{ "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." ] }