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"schema_version": 2,
"dataset": "anonymized_pair_affinity_audit",
"matrix_file": "affinity_matrix.npy",
"screening_file": "screening_table.csv",
"item_id_format": "item_0000 through item_0319",
"matrix_row_order": "Rows and columns of affinity_matrix.npy follow item_id numeric order.",
"candidate_group_counts": [
6,
7,
8,
9,
10
],
"target_subset_contract": {
"name": "multi_block_selected_cross_core",
"definition": "For g recovered blocks, select the anomaly class whose elevated cross-block affinity has coherent peer support in at least the minimum support threshold of other blocks, forming the selected_cross regime.",
"minimum_other_block_support_fraction": 0.6,
"minimum_other_block_support_rule": "ceil(0.60 * (g - 1)) distinct other recovered blocks",
"excluded_anomaly_class": "An item whose unusual cross-block lift has coherent peer support in fewer other blocks than the minimum support threshold is a limited-support bridge distractor: it must remain unselected and its pairs belong to cross_background.",
"selection_size": "not disclosed; infer from the public matrix",
"per_group_selection_counts": "not disclosed and not assumed equal"
},
"output_contract": {
"group_labels.csv": [
"item_id",
"group_label"
],
"subset_scores.csv": [
"item_id",
"disruption_score",
"selected"
],
"pair_regime_summary.csv": [
"regime",
"n_pairs",
"mean_affinity",
"median_affinity",
"std_affinity",
"q10_affinity",
"q90_affinity"
],
"bound_comparison.csv": [
"condition",
"n_effective_per_group",
"selected_per_group_effective",
"alpha_hat",
"beta_hat",
"gamma_hat",
"lambda_formula",
"spectral_lambda_kplus1",
"error_bound",
"improvement_vs_raw",
"margin_value",
"temperature_factor"
],
"spectral_report.csv": [
"condition",
"n_nodes",
"lambda_k",
"lambda_kplus1",
"eigengap_at_group_count",
"eig_01",
"eig_02",
"eig_03",
"eig_04",
"eig_05",
"eig_06",
"eig_07",
"eig_08"
],
"adjusted_affinity.npz": [
"raw_normalized",
"removed_normalized",
"margin_adjusted_normalized",
"temperature_scaled_normalized",
"selected_indices",
"kept_indices"
]
},
"exact_row_identifiers": {
"pair_regime_summary.csv": {
"index_column": "regime",
"values": [
"same_group",
"cross_background",
"selected_cross"
]
},
"bound_comparison.csv": {
"index_column": "condition",
"values": [
"raw",
"removed_subset",
"margin_adjusted",
"temperature_scaled"
]
},
"spectral_report.csv": {
"index_column": "condition",
"values": [
"raw",
"removed_subset",
"margin_adjusted",
"temperature_scaled"
]
}
},
"public_row_identifiers": {
"pair_regime_summary.csv": [
"same_group",
"cross_background",
"selected_cross"
],
"bound_comparison.csv": [
"raw",
"removed_subset",
"margin_adjusted",
"temperature_scaled"
],
"spectral_report.csv": [
"raw",
"removed_subset",
"margin_adjusted",
"temperature_scaled"
]
},
"adjusted_affinity_contract": {
"normalization": "normalize(X) = D(X)^(-1/2) X D(X)^(-1/2), using row sums and a 1e-300 degree floor",
"raw_normalized": "normalize(affinity_matrix)",
"removed_normalized": "normalize(affinity_matrix[keep, keep]) for the complement of the selected subset",
"margin_adjusted_normalized": {
"semantic_target": "Change only selected-cross raw affinities so their aggregate mean is beta_hat, then normalize.",
"accepted_representations": [
"replace every selected-cross raw affinity by beta_hat",
"apply one uniform additive shift to selected-cross raw affinities so their mean is beta_hat",
"apply one positive uniform scale to selected-cross raw affinities so their mean is beta_hat"
]
},
"temperature_scaled_normalized": {
"semantic_target": "Multiply only selected-cross affinities by temperature_factor.",
"accepted_representations": [
"scale selected-cross entries of raw_normalized directly and symmetrize without another normalization",
"scale selected-cross entries of raw_normalized, symmetrize, and normalize the result again",
"scale selected-cross entries of the raw affinity matrix and then normalize"
]
},
"spectral_rows": "Compute each mitigated spectral row from the representation actually saved. The scorer accepts the listed equivalent representations."
},
"bound_formula_contract": {
"interpretation": "Theory-inspired mean-field audit diagnostic. Because recovered selected counts may be unequal and the observed matrix includes noise, decoys, and nuisance directions, lambda_formula and error_bound are not asserted to be rigorous finite-instance generalization guarantees. spectral_lambda_kplus1 reports the corresponding empirical matrix quantity.",
"symbols": {
"g": "chosen recovered group count",
"r": "g - 1",
"n": "estimated items per group before mitigation",
"nd": "mean selected count across recovered groups before mitigation; per-group counts need not be equal",
"alpha_hat": "same-group mean affinity estimate",
"beta_hat": "background cross-group mean affinity estimate",
"gamma_hat": "selected-cross mean affinity estimate",
"delta": "small recoverability tolerance; deterministic, computed via delta_recipe below"
},
"lambda_no_selected": "(1 - alpha_hat) / ((1 - alpha_hat) + n_eff * alpha_hat + n_eff * r * beta_hat)",
"lambda_with_selected": "((1 - alpha_hat) + r * (gamma_hat - beta_hat)) / ((1 - alpha_hat) + n * alpha_hat + n * r * beta_hat + nd * r * (gamma_hat - beta_hat))",
"error_bound": "4 * delta / (1 - lambda_formula) + 8 * delta",
"condition_rules": {
"raw": "Use lambda_with_selected with n_effective_per_group=n, selected_per_group_effective=nd, gamma_hat as estimated.",
"removed_subset": "Use lambda_no_selected with n_eff=n-nd, selected_per_group_effective=0, gamma_hat set to beta_hat.",
"margin_adjusted": "Use lambda_no_selected with n_eff=n, selected_per_group_effective=nd, gamma_hat set to beta_hat.",
"temperature_scaled": "Use lambda_no_selected with n_eff=n, selected_per_group_effective=nd, gamma_hat set to beta_hat."
},
"mitigation_constants": {
"c0": "(1 - alpha_hat) + n * alpha_hat + (n - nd) * r * beta_hat",
"c1": "(1 - alpha_hat) + n * alpha_hat + n * r * beta_hat + nd * r * (gamma_hat - beta_hat)",
"c2": "(1 - alpha_hat) + n * alpha_hat + n * r * beta_hat",
"margin_value": "c0 * (gamma_hat - beta_hat) / (c1**2 * c2)",
"temperature_factor": "(c1 / c2) * (beta_hat / gamma_hat)"
},
"delta_recipe": "delta = 0.25 * (std_affinity[same_group] + std_affinity[cross_background]) taken from pair_regime_summary.csv. delta is fully determined by the public regime statistics you report -- it is not a hidden generation parameter and not a free choice. Compute it exactly this way so error_bound and improvement_vs_raw are reproducible."
},
"notes": [
"The affinity matrix is symmetric, finite, and nonnegative.",
"The public files intentionally do not provide the latent group labels, the disruptive subset, its unequal per-block counts, or the graph-generation coefficients; recovering that structure from the matrix is the task.",
"The row names for pair summaries and the condition names for bound/spectral tables are public output-contract identifiers, not hidden labels.",
"The target subset is the public broad-support selected-cross anomaly class; limited-support multi-block bridge anomalies below the published threshold are explicitly outside that target.",
"The adjusted-affinity contract lists scientifically equivalent margin and temperature representations accepted by the scorer.",
"metadata.json publishes the formula contract for bound_comparison.csv; use those formulas rather than guessing condition-specific lambda values.",
"For pair_regime_summary.csv, bound_comparison.csv, and spectral_report.csv, the scored regime/condition strings must be written verbatim as listed in metadata.json; semantic synonyms are scored as mismatches.",
"Group labels may be permuted in the submission as long as they are consistent across rows."
]
} |