slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
  ungroup()

apa_table(
  h6_static_family_best %>%
    transmute(
      Hypothesis = hypothesis,
      Family = metric_family,
      Metric = metric_short,
      Representation = coalesce(basis_object, object, state_type, state_vector_source, ""),
      Variant = str_trunc(coalesce(variant_label, ""), 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr_within_hypothesis)
    ),
  caption = "Table 21. H6 static diagnosticity: best predictor within each metric family."
)

Table 21. H6 static diagnosticity: best predictor within each metric family.

Hypothesis	Family	Metric	Representation	Variant	n	Spearman rho	p	q
H6_diagnosticity_choice_full	Classical vector baseline	Angular distance, reversed	contour_centroid	classical	66	.28	.024	.775
H6_diagnosticity_choice_full	Operator/density geometry	frobenius distance	rho_fit_global_density	gmm_bic | g=profile_likelihood | l=profile_like...	66	.40	< .001	.235
H6_diagnosticity_choice_full	Sequential QSM	QSM p(B|A)	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	66	.16	.187	.932
H6_diagnosticity_choice_full	Subspace/projector geometry	containment a to b	S_lowdin	bayesian_gmm | g=profile_likelihood | l=profile...	66	.22	.072	.932
H6_diagnosticity_rating	Classical vector baseline	Angular distance, reversed	contour_centroid	classical	44	.24	.119	.495
H6_diagnosticity_rating	Operator/density geometry	Containment asymmetry	rho_freq_density	gmm_bic | g=gavish_donoho | l=gavish_donoho	44	−.69	< .001	< .001
H6_diagnosticity_rating	Sequential QSM	QSM p(B|A)	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	44	.50	< .001	.036
H6_diagnosticity_rating	Subspace/projector geometry	max angle deg	S_lowdin	bayesian_gmm | g=permutation_pa | l=permutation_pa	44	.56	< .001	.013

h6_static_plot <- h6_static_family_best %>%
  mutate(
    label = paste0(str_replace(hypothesis, "H6_diagnosticity_", ""), "\n", metric_family),
    label = fct_reorder(label, abs_estimate)
  ) %>%
  ggplot(aes(x = label, y = estimate)) +
  geom_hline(yintercept = 0, linewidth = .35) +
  geom_col(width = .72) +
  coord_flip() +
  scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
  labs(
    title = "H6 static diagnosticity: best metric by family",
    subtitle = "Static pairwise metrics ignore explicit context, so this is a strict baseline.",
    x = NULL,
    y = "Spearman rho"
  ) +
  theme_apa7()

h6_static_plot

save_plot(h6_static_plot, "h6_static_best_by_family_v7.png", width = 8.5, height = 5.5)

14.3 H6b: contextualized similarity

Contextualized similarity evaluates concepts after they have been represented with respect to the contextual subspace. In vector form, this means comparing projected centroid states inside the context basis. In density form, it means filtering each conceptual density through the context projector and renormalizing. The density route is closer to a Lüders-style update, while the vector route is closer to contextual coordinates.

h6_context_top <- h6_context_rank %>%
  group_by(hypothesis) %>%
  slice_max(order_by = abs_estimate, n = params$top_n_metrics, with_ties = FALSE) %>%
  ungroup()

h6_context_family_best <- h6_context_rank %>%
  group_by(hypothesis, metric_family) %>%
  slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
  ungroup()

apa_table(
  h6_context_family_best %>%
    transmute(
      Hypothesis = hypothesis,
      Family = metric_family,
      Metric = metric_short,
      Object = coalesce(basis_object, density_object, state_vector_source, ""),
      Variant = str_trunc(coalesce(variant_label, ""), 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr_within_hypothesis)
    ),
  caption = "Table 22. H6 contextualized similarity: best predictor within each contextual family."
)

Table 22. H6 contextualized similarity: best predictor within each contextual family.

Hypothesis	Family	Metric	Object	Variant	n	Spearman rho	p	q
H6_diagnosticity_choice_full	Contextualized vector	Contextualized vector cosine	S_global	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	212	.29	< .001	< .001
H6_diagnosticity_choice_full	Lüders contextualized density	Contextual density HS inner	S_global	bayesian_gmm | g=profile_likelihood | l=profile...	212	.36	< .001	< .001

h6_context_plot <- h6_context_family_best %>%
  mutate(
    label = paste0(str_replace(hypothesis, "H6_diagnosticity_", ""), "\n", metric_family),
    label = fct_reorder(label, abs_estimate)
  ) %>%
  ggplot(aes(x = label, y = estimate)) +
  geom_hline(yintercept = 0, linewidth = .35) +
  geom_col(width = .72) +
  coord_flip() +
  scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
  labs(
    title = "H6 contextualized metrics",
    subtitle = "Vector contextualization and Lüders density contextualization are shown separately.",
    x = NULL,
    y = "Spearman rho"
  ) +
  theme_apa7()

h6_context_plot

save_plot(h6_context_plot, "h6_contextualized_best_by_family_v7.png", width = 8.5, height = 5)

14.4 H6c: perplexity-inhibited similarity

Perplexity-inhibited similarity implements the idea that the most plausible competing pair may share properties that become unhelpful or confusing for the target judgment. The model estimates a soft intersection for that pair and removes this shared structure from the initial concept before comparing it with each target. A strong negative result is not automatically a failure: it may indicate that the residual representation captures competition but maps onto the opposite behavioral choice rule.

h6_perplexity_top <- h6_perplexity_rank %>%
  group_by(hypothesis) %>%
  slice_max(order_by = abs_estimate, n = params$top_n_metrics, with_ties = FALSE) %>%
  ungroup()

h6_perplexity_family_best <- h6_perplexity_rank %>%
  group_by(hypothesis, metric_family) %>%
  slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
  ungroup()

apa_table(
  h6_perplexity_family_best %>%
    transmute(
      Hypothesis = hypothesis,
      Family = metric_family,
      Metric = metric_short,
      Object = coalesce(basis_object, density_object, ""),
      Variant = str_trunc(coalesce(variant_label, ""), 50),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr_within_hypothesis)
    ),
  caption = "Table 23. H6 perplexity-inhibited similarity predictors."
)

Table 23. H6 perplexity-inhibited similarity predictors.

Hypothesis	Family	Metric	Object	Variant	n	Spearman rho	p	q
H6_diagnosticity_choice_full	Perplexity-inhibited diagnostic	perplexity residual projector to target containment	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	212	−.26	< .001	.007

h6_perplexity_plot <- h6_perplexity_top %>%
  mutate(label = fct_reorder(str_wrap(metric_short, 32), abs_estimate)) %>%
  ggplot(aes(x = label, y = estimate)) +
  geom_hline(yintercept = 0, linewidth = .35) +
  geom_col(width = .72) +
  coord_flip() +
  facet_wrap(~ str_replace(hypothesis, "H6_diagnosticity_", ""), scales = "free_y") +
  scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .5)) +
  labs(
    title = "H6 perplexity-inhibited metrics",
    subtitle = "Negative signs can be meaningful: inhibition may reverse target preference depending on the chosen residual representation.",
    x = NULL,
    y = "Spearman rho"
  ) +
  theme_apa7()

h6_perplexity_plot

save_plot(h6_perplexity_plot, "h6_perplexity_top_correlations_v7.png", width = 9, height = 5.5)

14.5 H6d: diagnostic choice prediction accuracy

The accuracy analysis turns metric differences into pairwise choices. This is stricter than a correlation with graded human proportions. A model can track the continuous preference gradient yet fail to classify the winner for individual diagnostic pairs, especially when human choices are noisy or close to chance.

h6_choice_top <- h6_choice_accuracy %>%
  group_by(hypothesis, diagnostic_choice_set, metric_family_label) %>%
  slice_max(order_by = accuracy, n = 1, with_ties = FALSE) %>%
  ungroup() %>%
  arrange(hypothesis, diagnostic_choice_set, desc(accuracy))

apa_table(
  h6_choice_top %>%
    transmute(
      Hypothesis = hypothesis,
      `Choice set` = diagnostic_choice_set,
      Family = metric_family_label,
      Metric = metric_short_label(metric),
      Variant = str_trunc(variant_short(variant), 50),
      n,
      Accuracy = apa_num(accuracy, 2),
      `Mean |preference|` = apa_num(mean_abs_preference, 3)
    ),
  caption = "Table 24. H6 diagnostic pairwise choice prediction accuracy."
)

Table 24. H6 diagnostic pairwise choice prediction accuracy.

Hypothesis	Choice set	Family	Metric	Variant	n	Accuracy	Mean |preference|
H6_diagnosticity_choice_full	choice_candidates_only	Lüders contextualized density	Bures distance, reversed	bayesian_gmm | g=horn_wishart | l=horn_wishart	22	0.64	0.109
H6_diagnosticity_choice_full	choice_candidates_only	perplexity_inhibited_similarity	perplexity residual density to target containment	bayesian_gmm | g=permutation_pa | l=permutation_pa	22	0.59	0.198
H6_diagnosticity_choice_full	choice_candidates_only	Contextualized vector	Contextualized vector cosine	bayesian_gmm | g=profile_likelihood | l=profile...	22	0.55	0.039
H6_diagnosticity_choice_full	choice_full_with_context	Lüders contextualized density	Bures distance, reversed	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.64	0.094
H6_diagnosticity_choice_full	choice_full_with_context	perplexity_inhibited_similarity	Bures distance, reversed	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	66	0.62	0.112
H6_diagnosticity_choice_full	choice_full_with_context	Contextualized vector	Contextualized vector cosine	bayesian_gmm | g=profile_likelihood | l=profile...	66	0.56	0.031
H6_diagnosticity_choice_full	unknown	Lüders contextualized density	Bures distance, reversed	bayesian_gmm | g=horn_wishart | l=horn_wishart	76	0.62	0.112
H6_diagnosticity_choice_full	unknown	Contextualized vector	Contextualized vector cosine	bayesian_gmm | g=profile_likelihood | l=profile...	76	0.61	0.037
H6_diagnosticity_choice_full	unknown	perplexity_inhibited_similarity	perplexity residual density to target containment	bayesian_gmm | g=permutation_pa | l=permutation_pa	76	0.53	0.185

h6_choice_plot <- h6_choice_top %>%
  mutate(label = fct_reorder(paste0(diagnostic_choice_set, "\n", metric_family_label), accuracy)) %>%
  ggplot(aes(x = label, y = accuracy)) +
  geom_hline(yintercept = .50, linetype = "dashed", linewidth = .35) +
  geom_col(width = .72) +
  coord_flip() +
  scale_y_continuous(limits = c(0, 1), breaks = seq(0, 1, .10), labels = percent_format(accuracy = 1)) +
  labs(
    title = "H6 diagnostic choice prediction accuracy",
    subtitle = "Dashed line marks chance-level pairwise accuracy.",
    x = NULL,
    y = "Accuracy"
  ) +
  theme_apa7()

h6_choice_plot

save_plot(h6_choice_plot, "h6_diagnostic_choice_prediction_accuracy_v7.png", width = 8.5, height = 5)

h6_static_best <- h6_static_rank %>% group_by(hypothesis) %>% slice_head(n = 1) %>% ungroup()
h6_context_best <- h6_context_rank %>% group_by(hypothesis) %>% slice_head(n = 1) %>% ungroup()
h6_perp_best <- h6_perplexity_rank %>% group_by(hypothesis) %>% slice_head(n = 1) %>% ungroup()
cat(
  "**Interpretation.** Diagnosticity is the least reducible block. Static metrics provide a useful baseline, especially for ratings, but explicit context mechanisms are needed to evaluate the thesis-level account. ",
  "Contextualized density metrics usually test whether the context acts as a projection/filter. Perplexity metrics test whether removing shared properties of a plausible competing pair changes target similarity. If perplexity shows strong but negative correlations, this should not be hidden under the rug like a bad residual; it may indicate that the residual-state definition is capturing competition but with reversed decision mapping.\n"
)

Interpretation. Diagnosticity is the least reducible block. Static metrics provide a useful baseline, especially for ratings, but explicit context mechanisms are needed to evaluate the thesis-level account. Contextualized density metrics usually test whether the context acts as a projection/filter. Perplexity metrics test whether removing shared properties of a plausible competing pair changes target similarity. If perplexity shows strong but negative correlations, this should not be hidden under the rug like a bad residual; it may indicate that the residual-state definition is capturing competition but with reversed decision mapping.

14.6 H6e: diagnostic context as a priming-like condition

The thesis does not include a separate priming experiment among the Phase 2 instruments. The experimental structure closest to priming is the diagnosticity task: a context or distractor is inserted into the comparison set, and that context should change which features become diagnostic. In that sense, diagnosticity is a controlled contextual manipulation rather than a generic pairwise similarity judgment.

This section therefore asks a more specific question: does the relation between the context/distractor and each candidate target predict the human diagnostic response? If so, the context is acting like a prime: it changes the accessibility or diagnostic value of features before the participant evaluates the initial-target relation.

Two quantities are tested:

1. Context-target similarity. Is the candidate more likely to be chosen/rated highly when it is more similar to the context?
2. Context-minus-initial similarity. Is the candidate favored when it is more aligned with the context than with the initial concept, or vice versa?

The second contrast is especially useful because diagnosticity is not just ordinary relatedness. It is about how a contextual item changes the comparison space.

diagnostic_design_overview <- diagnostic_design

diagnostic_design_overview$design_type_safe <- if ("design_type" %in% names(diagnostic_design_overview)) as.character(diagnostic_design_overview$design_type) else NA_character_
diagnostic_design_overview$response_type_safe <- if ("response_type" %in% names(diagnostic_design_overview)) as.character(diagnostic_design_overview$response_type) else NA_character_
diagnostic_design_overview$condition_safe <- if ("condition" %in% names(diagnostic_design_overview)) as.character(diagnostic_design_overview$condition) else NA_character_
diagnostic_design_overview$context_safe <- if ("context" %in% names(diagnostic_design_overview)) as.character(diagnostic_design_overview$context) else NA_character_
diagnostic_design_overview$initial_safe <- if ("initial" %in% names(diagnostic_design_overview)) as.character(diagnostic_design_overview$initial) else NA_character_
diagnostic_design_overview$target_safe <- if ("target" %in% names(diagnostic_design_overview)) as.character(diagnostic_design_overview$target) else NA_character_

diagnostic_condition_overview <- diagnostic_design_overview %>%
  mutate(
    diagnostic_condition_family = case_when(
      str_detect(coalesce(design_type_safe, response_type_safe, condition_safe, ""), "choice_full|full_with_context") ~ "choice with context option",
      str_detect(coalesce(design_type_safe, response_type_safe, condition_safe, ""), "choice_candidates") ~ "choice candidates only",
      str_detect(coalesce(design_type_safe, response_type_safe, condition_safe, ""), "rating_candidates_plus_context") ~ "rating candidates plus context",
      str_detect(coalesce(design_type_safe, response_type_safe, condition_safe, ""), "rating_candidates") ~ "rating candidates only",
      TRUE ~ "diagnostic row"
    )
  ) %>%
  group_by(diagnostic_condition_family, context_safe) %>%
  summarise(
    n_rows = n(),
    n_initials = n_distinct(initial_safe, na.rm = TRUE),
    n_targets = n_distinct(target_safe, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(diagnostic_condition_family, context_safe)

apa_table(
  diagnostic_condition_overview %>%
    transmute(
      `Diagnostic condition` = diagnostic_condition_family,
      Context = context_safe,
      `n rows` = n_rows,
      `n initials` = n_initials,
      `n targets` = n_targets
    ),
  caption = "Table H6e-1. Diagnostic context/condition overview."
)

Table H6e-1. Diagnostic context/condition overview.

Diagnostic condition	Context	n rows	n initials	n targets
diagnostic row	alemania	10	1	3
diagnostic row	belgica	10	1	4
diagnostic row	bulgaria	10	1	3
diagnostic row	chile	10	1	4
diagnostic row	costa_rica	10	1	3
diagnostic row	cuba	10	1	3
diagnostic row	egipto	10	1	3
diagnostic row	espana	20	2	5
diagnostic row	francia	10	1	3
diagnostic row	honduras	10	1	3
diagnostic row	irak	10	1	3
diagnostic row	irlanda	10	1	3
diagnostic row	italia	10	1	3
diagnostic row	japon	10	1	3
diagnostic row	mongolia	10	1	3
diagnostic row	noruega	10	1	3
diagnostic row	nueva_zelanda	10	1	4
diagnostic row	paises_bajos	10	1	3
diagnostic row	polonia	10	1	3
diagnostic row	portugal	10	1	3
diagnostic row	rusia	10	1	3

write_table(diagnostic_condition_overview, "h6e_diagnostic_condition_overview.csv")

h6_pair_metric_lookup <- pairwise_metric_values %>%
  filter(!is_asymmetry_metric(metric_name)) %>%
  mutate(metric_value = similarity_orient_value(metric_name, value)) %>%
  distinct(metric_id, pair_id, .keep_all = TRUE) %>%
  select(any_of(c(
    "metric_id", "metric_source", "metric_family", "metric_name", "metric_short", "variant", "variant_label",
    "cluster_method", "global_k_method", "local_k_method", "basis_object", "object", "state_vector_source", "state_type",
    "pair_id", "metric_value"
  )))

h6_prime_option_rows <- diag_human_rows %>%
  mutate(
    context_target_pair_id = canonical_pair(context, target),
    initial_target_pair_id = canonical_pair(initial, target)
  )

h6_context_target_lookup <- h6_pair_metric_lookup %>%
  rename(context_target_pair_id = pair_id, context_target_metric = metric_value)

h6_initial_target_lookup <- h6_pair_metric_lookup %>%
  select(metric_id, pair_id, metric_value) %>%
  rename(initial_target_pair_id = pair_id, initial_target_metric = metric_value)

h6_prime_like_long <- h6_prime_option_rows %>%
  inner_join(h6_context_target_lookup, by = "context_target_pair_id") %>%
  inner_join(h6_initial_target_lookup, by = c("metric_id", "initial_target_pair_id")) %>%
  mutate(
    context_minus_initial_similarity = context_target_metric - initial_target_metric,
    abs_context_minus_initial_similarity = abs(context_minus_initial_similarity)
  )

h6_prime_context_target_rank <- cor_by_group(
  h6_prime_like_long,
  group_cols = c("hypothesis", rank_group_cols),
  x = "context_target_metric",
  y = "human_value"
) %>%
  mutate(priming_predictor = "context_target_similarity")

h6_prime_relative_rank <- cor_by_group(
  h6_prime_like_long,
  group_cols = c("hypothesis", rank_group_cols),
  x = "context_minus_initial_similarity",
  y = "human_value"
) %>%
  mutate(priming_predictor = "context_minus_initial_similarity")

h6_prime_abs_relative_rank <- cor_by_group(
  h6_prime_like_long,
  group_cols = c("hypothesis", rank_group_cols),
  x = "abs_context_minus_initial_similarity",
  y = "human_value"
) %>%
  mutate(priming_predictor = "absolute_context_initial_difference")

h6_prime_like_rank <- bind_rows(
  h6_prime_context_target_rank,
  h6_prime_relative_rank,
  h6_prime_abs_relative_rank
) %>%
  group_by(hypothesis, priming_predictor) %>%
  mutate(p_fdr_within_predictor = p.adjust(p.value, method = "BH")) %>%
  ungroup() %>%
  arrange(hypothesis, priming_predictor, desc(abs_estimate))

h6_prime_like_best <- h6_prime_like_rank %>%
  filter(!is.na(estimate)) %>%
  group_by(hypothesis, priming_predictor) %>%
  slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
  ungroup()

apa_table(
  h6_prime_like_best %>%
    transmute(
      Hypothesis = hypothesis,
      `Priming-like predictor` = priming_predictor,
      Metric = metric_short,
      Family = metric_family,
      Object = coalesce(basis_object, object, state_type, ""),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(p_fdr_within_predictor)
    ),
  caption = "Table H6e-2. Best context/prime-like predictors of diagnostic responses."
)

Table H6e-2. Best context/prime-like predictors of diagnostic responses.

Hypothesis	Priming-like predictor	Metric	Family	Object	n	Spearman rho	p	q
H6_diagnosticity_choice_full	absolute_context_initial_difference	a in b trace normalized	Operator/density geometry	rho_global_density	5	1.00	< .001	< .001
H6_diagnosticity_choice_full	context_minus_initial_similarity	containment a to b	Subspace/projector geometry	S_lowdin	5	1.00	< .001	< .001
H6_diagnosticity_choice_full	context_target_similarity	trace inner	Operator/density geometry	projector_mixture_freq	5	1.00	< .001	< .001
H6_diagnosticity_rating	absolute_context_initial_difference	b in a trace normalized	Operator/density geometry	P_concat_direct	44	−.41	.006	.809
H6_diagnosticity_rating	context_minus_initial_similarity	containment a to b	Subspace/projector geometry	S_lowdin	44	.40	.007	.853
H6_diagnosticity_rating	context_target_similarity	containment a to b	Subspace/projector geometry	S_lowdin	44	.56	< .001	.008

write_table(h6_prime_like_rank, "h6e_prime_like_context_target_rankings.csv")
write_table(h6_prime_like_best, "h6e_prime_like_best_by_predictor.csv")

if (nrow(h6_prime_like_best) > 0) {
  h6e_plot <- h6_prime_like_best %>%
    mutate(
      label = paste0(str_replace(hypothesis, "H6_diagnosticity_", ""), "\n", priming_predictor),
      label = fct_reorder(label, abs_estimate)
    ) %>%
    ggplot(aes(x = label, y = estimate, fill = metric_family)) +
    geom_hline(yintercept = 0, linewidth = .35) +
    geom_col(width = .70) +
    coord_flip() +
    scale_y_continuous(limits = c(-1, 1), breaks = seq(-1, 1, .25)) +
    labs(
      title = "Diagnostic context as a priming-like predictor",
      subtitle = "Best metric for each diagnostic outcome and context/initial contrast.",
      x = NULL,
      y = "Best Spearman rho"
    ) +
    theme_apa7()

  h6e_plot
  save_plot(h6e_plot, "h6e_diagnostic_context_as_prime_v10.png", width = 8.5, height = 6)
}

h6e_best_context <- h6_prime_like_best %>%
  filter(priming_predictor == "context_target_similarity") %>%
  arrange(desc(abs_estimate)) %>%
  slice_head(n = 1)

h6e_best_relative <- h6_prime_like_best %>%
  filter(priming_predictor == "context_minus_initial_similarity") %>%
  arrange(desc(abs_estimate)) %>%
  slice_head(n = 1)

context_sentence <- if (nrow(h6e_best_context) > 0) {
  paste0(
    "The strongest pure context-target predictor is ", h6e_best_context$metric_short[[1]], " from ",
    h6e_best_context$metric_family[[1]], " (rho = ", apa_r(h6e_best_context$estimate[[1]]), "). "
  )
} else {
  "No context-target predictor was estimable from the available pairwise metric table. "
}

relative_sentence <- if (nrow(h6e_best_relative) > 0) {
  paste0(
    "The strongest context-minus-initial predictor is ", h6e_best_relative$metric_short[[1]], " from ",
    h6e_best_relative$metric_family[[1]], " (rho = ", apa_r(h6e_best_relative$estimate[[1]]), "). "
  )
} else {
  "No context-minus-initial predictor was estimable from the available pairwise metric table. "
}

cat(
  "**Interpretation.** No separate priming task is present in the experimental instrument set, but the diagnostic context plays a priming-like role: it is the element that should shift which features are active or diagnostic in the comparison. ",
  context_sentence,
  relative_sentence,
  "If context-target similarity is predictive, the context behaves like an attractor or prime. If the context-minus-initial contrast is stronger, the effect is more specifically diagnostic: the context changes the relative usefulness of target features rather than merely increasing relatedness in general.\n"
)

Interpretation. No separate priming task is present in the experimental instrument set, but the diagnostic context plays a priming-like role: it is the element that should shift which features are active or diagnostic in the comparison. The strongest pure context-target predictor is trace inner from Operator/density geometry (rho = 1.00). The strongest context-minus-initial predictor is containment a to b from Subspace/projector geometry (rho = 1.00). If context-target similarity is predictive, the context behaves like an attractor or prime. If the context-minus-initial contrast is stronger, the effect is more specifically diagnostic: the context changes the relative usefulness of target features rather than merely increasing relatedness in general.

15 Representation alignment and variant sensitivity

This section is the methodological conscience of the notebook. The pipeline contains arbitrary decisions: clustering model, dimensionality rule, global versus local representation, projector versus density normalization. Alignment and sensitivity analyses ask whether the conclusions depend on those decisions. A result is more persuasive when the relevant family remains stable across variants, or when the best-performing variant has a clear theoretical reason for performing well.

These analyses are not direct hypothesis tests. They assess whether the representation choices are stable. If a metric works only because one arbitrary variant had a good day, that is less convincing than a metric family that remains competitive across clustering and dimensionality decisions.

apa_table(
  alignment_summary %>%
    transmute(
      `Object A` = object_a,
      `Object B` = object_b,
      n,
      `Mean HS cosine` = apa_num(mean_hs_cosine, 3),
      `SD HS cosine` = apa_num(sd_hs_cosine, 3),
      `Mean trace overlap` = apa_num(mean_trace_overlap, 3)
    ),
  caption = "Table 25. Representation alignment across objects within variants."
)

Table 25. Representation alignment across objects within variants.

Object A	Object B	n	Mean HS cosine	SD HS cosine	Mean trace overlap
rho_freq_density	rho_fit_global_density	952	0.992	0.019	0.020
projector_mixture_freq	projector_mixture_fit_global	952	0.988	0.021	0.745
rho_global_density	rho_fit_global_density	952	0.879	0.126	0.017
rho_global_density	rho_freq_density	952	0.873	0.130	0.017
P_global	projector_mixture_freq	952	0.870	0.133	0.750
P_global	projector_mixture_fit_global	952	0.869	0.136	0.763
P_global	P_concat_direct	952	0.755	0.244	0.755
P_global	P_lowdin	952	0.755	0.244	0.755

apa_table(
  variant_sensitivity_summary %>%
    transmute(
      Object = object,
      `Comparison type` = comparison_type,
      n,
      `Mean HS cosine` = apa_num(mean_hs_cosine, 3),
      `SD HS cosine` = apa_num(sd_hs_cosine, 3),
      `Mean Frobenius distance` = apa_num(mean_frobenius_distance, 3)
    ),
  caption = "Table 26. Variant sensitivity by representation object."
)

Table 26. Variant sensitivity by representation object.

Object	Comparison type	n	Mean HS cosine	SD HS cosine	Mean Frobenius distance
P_concat_direct	Both clustering and dimensionality	1428	0.519	0.141	12.332
P_concat_direct	Clustering only	476	0.589	0.182	11.186
P_concat_direct	Dimensionality only	1428	0.784	0.201	5.393
P_global	Both clustering and dimensionality	1440	0.755	0.176	5.254
P_global	Clustering only	480	1.000	0.000	0.000
P_global	Dimensionality only	1440	0.755	0.176	5.254
P_lowdin	Both clustering and dimensionality	1428	0.519	0.141	12.332
P_lowdin	Clustering only	476	0.589	0.182	11.186
P_lowdin	Dimensionality only	1428	0.784	0.201	5.393
projector_mixture_fit_global	Both clustering and dimensionality	1428	0.685	0.135	6.036
projector_mixture_fit_global	Clustering only	476	0.795	0.098	4.602
projector_mixture_fit_global	Dimensionality only	1428	0.753	0.174	4.646
projector_mixture_freq	Both clustering and dimensionality	1428	0.690	0.134	6.268
projector_mixture_freq	Clustering only	476	0.799	0.090	4.816
projector_mixture_freq	Dimensionality only	1428	0.760	0.174	4.810
rho_fit_global_density	Both clustering and dimensionality	1428	0.706	0.129	0.112
rho_fit_global_density	Clustering only	476	0.814	0.084	0.081
rho_fit_global_density	Dimensionality only	1428	0.766	0.169	0.094
rho_freq_density	Both clustering and dimensionality	1428	0.696	0.133	0.115
rho_freq_density	Clustering only	476	0.803	0.090	0.084
rho_freq_density	Dimensionality only	1428	0.761	0.172	0.096
rho_global_density	Both clustering and dimensionality	1440	0.755	0.176	0.105
rho_global_density	Clustering only	480	1.000	0.000	0.000
rho_global_density	Dimensionality only	1440	0.755	0.176	0.105

alignment_plot <- alignment_summary %>%
  mutate(pair = fct_reorder(paste(object_a, object_b, sep = " vs "), mean_hs_cosine)) %>%
  ggplot(aes(x = pair, y = mean_hs_cosine)) +
  geom_col(width = .72) +
  coord_flip() +
  scale_y_continuous(limits = c(0, 1), breaks = seq(0, 1, .1)) +
  labs(
    title = "Representation alignment",
    subtitle = "Higher Hilbert-Schmidt cosine means two representations encode similar structure.",
    x = NULL,
    y = "Mean HS cosine"
  ) +
  theme_apa7()

alignment_plot

save_plot(alignment_plot, "representation_alignment_summary_v7.png", width = 8.5, height = 5.5)

variant_plot <- variant_sensitivity_summary %>%
  filter(comparison_type != "No detected change") %>%
  mutate(object = fct_reorder(object, mean_hs_cosine)) %>%
  ggplot(aes(x = object, y = mean_hs_cosine, fill = comparison_type)) +
  geom_col(position = position_dodge(width = .72), width = .62) +
  coord_flip() +
  scale_y_continuous(limits = c(0, 1), breaks = seq(0, 1, .1)) +
  scale_fill_manual(values = report_palette) +
  labs(
    title = "Variant sensitivity",
    subtitle = "Lower values indicate stronger dependence on clustering or dimensionality choices.",
    x = NULL,
    y = "Mean HS cosine"
  ) +
  theme_apa7()

variant_plot

save_plot(variant_plot, "variant_sensitivity_summary_v7.png", width = 8.5, height = 5.5)

16 Cross-hypothesis comparison

The cross-hypothesis map should not be read as a winner-takes-all table. It is a diagnostic map of which formal family is useful for which psychological operation. A good theory need not use the same metric everywhere. In fact, the interesting pattern is that different tasks appear to recruit different levels of representation: centroid vectors for explicit similarity, containment for asymmetry and salience, Bures/fidelity-like geometry for triplets, and contextualized or residual-state mechanisms for diagnosticity.

family_heatmap_data <- bind_rows(
  h1_rank_all %>% mutate(analysis_block = "H1 asymmetry"),
  h2_rank_all %>% mutate(analysis_block = "H2 salience"),
  h3_rating_rank %>% mutate(analysis_block = "H3 similarity"),
  h3_order_rank %>% mutate(analysis_block = "H3 order"),
  h6_static_rank %>% mutate(analysis_block = str_replace(hypothesis, "H6_diagnosticity_", "H6 static "))
) %>%
  mutate(metric_family = metric_family_from_source(metric_source)) %>%
  group_by(analysis_block, metric_family) %>%
  slice_max(order_by = abs_estimate, n = 1, with_ties = FALSE) %>%
  ungroup()

family_heatmap <- family_heatmap_data %>%
  ggplot(aes(x = metric_family, y = analysis_block, fill = estimate)) +
  geom_tile(color = "white", linewidth = .5) +
  geom_text(aes(label = apa_r(estimate)), size = 3, family = "serif") +
  scale_fill_gradient2(low = "#2166AC", mid = "white", high = "#B2182B", midpoint = 0, limits = c(-1, 1)) +
  labs(
    title = "Best association by metric family and analysis block",
    subtitle = "Cells show the best Spearman rho within each family. This is a map, not a multiple-comparison victory parade.",
    x = NULL,
    y = NULL,
    fill = "rho"
  ) +
  theme_apa7() +
  theme(axis.text.x = element_text(angle = 35, hjust = 1))

family_heatmap

save_plot(family_heatmap, "cross_hypothesis_metric_family_heatmap_v7.png", width = 9.5, height = 5.8)

apa_table(
  best_predictor_by_block %>%
    transmute(
      `Analysis block` = display_block,
      Family = metric_family,
      Metric = display_metric,
      Representation = coalesce(basis_object, object, density_object, state_type, state_vector_source, ""),
      Variant = str_trunc(coalesce(variant_label, variant_short(variant), ""), 55),
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      q = apa_p(coalesce(p_fdr_within_hypothesis, p_fdr))
    ),
  caption = "Table 27. Cross-hypothesis best predictors."
)

Table 27. Cross-hypothesis best predictors.

Analysis block	Family	Metric	Representation	Variant	n	Spearman rho	p	q
H1 ipsative asymmetry	Subspace/projector geometry	Containment asymmetry	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	30	.90	< .001	< .001
H2 salience	Subspace/projector geometry	Containment asymmetry	S_lowdin	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	30	−.90	< .001	< .001
H2b Likert salience	Corpus frequency baseline	log10 n occurrences	concept-level representation		44	.89	< .001	< .001
H3 Likert similarity	Classical vector baseline	Angular distance, reversed	contour_centroid	classical	89	.51	< .001	< .001
H3 order asymmetry	Operator/density geometry	Containment asymmetry	P_concat_direct	bayesian_gmm | g=gavish_donoho | l=gavish_donoho	89	.32	.002	.029
H4 additive triangle	Triplet distance geometry	Bures distance, reversed	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	66	.49	< .001	< .001
H4 multiplicative triangle	Triplet similarity geometry	Density fidelity	S_global	bayesian_gmm | g=profile_likelihood | l=profile_like...	66	.55	< .001	< .001
H6 static H6_diagnosticity_choice_full	Operator/density geometry	frobenius distance	rho_fit_global_density	gmm_bic | g=profile_likelihood | l=profile_likelihood	66	.40	< .001	.235
H6 static H6_diagnosticity_rating	Operator/density geometry	Containment asymmetry	rho_freq_density	gmm_bic | g=gavish_donoho | l=gavish_donoho	44	−.69	< .001	< .001
H6 contextualized H6_diagnosticity_choice_full	Lüders contextualized density	Contextual density HS inner	S_global	bayesian_gmm | g=profile_likelihood | l=profile_like...	212	.36	< .001	< .001
H6 perplexity H6_diagnosticity_choice_full	Perplexity-inhibited diagnostic	perplexity residual projector to target containment	S_global	bayesian_gmm | g=horn_wishart | l=horn_wishart	212	−.26	< .001	.007

17 Data-first check: observed conditions and response times

The previous sections use the thesis and the human-aligned Phase 4 designs as the main organizational frame. That is appropriate for the paper logic, but it is not enough for the exploratory analyses. Some variables were collected but not fully developed in the thesis document, especially response times and the explicit contextuality/priming markers (mediator, pseudoword, and congruent_priming). For those variables, the empirical data files are the authoritative source. Methodology, for once, does not have to pretend the appendix remembered everything.

This section therefore performs a data-driven audit of the observed experimental structure. It asks: (a) which extra conditions were actually collected, (b) which tasks have usable response times, and (c) whether those conditions should moderate the main semantic contrasts.

# A slightly more readable plotting theme for the data-driven extension.
# The previous report keeps APA-like tables; these figures prioritize clarity.
theme_report <- function(base_size = 12) {
  ggplot2::theme_minimal(base_size = base_size) +
    theme(
      panel.grid.minor = element_blank(),
      panel.grid.major.y = element_blank(),
      plot.title = element_text(face = "bold", size = base_size + 2, margin = margin(b = 5)),
      plot.subtitle = element_text(size = base_size, margin = margin(b = 8)),
      axis.title = element_text(size = base_size),
      axis.text = element_text(size = base_size - 1),
      legend.position = "bottom",
      legend.title = element_blank(),
      strip.text = element_text(face = "bold"),
      plot.margin = margin(8, 16, 8, 8)
    )
}

phase2_tables_dir <- if (dir.exists(file.path(phase2_dir, "tables"))) file.path(phase2_dir, "tables") else phase2_dir

phase2_observed_files <- list(
  responses_all = file.path(phase2_tables_dir, "responses_all_long.csv"),
  contextuality_aggregate = file.path(phase2_tables_dir, "responses_contextuality_aggregate_main.csv"),
  contextuality_raw = file.path(phase2_tables_dir, "responses_contextuality_raw_long.csv"),
  rt_summary = file.path(phase2_tables_dir, "rt_summary_phase2.csv"),
  items_catalog = file.path(phase2_tables_dir, "items_catalog_phase2.csv"),
  data_dictionary = file.path(phase2_tables_dir, "data_dictionary_phase2.csv")
)

responses_all_observed <- read_csv_fast(phase2_observed_files$responses_all, required = FALSE)
rt_summary_observed <- read_csv_fast(phase2_observed_files$rt_summary, required = FALSE)
items_catalog_observed <- read_csv_fast(phase2_observed_files$items_catalog, required = FALSE)
data_dictionary_observed <- read_csv_fast(phase2_observed_files$data_dictionary, required = FALSE)

if (nrow(responses_all_observed) > 0) {
  responses_all_observed <- responses_all_observed %>%
    mutate(
      rt_ms = as.numeric(rt_ms),
      log_rt = as.numeric(log_rt),
      rating = as.numeric(rating),
      mediator = as.numeric(mediator),
      pseudoword = as.numeric(pseudoword),
      congruent_priming = as.numeric(congruent_priming),
      rt_clean = !is.na(rt_ms) & rt_ms >= 300 & rt_ms <= 30000,
      response_binary_d = case_when(
        as.character(response_coded) == "d" ~ 1,
        as.character(response_coded) == "a" ~ 0,
        TRUE ~ NA_real_
      ),
      selected_first = case_when(
        as.character(response_coded) == "a" ~ 1,
        as.character(response_coded) == "d" ~ 0,
        TRUE ~ NA_real_
      )
    )
}

17.1 Observed condition structure

The observed data show that the contextuality task carries three condition variables that are not merely decorative metadata:

• mediator: whether the context is semantically mediated by the target concept.
• pseudoword: whether the context is an invented/novel form rather than a lexicalized term.
• congruent_priming: whether the prime/context is congruent with the expected conceptual activation.

This means that the “priming” issue should not be inferred only from the diagnosticity block. In the actual data, priming-like information is explicitly available in the contextuality task.

observed_condition_audit <- responses_all_observed %>%
  summarise(
    total_rows = n(),
    rows_with_rt = sum(!is.na(rt_ms)),
    rows_with_clean_rt = sum(rt_clean, na.rm = TRUE),
    rows_with_mediator = sum(!is.na(mediator)),
    rows_with_pseudoword = sum(!is.na(pseudoword)),
    rows_with_congruent_priming = sum(!is.na(congruent_priming)),
    contextuality_rows = sum(experiment == "contextuality", na.rm = TRUE),
    diagnosticity_rows = sum(experiment == "diagnosticity", na.rm = TRUE),
    saliency_rows = sum(experiment == "saliency", na.rm = TRUE),
    asymmetry_rows = sum(experiment == "asymmetry", na.rm = TRUE)
  ) %>%
  pivot_longer(everything(), names_to = "quantity", values_to = "value")

apa_table(
  observed_condition_audit,
  caption = "Table 28. Data-driven audit of observed extra variables in the tidy human data."
)

Table 28. Data-driven audit of observed extra variables in the tidy human data.

quantity	value
total_rows	101119
rows_with_rt	77110
rows_with_clean_rt	76694
rows_with_mediator	5180
rows_with_pseudoword	5180
rows_with_congruent_priming	3332
contextuality_rows	5180
diagnosticity_rows	11429
saliency_rows	27380
asymmetry_rows	44550

write_table(observed_condition_audit, "table_28_observed_condition_audit.csv")

contextuality_condition_summary <- responses_all_observed %>%
  filter(experiment == "contextuality") %>%
  mutate(
    mediator = factor(mediator, levels = c(0, 1), labels = c("No mediator", "Mediator")),
    pseudoword = factor(pseudoword, levels = c(0, 1), labels = c("Lexical context", "Pseudoword")),
    congruent_priming = factor(congruent_priming, levels = c(0, 1), labels = c("Incongruent/other", "Congruent prime"))
  ) %>%
  group_by(mediator, pseudoword, congruent_priming) %>%
  summarise(
    n = n(),
    n_clean_rt = sum(rt_clean, na.rm = TRUE),
    prop_d_response = mean(response_binary_d, na.rm = TRUE),
    median_rt = median(rt_ms[rt_clean], na.rm = TRUE),
    mean_log_rt = mean(log_rt[rt_clean], na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(mediator, pseudoword, congruent_priming)

apa_table(
  contextuality_condition_summary %>%
    mutate(
      prop_d_response = apa_num(prop_d_response, 3),
      median_rt = apa_num(median_rt, 1),
      mean_log_rt = apa_num(mean_log_rt, 3)
    ),
  caption = "Table 29. Observed contextuality/priming condition structure and response times."
)

Table 29. Observed contextuality/priming condition structure and response times.

mediator	pseudoword	congruent_priming	n	n_clean_rt	prop_d_response	median_rt	mean_log_rt
No mediator	Lexical context	NA	1278	1278	0.667	1627.2	7.427
No mediator	Pseudoword	NA	570	569	0.546	1693.4	7.480
Mediator	Lexical context	Incongruent/other	1272	1271	0.645	2013.0	7.631
Mediator	Lexical context	Congruent prime	1029	1027	0.661	2063.2	7.639
Mediator	Pseudoword	Incongruent/other	1031	1031	0.558	2066.3	7.657

write_table(contextuality_condition_summary, "table_29_observed_contextuality_condition_summary.csv")

contextuality_condition_plot <- contextuality_condition_summary %>%
  mutate(
    condition_label = paste(mediator, pseudoword, congruent_priming, sep = "\n"),
    condition_label = fct_reorder(condition_label, median_rt)
  ) %>%
  ggplot(aes(x = condition_label, y = median_rt, fill = mediator)) +
  geom_col(width = .72, alpha = .88) +
  geom_text(aes(label = round(median_rt)), hjust = -0.10, size = 3.2) +
  coord_flip() +
  scale_fill_manual(values = c("#6BAED6", "#2171B5")) +
  scale_y_continuous(expand = expansion(mult = c(0, .12))) +
  labs(
    title = "Observed contextuality/priming conditions differ in response time",
    subtitle = "Median clean RT by mediator, pseudoword, and congruent-priming markers.",
    x = NULL,
    y = "Median RT (ms)"
  ) +
  theme_report()

contextuality_condition_plot

save_plot(contextuality_condition_plot, "observed_contextuality_condition_rt_v11.png", width = 9, height = 5.2)

17.2 Response-time availability and task-level interpretation

Response times are available for asymmetry, salience, and contextuality, but not uniformly for all blocks. This matters because RTs offer a different dependent variable: not what people chose, but how hard it was for them to decide. In this framework, RT is not an afterthought. If a concept pair has a clear inclusion relation, high salience contrast, or strong contextual activation, the response should often be faster. Conversely, ambiguous pairs, weak contrasts, or conflicting contexts should produce slower responses.

rt_task_summary_observed <- responses_all_observed %>%
  group_by(experiment, subexperiment, response_type) %>%
  summarise(
    n_rows = n(),
    n_rt = sum(!is.na(rt_ms)),
    n_clean_rt = sum(rt_clean, na.rm = TRUE),
    median_rt = median(rt_ms[rt_clean], na.rm = TRUE),
    mean_rt = mean(rt_ms[rt_clean], na.rm = TRUE),
    sd_rt = sd(rt_ms[rt_clean], na.rm = TRUE),
    pct_rt_lt_300 = mean(rt_ms < 300, na.rm = TRUE),
    pct_rt_gt_30000 = mean(rt_ms > 30000, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  mutate(
    pct_rt_lt_300 = 100 * pct_rt_lt_300,
    pct_rt_gt_30000 = 100 * pct_rt_gt_30000
  )

apa_table(
  rt_task_summary_observed %>%
    mutate(
      median_rt = apa_num(median_rt, 1),
      mean_rt = apa_num(mean_rt, 1),
      sd_rt = apa_num(sd_rt, 1),
      pct_rt_lt_300 = apa_num(pct_rt_lt_300, 2),
      pct_rt_gt_30000 = apa_num(pct_rt_gt_30000, 2)
    ),
  caption = "Table 30. Response-time availability and task-level RT summaries."
)

Table 30. Response-time availability and task-level RT summaries.

experiment	subexperiment	response_type	n_rows	n_rt	n_clean_rt	median_rt	mean_rt	sd_rt	pct_rt_lt_300	pct_rt_gt_30000
asymmetry	asymmetry_1_forced_choice	forced_choice_ad	11250	11250	11239	2930.1	3634.9	2530.2	0.01	0.09
asymmetry	asymmetry_2_a_direct	rating_1_9	17370	17370	17164	3146.8	3686.7	2131.6	1.13	0.06
asymmetry	asymmetry_2_b_reverse	rating_1_9	15930	15930	15740	2977.4	3462.7	1947.8	1.13	0.06
contextuality	contextuality_aggregate_main	binary_a_d_modal_aggregate	5180	5180	5176	1887.7	2397.1	1931.8	0.02	0.06
diagnosticity	diagnosticity_1_choice_cleaned	choice_country_code	4059	0	0
diagnosticity	diagnosticity_2_rating_cleaned	rating_0_6	7370	0	0
gk	gk_test	binary_correct	12580	0	0
saliency	saliency_1_forced_choice	forced_choice_ad	11100	11100	11098	1566.3	1965.2	1390.2	0.00	0.02
saliency	saliency_2_single_rating	rating_1_9	16280	16280	16277	1924.6	2344.9	1614.6	0.01	0.01

write_table(rt_task_summary_observed, "table_30_observed_rt_summary_by_task.csv")

rt_task_plot <- rt_task_summary_observed %>%
  filter(n_clean_rt > 0) %>%
  mutate(
    task_label = str_replace_all(subexperiment, "_", " "),
    task_label = fct_reorder(task_label, median_rt)
  ) %>%
  ggplot(aes(x = task_label, y = median_rt, fill = experiment)) +
  geom_col(width = .70, alpha = .88) +
  geom_text(aes(label = round(median_rt)), hjust = -0.12, size = 3.2) +
  coord_flip() +
  scale_fill_manual(values = c(
    "asymmetry" = "#756BB1",
    "saliency" = "#31A354",
    "contextuality" = "#3182BD",
    "diagnosticity" = "#E6550D",
    "gk" = "#636363"
  )) +
  scale_y_continuous(expand = expansion(mult = c(0, .15))) +
  labs(
    title = "Median response time by task",
    subtitle = "Only clean RTs between 300 ms and 30,000 ms are summarized.",
    x = NULL,
    y = "Median RT (ms)"
  ) +
  theme_report()

rt_task_plot

save_plot(rt_task_plot, "observed_rt_by_task_v11.png", width = 9, height = 5)

17.3 Forced-choice RT as decision clarity

For forced-choice asymmetry and salience, the simplest RT hypothesis is a clarity hypothesis: items with a stronger human preference should be answered faster. This does not require adding a new conceptual mechanism. It follows from the same logic as containment and salience contrast: a strong directional relation should reduce competition between alternatives.

forced_choice_rt_item_summary <- responses_all_observed %>%
  filter(
    subexperiment %in% c("asymmetry_1_forced_choice", "saliency_1_forced_choice"),
    rt_clean,
    !is.na(selected_first)
  ) %>%
  group_by(experiment, subexperiment, item_label_original, stimulus_1_code, stimulus_2_code) %>%
  summarise(
    n = n(),
    prop_choose_first = mean(selected_first, na.rm = TRUE),
    choice_clarity = abs(prop_choose_first - .5),
    median_rt = median(rt_ms, na.rm = TRUE),
    mean_log_rt = mean(log_rt, na.rm = TRUE),
    .groups = "drop"
  )

forced_choice_rt_clarity_tests <- forced_choice_rt_item_summary %>%
  group_by(experiment, subexperiment) %>%
  group_modify(~safe_cor(.x, x = "choice_clarity", y = "median_rt", method = "spearman")) %>%
  ungroup() %>%
  mutate(
    interpretation = case_when(
      estimate < 0 ~ "Clearer forced choices are faster",
      estimate > 0 ~ "Clearer forced choices are slower",
      TRUE ~ "No monotonic RT-clarity trend"
    )
  )

apa_table(
  forced_choice_rt_clarity_tests %>%
    transmute(
      Experiment = experiment,
      Task = subexperiment,
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value),
      Interpretation = interpretation
    ),
  caption = "Table 31. Forced-choice response times as a function of item-level decision clarity."
)

Table 31. Forced-choice response times as a function of item-level decision clarity.

Experiment	Task	n	Spearman rho	p	Interpretation
asymmetry	asymmetry_1_forced_choice	30	−.69	< .001	Clearer forced choices are faster
saliency	saliency_1_forced_choice	30	−.86	< .001	Clearer forced choices are faster

write_table(forced_choice_rt_clarity_tests, "table_31_forced_choice_rt_decision_clarity.csv")

forced_choice_rt_plot <- forced_choice_rt_item_summary %>%
  mutate(task = recode(experiment, asymmetry = "Ipsative asymmetry", saliency = "Ipsative salience")) %>%
  ggplot(aes(x = choice_clarity, y = median_rt)) +
  geom_point(aes(fill = task), shape = 21, size = 2.8, alpha = .78, color = "white") +
  geom_smooth(method = "lm", se = TRUE, linewidth = .8, color = "#252525") +
  facet_wrap(~task, scales = "free_y") +
  scale_fill_manual(values = c("Ipsative asymmetry" = "#756BB1", "Ipsative salience" = "#31A354")) +
  labs(
    title = "Forced-choice RT tracks decision clarity",
    subtitle = "Choice clarity is |P(choose first) − .50| at the item level.",
    x = "Item-level choice clarity",
    y = "Median RT (ms)"
  ) +
  theme_report()

forced_choice_rt_plot

save_plot(forced_choice_rt_plot, "forced_choice_rt_decision_clarity_v11.png", width = 9, height = 4.8)

17.4 Single-concept salience RT and dimensionality

For Likert salience, RT can be interpreted differently. A highly salient concept may be rated quickly because it is familiar and richly represented, but a concept with many semantic dimensions may also require more integration. These two interpretations compete: frequency/familiarity predicts faster RT; semantic richness may predict either faster access or slower deliberation depending on how the rating task is solved.

single_salience_rt_summary <- responses_all_observed %>%
  filter(subexperiment == "saliency_2_single_rating", rt_clean, !is.na(rating)) %>%
  group_by(target = stimulus_1_code) %>%
  summarise(
    n = n(),
    mean_salience_rating = mean(rating, na.rm = TRUE),
    median_salience_rating = median(rating, na.rm = TRUE),
    median_rt = median(rt_ms, na.rm = TRUE),
    mean_log_rt = mean(log_rt, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  filter(
    is.finite(mean_salience_rating),
    is.finite(median_rt)
  )

single_salience_rt_tests <- tibble(
  predictor = c("mean_salience_rating", "median_salience_rating"),
  outcome = "median_rt"
) %>%
  rowwise() %>%
  mutate(test = list(safe_cor(single_salience_rt_summary, x = predictor, y = outcome, method = "spearman"))) %>%
  unnest(test) %>%
  ungroup()

fit_linear_quadratic <- function(data, predictor, outcome = "median_rt") {
  d <- data %>%
    filter(!is.na(.data[[predictor]]), !is.na(.data[[outcome]])) %>%
    filter(is.finite(.data[[predictor]]), is.finite(.data[[outcome]]))

  if (nrow(d) < 5 || n_distinct(d[[predictor]]) < 3) {
    return(list(
      comparison = tibble(
        predictor = predictor,
        outcome = outcome,
        model = c("Linear", "Quadratic"),
        n = nrow(d),
        r_squared = NA_real_,
        adj_r_squared = NA_real_,
        AIC = NA_real_,
        BIC = NA_real_,
        delta_r2_vs_linear = c(NA_real_, NA_real_),
        quadratic_increment_p = c(NA_real_, NA_real_)
      ),
      coefficients = tibble(
        predictor = predictor,
        outcome = outcome,
        model = c("Linear", "Quadratic"),
        term = "model_not_estimable",
        estimate = NA_real_,
        std.error = NA_real_,
        statistic = NA_real_,
        p.value = NA_real_
      )
    ))
  }

  linear_formula <- reformulate(predictor, response = outcome)
  quadratic_formula <- as.formula(paste0(outcome, " ~ ", predictor, " + I(", predictor, "^2)"))

  linear_fit <- lm(linear_formula, data = d)
  quadratic_fit <- lm(quadratic_formula, data = d)

  linear_glance <- broom::glance(linear_fit)
  quadratic_glance <- broom::glance(quadratic_fit)
  nested_comparison <- anova(linear_fit, quadratic_fit)

  comparison <- bind_rows(
    tibble(
      predictor = predictor,
      outcome = outcome,
      model = "Linear",
      n = stats::nobs(linear_fit),
      r_squared = linear_glance$r.squared,
      adj_r_squared = linear_glance$adj.r.squared,
      AIC = AIC(linear_fit),
      BIC = BIC(linear_fit),
      delta_r2_vs_linear = NA_real_,
      quadratic_increment_p = NA_real_
    ),
    tibble(
      predictor = predictor,
      outcome = outcome,
      model = "Quadratic",
      n = stats::nobs(quadratic_fit),
      r_squared = quadratic_glance$r.squared,
      adj_r_squared = quadratic_glance$adj.r.squared,
      AIC = AIC(quadratic_fit),
      BIC = BIC(quadratic_fit),
      delta_r2_vs_linear = quadratic_glance$r.squared - linear_glance$r.squared,
      quadratic_increment_p = nested_comparison$`Pr(>F)`[[2]]
    )
  )

  coefficients <- bind_rows(
    broom::tidy(linear_fit) %>% mutate(model = "Linear"),
    broom::tidy(quadratic_fit) %>% mutate(model = "Quadratic")
  ) %>%
    mutate(predictor = predictor, outcome = outcome) %>%
    select(predictor, outcome, model, term, estimate, std.error, statistic, p.value)

  list(comparison = comparison, coefficients = coefficients)
}

single_salience_rt_model_objects <- list(
  mean_salience_rating = fit_linear_quadratic(single_salience_rt_summary, "mean_salience_rating", "median_rt"),
  median_salience_rating = fit_linear_quadratic(single_salience_rt_summary, "median_salience_rating", "median_rt")
)

single_salience_rt_model_comparison <- bind_rows(lapply(single_salience_rt_model_objects, `[[`, "comparison"))
single_salience_rt_model_coefficients <- bind_rows(lapply(single_salience_rt_model_objects, `[[`, "coefficients"))

apa_table(
  single_salience_rt_tests %>%
    transmute(
      Predictor = predictor,
      Outcome = outcome,
      n,
      `Spearman rho` = apa_r(estimate),
      p = apa_p(p.value)
    ),
  caption = "Table 32. Single-concept salience ratings and response times."
)

Table 32. Single-concept salience ratings and response times.

Predictor	Outcome	n	Spearman rho	p
mean_salience_rating	median_rt	44	.36	.016
median_salience_rating	median_rt	44	.33	.030

write_table(single_salience_rt_tests, "table_32_single_salience_rt_tests.csv")

apa_table(
  single_salience_rt_model_comparison %>%
    transmute(
      Predictor = predictor,
      Outcome = outcome,
      Model = model,
      n,
      `R²` = apa_num(r_squared, 3),
      `Adjusted R²` = apa_num(adj_r_squared, 3),
      AIC = apa_num(AIC, 2),
      BIC = apa_num(BIC, 2),
      `ΔR² vs linear` = apa_num(delta_r2_vs_linear, 3),
      `Quadratic increment p` = apa_p(quadratic_increment_p)
    ),
  caption = "Table 32b. Linear versus quadratic models for single-concept salience and response time."
)

Table 32b. Linear versus quadratic models for single-concept salience and response time.

Predictor	Outcome	Model	n	R²	Adjusted R²	AIC	BIC	ΔR² vs linear	Quadratic increment p
mean_salience_rating	median_rt	Linear	44	0.085	0.063	607.83	613.19
mean_salience_rating	median_rt	Quadratic	44	0.680	0.665	563.55	570.69	0.595	< .001
median_salience_rating	median_rt	Linear	44	0.081	0.059	608.05	613.40
median_salience_rating	median_rt	Quadratic	44	0.513	0.489	582.11	589.24	0.432	< .001

write_table(single_salience_rt_model_comparison, "table_32b_single_salience_rt_linear_quadratic_comparison.csv")

apa_table(
  single_salience_rt_model_coefficients %>%
    transmute(
      Predictor = predictor,
      Model = model,
      Term = term,
      b = apa_num(estimate, 3),
      SE = apa_num(std.error, 3),
      t = apa_num(statistic, 2),
      p = apa_p(p.value)
    ),
  caption = "Table 32c. Coefficients from linear and quadratic RT models."
)

Table 32c. Coefficients from linear and quadratic RT models.

Predictor	Model	Term	b	SE	t	p
mean_salience_rating	Linear	(Intercept)	1792.407	84.599	21.19	< .001
mean_salience_rating	Linear	mean_salience_rating	33.394	16.898	1.98	.055
mean_salience_rating	Quadratic	(Intercept)	814.413	122.816	6.63	< .001
mean_salience_rating	Quadratic	mean_salience_rating	515.786	56.115	9.19	< .001
mean_salience_rating	Quadratic	I(mean_salience_rating^2)	-48.776	5.581	-8.74	< .001
median_salience_rating	Linear	(Intercept)	1819.085	74.215	24.51	< .001
median_salience_rating	Linear	median_salience_rating	27.645	14.404	1.92	.062
median_salience_rating	Quadratic	(Intercept)	1278.015	105.069	12.16	< .001
median_salience_rating	Quadratic	median_salience_rating	322.639	50.054	6.45	< .001
median_salience_rating	Quadratic	I(median_salience_rating^2)	-30.130	4.996	-6.03	< .001

write_table(single_salience_rt_model_coefficients, "table_32c_single_salience_rt_linear_quadratic_coefficients.csv")

mean_quad_row <- single_salience_rt_model_comparison %>%
  filter(predictor == "mean_salience_rating", model == "Quadratic") %>%
  slice_head(n = 1)

mean_linear_row <- single_salience_rt_model_comparison %>%
  filter(predictor == "mean_salience_rating", model == "Linear") %>%
  slice_head(n = 1)

quad_coef_row <- single_salience_rt_model_coefficients %>%
  filter(predictor == "mean_salience_rating", model == "Quadratic", str_detect(term, "\\^2")) %>%
  slice_head(n = 1)

if (nrow(mean_quad_row) > 0 && nrow(mean_linear_row) > 0) {
  curvature_direction <- case_when(
    nrow(quad_coef_row) == 0 | is.na(quad_coef_row$estimate[[1]]) ~ "unknown curvature",
    quad_coef_row$estimate[[1]] < 0 ~ "an inverted-U pattern",
    quad_coef_row$estimate[[1]] > 0 ~ "a U-shaped pattern",
    TRUE ~ "no visible curvature"
  )

  cat(paste0(
    "**Interpretation.** The linear model tests whether response time changes monotonically with single-concept salience. ",
    "The quadratic model tests whether intermediate salience values are processed differently from very low or very high salience values. ",
    "For the mean salience predictor, the quadratic model changes explained variance by ΔR² = ",
    apa_num(mean_quad_row$delta_r2_vs_linear[[1]], 3),
    " relative to the linear model, with incremental p ",
    apa_p(mean_quad_row$quadratic_increment_p[[1]]),
    ". The estimated curvature suggests ", curvature_direction,
    ". If this quadratic term is reliable, the result would fit a two-process reading: very low-salience concepts may be answered quickly because they are easy to reject as prominent, very high-salience concepts may be answered quickly because they are familiar, and intermediate concepts may require more deliberative integration. A splendidly inconvenient pattern for anyone hoping cognition was linear.\n"
  ))
}

Interpretation. The linear model tests whether response time changes monotonically with single-concept salience. The quadratic model tests whether intermediate salience values are processed differently from very low or very high salience values. For the mean salience predictor, the quadratic model changes explained variance by ΔR² = 0.595 relative to the linear model, with incremental p < .001. The estimated curvature suggests an inverted-U pattern. If this quadratic term is reliable, the result would fit a two-process reading: very low-salience concepts may be answered quickly because they are easy to reject as prominent, very high-salience concepts may be answered quickly because they are familiar, and intermediate concepts may require more deliberative integration. A splendidly inconvenient pattern for anyone hoping cognition was linear.

single_salience_rt_plot <- single_salience_rt_summary %>%
  ggplot(aes(x = mean_salience_rating, y = median_rt)) +
  geom_point(shape = 21, size = 3.2, alpha = .84, fill = "#31A354", color = "white", stroke = .45) +
  geom_smooth(
    method = "lm",
    formula = y ~ x,
    se = FALSE,
    linewidth = .75,
    linetype = "dashed",
    color = "#595959"
  ) +
  geom_smooth(
    method = "lm",
    formula = y ~ poly(x, 2, raw = TRUE),
    se = TRUE,
    linewidth = 1.05,
    color = "#0072B2",
    fill = "#D9EAF7",
    alpha = .35
  ) +
  labs(
    title = "Single-concept salience and response time",
    subtitle = "Dashed line = simple linear model; blue curve = quadratic model.",
    x = "Mean Likert salience rating",
    y = "Median RT (ms)"
  ) +
  theme_report()

single_salience_rt_plot

save_plot(single_salience_rt_plot, "single_salience_rating_rt_linear_quadratic_v12.png", width = 8, height = 5.2)

17.5 Data-driven priming/contextuality models

The contextuality block contains an explicit priming-related variable. This gives us a cleaner interpretation than treating diagnosticity as the only context effect. The diagnosticity task is a higher-level contextual choice problem; the contextuality task is the more direct place to evaluate whether congruent primes, mediators, and pseudowords alter binary judgments and response speed.

contextuality_model_data <- responses_all_observed %>%
  filter(experiment == "contextuality") %>%
  mutate(
    mediator_f = factor(mediator, levels = c(0, 1), labels = c("no_mediator", "mediator")),
    pseudoword_f = factor(pseudoword, levels = c(0, 1), labels = c("lexical", "pseudoword")),
    congruent_priming_f = factor(congruent_priming, levels = c(0, 1), labels = c("not_congruent", "congruent"))
  )

fit_tidy_safe <- function(expr) {
  tryCatch(
    broom::tidy(expr),
    error = function(e) tibble(term = "model_failed", estimate = NA_real_, std.error = NA_real_, statistic = NA_real_, p.value = NA_real_, note = e$message)
  )
}

contextuality_binary_model <- contextuality_model_data %>%
  filter(!is.na(response_binary_d), !is.na(mediator_f), !is.na(pseudoword_f))

contextuality_binary_model_table <- if (nrow(contextuality_binary_model) > 0) {
  fit_tidy_safe(glm(response_binary_d ~ mediator_f * pseudoword_f + mediator_f * congruent_priming_f, data = contextuality_binary_model, family = binomial())) %>%
    mutate(model = "Binary contextuality response")
} else {
  tibble(model = "Binary contextuality response", term = "no_data", estimate = NA_real_, std.error = NA_real_, statistic = NA_real_, p.value = NA_real_)
}

contextuality_rt_model_data <- contextuality_model_data %>%
  filter(rt_clean, !is.na(log_rt), !is.na(mediator_f), !is.na(pseudoword_f))

contextuality_rt_model_table <- if (nrow(contextuality_rt_model_data) > 0) {
  fit_tidy_safe(lm(log_rt ~ mediator_f * pseudoword_f + mediator_f * congruent_priming_f, data = contextuality_rt_model_data)) %>%
    mutate(model = "Log RT contextuality")
} else {
  tibble(model = "Log RT contextuality", term = "no_data", estimate = NA_real_, std.error = NA_real_, statistic = NA_real_, p.value = NA_real_)
}

contextuality_model_tables <- bind_rows(contextuality_binary_model_table, contextuality_rt_model_table)

apa_table(
  contextuality_model_tables %>%
    transmute(
      Model = model,
      Term = term,
      Estimate = apa_num(estimate, 3),
      SE = apa_num(std.error, 3),
      Statistic = apa_num(statistic, 2),
      p = apa_p(p.value)
    ),
  caption = "Table 33. Data-driven contextuality/priming models from observed tidy data."
)

Table 33. Data-driven contextuality/priming models from observed tidy data.

Model	Term	Estimate	SE	Statistic	p
Binary contextuality response	model_failed
Log RT contextuality	model_failed

write_table(contextuality_model_tables, "table_33_contextuality_priming_models.csv")

17.6 Implications for the interpretation of previous sections

The data-driven audit changes how the exploratory part of the report should be read:

1. Salience/similarity conditions from the annex remain useful as planned item-level design factors, but they should not be the only moderators considered.
2. Contextuality has explicit priming-related variables (congruent_priming, mediator, pseudoword). These should be analyzed directly rather than reconstructed from the thesis narrative.
3. RTs are available for asymmetry, salience, and contextuality. RT should therefore be treated as a secondary behavioral outcome: it can test whether computational clarity, salience contrast, or contextual congruence reduces decision difficulty.
4. Diagnosticity lacks RT in the tidy output, so diagnostic context should be analyzed mainly through choice/rating behavior unless a different raw source is recovered.

For the paper, this suggests a clean separation: Phase 4 main results predict what humans choose or rate; the RT extensions test how difficult those decisions are. If the same computational metric predicts both choice direction and speed, the model has a stronger psychological interpretation. If it predicts choice but not RT, it may still describe the endpoint of judgment without describing processing fluency.

18 Main analytical conclusions

The main conclusion is not that quantum-like metrics universally outperform classical baselines. That would be too convenient, and convenience is usually where theories go to become marketing. The more useful conclusion is differentiated: classical centroids are strong for scalar similarity ratings, while subspace and density-like metrics are much stronger for directional, relational, and context-sensitive phenomena.

cat(
  "1. **Asymmetry and salience** are best captured by directional quantum-like structure, especially containment asymmetry. The relevant object is not merely a vector, but a relation of inclusion between conceptual subspaces.\n\n",
  "2. **Explicit Likert similarity** is the friendliest domain for classical vector baselines. If centroid cosine performs strongly here, that supports the interpretation that average semantic proximity is enough for scalar similarity ratings.\n\n",
  "3. **Triplet structure** is better evaluated through continuous residuals than through rare binary violations. Bures/fidelity/overlap-type metrics are especially useful because they summarize geometry without reducing everything to a raw cosine.\n\n",
  "4. **Diagnosticity** is mixed by design, because it involves context. Static metrics can predict some rating structure, but contextualized and perplexity-inhibited metrics are the theoretically more relevant families.\n\n",
  "5. **Robustness matters.** If the same family wins across Bayesian GMM and GMM-BIC or across several dimensionality criteria, it deserves more trust. If a result depends on one exact variant, it deserves a smaller font and a suspicious look.\n"
)

1. Asymmetry and salience are best captured by directional quantum-like structure, especially containment asymmetry. The relevant object is not merely a vector, but a relation of inclusion between conceptual subspaces.

2. Explicit Likert similarity is the friendliest domain for classical vector baselines. If centroid cosine performs strongly here, that supports the interpretation that average semantic proximity is enough for scalar similarity ratings.

3. Triplet structure is better evaluated through continuous residuals than through rare binary violations. Bures/fidelity/overlap-type metrics are especially useful because they summarize geometry without reducing everything to a raw cosine.

4. Diagnosticity is mixed by design, because it involves context. Static metrics can predict some rating structure, but contextualized and perplexity-inhibited metrics are the theoretically more relevant families.

5. Robustness matters. If the same family wins across Bayesian GMM and GMM-BIC or across several dimensionality criteria, it deserves more trust. If a result depends on one exact variant, it deserves a smaller font and a suspicious look.

19 Interpretation guide for writing the paper

The results should be written as a differentiated account of conceptual similarity. The model does not need to defeat cosine everywhere. Instead, the strongest claim is that different psychological tasks expose different formal levels of conceptual representation:

• Explicit Likert similarity is well approximated by average semantic proximity. This supports the centroid as a strong classical baseline.
• Ipsative asymmetry and salience require directional structure. Containment between subspaces is the theoretically central mechanism.
• Triangular and multiplicative structure is better evaluated with distance/fidelity-like relations between subspace-derived objects than with raw vector similarity.
• Diagnosticity requires explicit context or competition mechanisms; static pairwise similarity is informative but incomplete.

The arbitrary choices in the pipeline should be reported transparently. The article should emphasize that the analysis intentionally retains several dimensionality and clustering variants to check whether results are metric-family effects rather than isolated parameter accidents.

20 Exported files

All tables and figures are written to:

paths$output_dir

[1] "/home/alex/Documentos/RESEARCH/QuantumNLP/Paper1_StructuralModel/Computational_data/phase4_R_analysis_outputs_v12"

list.files(file.path(output_dir, "tables"), pattern = "\\.csv$", full.names = FALSE) %>% head(20)

 [1] "best_predictor_by_analysis_block.csv"                "cosine_vs_quantum_comparisons.csv"                  
 [3] "h1_all_metric_rankings.csv"                          "h1_directional_metric_rankings.csv"                 
 [5] "h2_all_metric_rankings.csv"                          "h2_directional_metric_rankings.csv"                 
 [7] "h2b_likert_salience_by_target.csv"                   "h2b_likert_salience_dimensionality_correlations.csv"
 [9] "h2b_likert_salience_frequency_adjusted_models.csv"   "h2c_annex_condition_audit.csv"                      
[11] "h2c_concept_condition_summary.csv"                   "h2c_concept_condition_tests.csv"                    
[13] "h2c_human_condition_summary.csv"                     "h2c_pairwise_condition_metric_tests.csv"            
[15] "h2c_similarity_condition_lm.csv"                     "h2c_similarity_condition_summary.csv"               
[17] "h2d_best_metric_by_condition.csv"                    "h2d_condition_metric_rankings.csv"                  
[19] "h2d_condition_moderation_models.csv"                 "h3_human_order_asymmetry_test.csv"                  

list.files(file.path(output_dir, "figures"), pattern = "\\.png$", full.names = FALSE) %>% head(20)

 [1] "cross_hypothesis_metric_family_heatmap_v7.png"               
 [2] "executive_cosine_vs_quantum_comparison.png"                  
 [3] "forced_choice_rt_decision_clarity_v11.png"                   
 [4] "h1_primary_metric_scatter_v7.png"                            
 [5] "h1_top_directional_metric_correlations_v7.png"               
 [6] "h2_primary_metric_scatter_v7.png"                            
 [7] "h2_top_directional_metric_correlations_v7.png"               
 [8] "h2b_likert_salience_best_predictor_scatter_v8.png"           
 [9] "h2b_likert_salience_dimensionality_correlations_v8.png"      
[10] "h2b_likert_salience_frequency_scatter_v8.png"                
[11] "h2c_best_computational_similarity_condition_separator_v9.png"
[12] "h2c_concept_salience_dimensionality_by_planned_label_v9.png" 
[13] "h2c_ipsative_responses_by_salience_condition_v9.png"         
[14] "h3_rating_best_by_metric_family_v7.png"                      
[15] "h3_rating_primary_metric_scatter_v7.png"                     
[16] "h4_additive_primary_residual_scatter_v7.png"                 
[17] "h4_additive_triangle_top_correlations_v7.png"                
[18] "h4_mti_top_correlations_v7.png"                              
[19] "h6_contextualized_best_by_family_v7.png"                     
[20] "h6_diagnostic_choice_prediction_accuracy_v7.png"             

21 Session information

sessionInfo()

R version 4.4.2 (2024-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.4 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=es_ES.UTF-8       LC_NUMERIC=C               LC_TIME=es_ES.UTF-8        LC_COLLATE=es_ES.UTF-8    
 [5] LC_MONETARY=es_ES.UTF-8    LC_MESSAGES=es_ES.UTF-8    LC_PAPER=es_ES.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C             LC_MEASUREMENT=es_ES.UTF-8 LC_IDENTIFICATION=C       

time zone: Europe/Madrid
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] fs_1.6.6        scales_1.4.0    knitr_1.51      broom_1.0.7     vroom_1.6.5     lubridate_1.9.3 forcats_1.0.0  
 [8] stringr_1.5.2   dplyr_1.1.4     purrr_1.1.0     readr_2.1.6     tidyr_1.3.1     tibble_3.3.0    ggplot2_4.0.0  
[15] tidyverse_2.0.0

loaded via a namespace (and not attached):
 [1] generics_0.1.4     lattice_0.22-5     stringi_1.8.7      hms_1.1.3          digest_0.6.37      magrittr_2.0.4    
 [7] evaluate_1.0.5     grid_4.4.2         timechange_0.3.0   RColorBrewer_1.1-3 fastmap_1.2.0      Matrix_1.7-1      
[13] jsonlite_2.0.0     backports_1.5.0    mgcv_1.9-3         textshaping_1.0.4  cli_3.6.5          rlang_1.1.6       
[19] crayon_1.5.3       splines_4.4.2      bit64_4.5.2        withr_3.0.2        yaml_2.3.10        tools_4.4.2       
[25] parallel_4.4.2     tzdb_0.4.0         vctrs_0.6.5        R6_2.6.1           lifecycle_1.0.4    htmlwidgets_1.6.4 
[31] bit_4.5.0          ragg_1.5.0         pkgconfig_2.0.3    pillar_1.11.1      gtable_0.3.6       glue_1.8.0        
[37] systemfonts_1.3.1  xfun_0.53          tidyselect_1.2.1   rstudioapi_0.17.1  farver_2.1.2       nlme_3.1-167      
[43] htmltools_0.5.8.1  labeling_0.4.3     rmarkdown_2.30     compiler_4.4.2     S7_0.2.0