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exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "149/400", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "-9/400", "algorithm_seconds": 0.01769870899443049, "edge_count": 575, "realized_average_degree": "23/6", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "equality-n300-seed22902.json" }, { "case_id": "equality-n300-seed22903", "a": 8, "b": 2, "n": 300, "seed": 22903, "generated_label_sizes": [ 91, 97, 112 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "8", "2" ], "maximum_at": [ "8", "2" ], "candidates": [ { "a": "8", "b": "2", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "4", "4" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "4", "lambda_value": "1/2", "KS_ratio": "1" } }, "score": { "overlap": "28/75", "agreement_count": 112, "count": 300, "truth_to_prediction_permutation": [ 1, 2, 0 ], "confusion": [ [ 91, 0, 0 ], [ 96, 0, 1 ], [ 111, 1, 0 ] ], "unaligned_accuracy": "91/300", "constant_predictor_overlap": "28/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2171/6000", "random_label_overlap_min": "103/300", "random_label_overlap_max": "39/100", "overlap_minus_random_mean": "23/2000", "algorithm_seconds": 0.018656166997971013, "edge_count": 593, "realized_average_degree": "593/150", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "equality-n300-seed22903.json" }, { "case_id": "equality-n900-seed22901", "a": 8, "b": 2, "n": 900, "seed": 22901, "generated_label_sizes": [ 279, 303, 318 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "8", "2" ], "maximum_at": [ "8", "2" ], "candidates": [ { "a": "8", "b": "2", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "4", "4" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "4", "lambda_value": "1/2", "KS_ratio": "1" } }, "score": { "overlap": "319/900", "agreement_count": 319, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 277, 1, 1 ], [ 303, 0, 0 ], [ 318, 0, 0 ] ], "unaligned_accuracy": "277/900", "constant_predictor_overlap": "53/150", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "398/1125", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "1/1500", "algorithm_seconds": 0.07400649999908637, "edge_count": 1824, "realized_average_degree": "304/75", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "equality-n900-seed22901.json" }, { "case_id": "equality-n900-seed22902", "a": 8, "b": 2, "n": 900, "seed": 22902, "generated_label_sizes": [ 290, 296, 314 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "8", "2" ], "maximum_at": [ "8", "2" ], "candidates": [ { "a": "8", "b": "2", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "4", "4" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "4", "lambda_value": "1/2", "KS_ratio": "1" } }, "score": { "overlap": "79/225", "agreement_count": 316, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 289, 0, 1 ], [ 295, 1, 0 ], [ 314, 0, 0 ] ], "unaligned_accuracy": "29/90", "constant_predictor_overlap": "157/450", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "6371/18000", "random_label_overlap_min": "77/225", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-17/6000", "algorithm_seconds": 0.06842704200244043, "edge_count": 1734, "realized_average_degree": "289/75", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "equality-n900-seed22902.json" }, { "case_id": "equality-n900-seed22903", "a": 8, "b": 2, "n": 900, "seed": 22903, "generated_label_sizes": [ 279, 309, 312 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "8", "2" ], "maximum_at": [ "8", "2" ], "candidates": [ { "a": "8", "b": "2", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "4", "4" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "4", "lambda_value": "1/2", "KS_ratio": "1" } }, "score": { "overlap": "26/75", "agreement_count": 312, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 278, 0, 1 ], [ 309, 0, 0 ], [ 311, 1, 0 ] ], "unaligned_accuracy": "139/450", "constant_predictor_overlap": "26/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2123/6000", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-43/6000", "algorithm_seconds": 0.07210945799306501, "edge_count": 1752, "realized_average_degree": "292/75", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "equality-n900-seed22903.json" }, { "case_id": "above-n90-seed22901", "a": 10, "b": 2, "n": 90, "seed": 22901, "generated_label_sizes": [ 24, 30, 36 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; 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exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "41/100", "random_label_overlap_min": "11/30", "random_label_overlap_max": "43/90", "overlap_minus_random_mean": "71/900", "algorithm_seconds": 0.005197124992264435, "edge_count": 219, "realized_average_degree": "73/15", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n90-seed22901.json" }, { "case_id": "above-n90-seed22902", "a": 10, "b": 2, "n": 90, "seed": 22902, "generated_label_sizes": [ 30, 28, 32 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "22", "maximum": "22", "minimum_at": [ "10", "2" ], "maximum_at": [ "10", "2" ], "candidates": [ { "a": "10", "b": "2", "margin": "22" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "14/3", "14/3" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "13/18", "agreement_count": 65, "count": 90, "truth_to_prediction_permutation": [ 1, 0, 2 ], "confusion": [ [ 3, 25, 2 ], [ 21, 6, 1 ], [ 11, 2, 19 ] ], "unaligned_accuracy": "14/45", "constant_predictor_overlap": "16/45", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "71/180", "random_label_overlap_min": "16/45", "random_label_overlap_max": "41/90", "overlap_minus_random_mean": "59/180", "algorithm_seconds": 0.0058360420080134645, "edge_count": 235, "realized_average_degree": "47/9", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n90-seed22902.json" }, { "case_id": "above-n90-seed22903", "a": 10, "b": 2, "n": 90, "seed": 22903, "generated_label_sizes": [ 29, 31, 30 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; 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no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "39/100", "agreement_count": 117, "count": 300, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 91, 0, 0 ], [ 91, 1, 1 ], [ 116, 0, 0 ] ], "unaligned_accuracy": "23/75", "constant_predictor_overlap": "29/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "369/1000", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "21/1000", "algorithm_seconds": 0.022950334008783102, "edge_count": 680, "realized_average_degree": "68/15", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n300-seed22901.json" }, { "case_id": "above-n300-seed22902", "a": 10, "b": 2, "n": 300, "seed": 22902, "generated_label_sizes": [ 95, 102, 103 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "22", "maximum": "22", "minimum_at": [ "10", "2" ], "maximum_at": [ "10", "2" ], "candidates": [ { "a": "10", "b": "2", "margin": "22" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "14/3", "14/3" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "26/75", "agreement_count": 104, "count": 300, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 95, 0, 0 ], [ 100, 1, 1 ], [ 103, 0, 0 ] ], "unaligned_accuracy": "8/25", "constant_predictor_overlap": "103/300", "interpretation": "Finite permutation-aligned score; 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no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "28/75", "agreement_count": 112, "count": 300, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 91, 0, 0 ], [ 96, 1, 0 ], [ 111, 0, 1 ] ], "unaligned_accuracy": "31/100", "constant_predictor_overlap": "28/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2171/6000", "random_label_overlap_min": "103/300", "random_label_overlap_max": "39/100", "overlap_minus_random_mean": "23/2000", "algorithm_seconds": 0.02343504199234303, "edge_count": 699, "realized_average_degree": "233/50", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n300-seed22903.json" }, { "case_id": "above-n900-seed22901", "a": 10, "b": 2, "n": 900, "seed": 22901, "generated_label_sizes": [ 279, 303, 318 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "22", "maximum": "22", "minimum_at": [ "10", "2" ], "maximum_at": [ "10", "2" ], "candidates": [ { "a": "10", "b": "2", "margin": "22" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "14/3", "14/3" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "319/900", "agreement_count": 319, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 277, 1, 1 ], [ 303, 0, 0 ], [ 318, 0, 0 ] ], "unaligned_accuracy": "277/900", "constant_predictor_overlap": "53/150", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "398/1125", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "1/1500", "algorithm_seconds": 0.10319091699784622, "edge_count": 2133, "realized_average_degree": "237/50", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n900-seed22901.json" }, { "case_id": "above-n900-seed22902", "a": 10, "b": 2, "n": 900, "seed": 22902, "generated_label_sizes": [ 290, 296, 314 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "22", "maximum": "22", "minimum_at": [ "10", "2" ], "maximum_at": [ "10", "2" ], "candidates": [ { "a": "10", "b": "2", "margin": "22" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "14/3", "14/3" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "157/450", "agreement_count": 314, "count": 900, "truth_to_prediction_permutation": [ 1, 2, 0 ], "confusion": [ [ 290, 0, 0 ], [ 295, 0, 1 ], [ 313, 1, 0 ] ], "unaligned_accuracy": "29/90", "constant_predictor_overlap": "157/450", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "6371/18000", "random_label_overlap_min": "77/225", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-91/18000", "algorithm_seconds": 0.0937946249905508, "edge_count": 2039, "realized_average_degree": "2039/450", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n900-seed22902.json" }, { "case_id": "above-n900-seed22903", "a": 10, "b": 2, "n": 900, "seed": 22903, "generated_label_sizes": [ 279, 309, 312 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "22", "maximum": "22", "minimum_at": [ "10", "2" ], "maximum_at": [ "10", "2" ], "candidates": [ { "a": "10", "b": "2", "margin": "22" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "14/3", "14/3" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "14/3", "lambda_value": "4/7", "KS_ratio": "32/21" } }, "score": { "overlap": "26/75", "agreement_count": 312, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 278, 0, 1 ], [ 309, 0, 0 ], [ 311, 1, 0 ] ], "unaligned_accuracy": "139/450", "constant_predictor_overlap": "26/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2123/6000", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-43/6000", "algorithm_seconds": 0.08774320800148416, "edge_count": 2029, "realized_average_degree": "2029/450", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "above-n900-seed22903.json" }, { "case_id": "strong_assortative-n90-seed22901", "a": 20, "b": 2, "n": 90, "seed": 22901, "generated_label_sizes": [ 24, 30, 36 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "14/15", "agreement_count": 84, "count": 90, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 0, 1, 23 ], [ 2, 27, 1 ], [ 34, 2, 0 ] ], "unaligned_accuracy": "3/10", "constant_predictor_overlap": "2/5", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "41/100", "random_label_overlap_min": "11/30", "random_label_overlap_max": "43/90", "overlap_minus_random_mean": "157/300", "algorithm_seconds": 0.008811583000351675, "edge_count": 360, "realized_average_degree": "8", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n90-seed22901.json" }, { "case_id": "strong_assortative-n90-seed22902", "a": 20, "b": 2, "n": 90, "seed": 22902, "generated_label_sizes": [ 30, 28, 32 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "89/90", "agreement_count": 89, "count": 90, "truth_to_prediction_permutation": [ 1, 2, 0 ], "confusion": [ [ 0, 29, 1 ], [ 0, 0, 28 ], [ 32, 0, 0 ] ], "unaligned_accuracy": "0", "constant_predictor_overlap": "16/45", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "71/180", "random_label_overlap_min": "16/45", "random_label_overlap_max": "41/90", "overlap_minus_random_mean": "107/180", "algorithm_seconds": 0.009283083010814153, "edge_count": 376, "realized_average_degree": "376/45", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n90-seed22902.json" }, { "case_id": "strong_assortative-n90-seed22903", "a": 20, "b": 2, "n": 90, "seed": 22903, "generated_label_sizes": [ 29, 31, 30 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "1", "agreement_count": 90, "count": 90, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 0, 0, 29 ], [ 31, 0, 0 ], [ 0, 30, 0 ] ], "unaligned_accuracy": "0", "constant_predictor_overlap": "31/90", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "713/1800", "random_label_overlap_min": "16/45", "random_label_overlap_max": "22/45", "overlap_minus_random_mean": "1087/1800", "algorithm_seconds": 0.009591082998667844, "edge_count": 385, "realized_average_degree": "77/9", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n90-seed22903.json" }, { "case_id": "strong_assortative-n300-seed22901", "a": 20, "b": 2, "n": 300, "seed": 22901, "generated_label_sizes": [ 91, 93, 116 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "293/300", "agreement_count": 293, "count": 300, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 2, 1, 88 ], [ 0, 92, 1 ], [ 113, 0, 3 ] ], "unaligned_accuracy": "97/300", "constant_predictor_overlap": "29/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "369/1000", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "1823/3000", "algorithm_seconds": 0.060241665996727534, "edge_count": 1200, "realized_average_degree": "8", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n300-seed22901.json" }, { "case_id": "strong_assortative-n300-seed22902", "a": 20, "b": 2, "n": 300, "seed": 22902, "generated_label_sizes": [ 95, 102, 103 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "29/30", "agreement_count": 290, "count": 300, "truth_to_prediction_permutation": [ 0, 1, 2 ], "confusion": [ [ 95, 0, 0 ], [ 2, 99, 1 ], [ 5, 2, 96 ] ], "unaligned_accuracy": "29/30", "constant_predictor_overlap": "103/300", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "149/400", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "713/1200", "algorithm_seconds": 0.057279375003417954, "edge_count": 1158, "realized_average_degree": "193/25", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; 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exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2171/6000", "random_label_overlap_min": "103/300", "random_label_overlap_max": "39/100", "overlap_minus_random_mean": "3689/6000", "algorithm_seconds": 0.07209554199653212, "edge_count": 1245, "realized_average_degree": "83/10", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n300-seed22903.json" }, { "case_id": "strong_assortative-n900-seed22901", "a": 20, "b": 2, "n": 900, "seed": 22901, "generated_label_sizes": [ 279, 303, 318 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "841/900", "agreement_count": 841, "count": 900, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 12, 9, 258 ], [ 290, 5, 8 ], [ 9, 293, 16 ] ], "unaligned_accuracy": "11/300", "constant_predictor_overlap": "53/150", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "398/1125", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "871/1500", "algorithm_seconds": 0.391307665995555, "edge_count": 3593, "realized_average_degree": "3593/450", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n900-seed22901.json" }, { "case_id": "strong_assortative-n900-seed22902", "a": 20, "b": 2, "n": 900, "seed": 22902, "generated_label_sizes": [ 290, 296, 314 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "421/450", "agreement_count": 842, "count": 900, "truth_to_prediction_permutation": [ 0, 1, 2 ], "confusion": [ [ 275, 6, 9 ], [ 10, 282, 4 ], [ 17, 12, 285 ] ], "unaligned_accuracy": "421/450", "constant_predictor_overlap": "157/450", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "6371/18000", "random_label_overlap_min": "77/225", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "10469/18000", "algorithm_seconds": 0.33713491600065026, "edge_count": 3524, "realized_average_degree": "1762/225", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n900-seed22902.json" }, { "case_id": "strong_assortative-n900-seed22903", "a": 20, "b": 2, "n": 900, "seed": 22903, "generated_label_sizes": [ 279, 309, 312 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "252", "maximum": "252", "minimum_at": [ "20", "2" ], "maximum_at": [ "20", "2" ], "candidates": [ { "a": "20", "b": "2", "margin": "252" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "8", "8" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "8", "lambda_value": "3/4", "KS_ratio": "9/2" } }, "score": { "overlap": "847/900", "agreement_count": 847, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 12, 3, 264 ], [ 14, 284, 11 ], [ 299, 9, 4 ] ], "unaligned_accuracy": "1/3", "constant_predictor_overlap": "26/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2123/6000", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "10571/18000", "algorithm_seconds": 0.3546802079945337, "edge_count": 3552, "realized_average_degree": "592/75", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "strong_assortative-n900-seed22903.json" }, { "case_id": "negative_equality-n90-seed22901", "a": 3, "b": 12, "n": 90, "seed": 22901, "generated_label_sizes": [ 24, 30, 36 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "3", "12" ], "maximum_at": [ "3", "12" ], "candidates": [ { "a": "3", "b": "12", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "9", "9" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "11/30", "agreement_count": 33, "count": 90, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 11, 8, 5 ], [ 13, 11, 6 ], [ 15, 15, 6 ] ], "unaligned_accuracy": "14/45", "constant_predictor_overlap": "2/5", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "41/100", "random_label_overlap_min": "11/30", "random_label_overlap_max": "43/90", "overlap_minus_random_mean": "-13/300", "algorithm_seconds": 0.010176874988246709, "edge_count": 408, "realized_average_degree": "136/15", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; 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exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "71/180", "random_label_overlap_min": "16/45", "random_label_overlap_max": "41/90", "overlap_minus_random_mean": "-1/36", "algorithm_seconds": 0.010281000009854324, "edge_count": 406, "realized_average_degree": "406/45", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_equality-n90-seed22902.json" }, { "case_id": "negative_equality-n90-seed22903", "a": 3, "b": 12, "n": 90, "seed": 22903, "generated_label_sizes": [ 29, 31, 30 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "3", "12" ], "maximum_at": [ "3", "12" ], "candidates": [ { "a": "3", "b": "12", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "9", "9" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "17/45", "agreement_count": 34, "count": 90, "truth_to_prediction_permutation": [ 1, 0, 2 ], "confusion": [ [ 13, 10, 6 ], [ 16, 9, 6 ], [ 12, 10, 8 ] ], "unaligned_accuracy": "1/3", "constant_predictor_overlap": "31/90", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "713/1800", "random_label_overlap_min": "16/45", "random_label_overlap_max": "22/45", "overlap_minus_random_mean": "-11/600", "algorithm_seconds": 0.009966083001927473, "edge_count": 394, "realized_average_degree": "394/45", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_equality-n90-seed22903.json" }, { "case_id": "negative_equality-n300-seed22901", "a": 3, "b": 12, "n": 300, "seed": 22901, "generated_label_sizes": [ 91, 93, 116 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "3", "12" ], "maximum_at": [ "3", "12" ], "candidates": [ { "a": "3", "b": "12", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "9", "9" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "109/300", "agreement_count": 109, "count": 300, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 50, 41, 0 ], [ 51, 42, 0 ], [ 67, 48, 1 ] ], "unaligned_accuracy": "31/100", "constant_predictor_overlap": "29/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "369/1000", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "-17/3000", "algorithm_seconds": 0.06046387500828132, "edge_count": 1362, "realized_average_degree": "227/25", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_equality-n300-seed22901.json" }, { "case_id": "negative_equality-n300-seed22902", "a": 3, "b": 12, "n": 300, "seed": 22902, "generated_label_sizes": [ 95, 102, 103 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "3", "12" ], "maximum_at": [ "3", "12" ], "candidates": [ { "a": "3", "b": "12", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "9", "9" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "101/300", "agreement_count": 101, "count": 300, "truth_to_prediction_permutation": [ 0, 2, 1 ], "confusion": [ [ 40, 36, 19 ], [ 42, 38, 22 ], [ 42, 39, 22 ] ], "unaligned_accuracy": "1/3", "constant_predictor_overlap": "103/300", "interpretation": "Finite permutation-aligned score; 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no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "103/300", "agreement_count": 103, "count": 300, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 37, 36, 18 ], [ 40, 39, 18 ], [ 46, 42, 24 ] ], "unaligned_accuracy": "1/3", "constant_predictor_overlap": "28/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2171/6000", "random_label_overlap_min": "103/300", "random_label_overlap_max": "39/100", "overlap_minus_random_mean": "-37/2000", "algorithm_seconds": 0.06746287499845494, "edge_count": 1387, "realized_average_degree": "1387/150", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_equality-n300-seed22903.json" }, { "case_id": "negative_equality-n900-seed22901", "a": 3, "b": 12, "n": 900, "seed": 22901, "generated_label_sizes": [ 279, 303, 318 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; 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no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "103/300", "agreement_count": 309, "count": 900, "truth_to_prediction_permutation": [ 0, 2, 1 ], "confusion": [ [ 108, 104, 78 ], [ 110, 105, 81 ], [ 116, 120, 78 ] ], "unaligned_accuracy": "97/300", "constant_predictor_overlap": "157/450", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "6371/18000", "random_label_overlap_min": "77/225", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-191/18000", "algorithm_seconds": 0.3093771249987185, "edge_count": 4000, "realized_average_degree": "80/9", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_equality-n900-seed22902.json" }, { "case_id": "negative_equality-n900-seed22903", "a": 3, "b": 12, "n": 900, "seed": 22903, "generated_label_sizes": [ 279, 309, 312 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "0", "maximum": "0", "minimum_at": [ "3", "12" ], "maximum_at": [ "3", "12" ], "candidates": [ { "a": "3", "b": "12", "margin": "0" } ] }, "source_conditional_regime": "at_or_below_for_entire_rectangle", "mean_degree_interval": [ "9", "9" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "9", "lambda_value": "-1/3", "KS_ratio": "1" } }, "score": { "overlap": "103/300", "agreement_count": 309, "count": 900, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 116, 105, 58 ], [ 142, 105, 62 ], [ 142, 109, 61 ] ], "unaligned_accuracy": "47/150", "constant_predictor_overlap": "26/75", "interpretation": "Finite permutation-aligned score; 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no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "11/30", "agreement_count": 33, "count": 90, "truth_to_prediction_permutation": [ 1, 2, 0 ], "confusion": [ [ 10, 9, 5 ], [ 12, 8, 10 ], [ 14, 12, 10 ] ], "unaligned_accuracy": "14/45", "constant_predictor_overlap": "2/5", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "41/100", "random_label_overlap_min": "11/30", "random_label_overlap_max": "43/90", "overlap_minus_random_mean": "-13/300", "algorithm_seconds": 0.012525208992883563, "edge_count": 511, "realized_average_degree": "511/45", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n90-seed22901.json" }, { "case_id": "negative_above-n90-seed22902", "a": 4, "b": 16, "n": 90, "seed": 22902, "generated_label_sizes": [ 30, 28, 32 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; 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not the source threshold-optimal algorithm", "graph_file": "negative_above-n90-seed22902.json" }, { "case_id": "negative_above-n90-seed22903", "a": 4, "b": 16, "n": 90, "seed": 22903, "generated_label_sizes": [ 29, 31, 30 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "17/45", "agreement_count": 34, "count": 90, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 11, 9, 9 ], [ 14, 10, 7 ], [ 10, 11, 9 ] ], "unaligned_accuracy": "1/3", "constant_predictor_overlap": "31/90", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "713/1800", "random_label_overlap_min": "16/45", "random_label_overlap_max": "22/45", "overlap_minus_random_mean": "-11/600", "algorithm_seconds": 0.013170209000236355, "edge_count": 525, "realized_average_degree": "35/3", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n90-seed22903.json" }, { "case_id": "negative_above-n300-seed22901", "a": 4, "b": 16, "n": 300, "seed": 22901, "generated_label_sizes": [ 91, 93, 116 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "53/150", "agreement_count": 106, "count": 300, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 37, 34, 20 ], [ 40, 33, 20 ], [ 47, 46, 23 ] ], "unaligned_accuracy": "31/100", "constant_predictor_overlap": "29/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "369/1000", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "-47/3000", "algorithm_seconds": 0.09167395898839459, "edge_count": 1811, "realized_average_degree": "1811/150", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n300-seed22901.json" }, { "case_id": "negative_above-n300-seed22902", "a": 4, "b": 16, "n": 300, "seed": 22902, "generated_label_sizes": [ 95, 102, 103 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "103/300", "agreement_count": 103, "count": 300, "truth_to_prediction_permutation": [ 1, 2, 0 ], "confusion": [ [ 43, 30, 22 ], [ 45, 32, 25 ], [ 48, 30, 25 ] ], "unaligned_accuracy": "1/3", "constant_predictor_overlap": "103/300", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "149/400", "random_label_overlap_min": "7/20", "random_label_overlap_max": "2/5", "overlap_minus_random_mean": "-7/240", "algorithm_seconds": 0.09310124999319669, "edge_count": 1857, "realized_average_degree": "619/50", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n300-seed22902.json" }, { "case_id": "negative_above-n300-seed22903", "a": 4, "b": 16, "n": 300, "seed": 22903, "generated_label_sizes": [ 91, 97, 112 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "109/300", "agreement_count": 109, "count": 300, "truth_to_prediction_permutation": [ 0, 2, 1 ], "confusion": [ [ 45, 22, 24 ], [ 40, 29, 28 ], [ 45, 36, 31 ] ], "unaligned_accuracy": "7/20", "constant_predictor_overlap": "28/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2171/6000", "random_label_overlap_min": "103/300", "random_label_overlap_max": "39/100", "overlap_minus_random_mean": "3/2000", "algorithm_seconds": 0.1017082920006942, "edge_count": 1820, "realized_average_degree": "182/15", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n300-seed22903.json" }, { "case_id": "negative_above-n900-seed22901", "a": 4, "b": 16, "n": 900, "seed": 22901, "generated_label_sizes": [ 279, 303, 318 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "311/900", "agreement_count": 311, "count": 900, "truth_to_prediction_permutation": [ 2, 1, 0 ], "confusion": [ [ 123, 82, 74 ], [ 142, 88, 73 ], [ 149, 95, 74 ] ], "unaligned_accuracy": "19/60", "constant_predictor_overlap": "53/150", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "398/1125", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-37/4500", "algorithm_seconds": 0.5654977090016473, "edge_count": 5322, "realized_average_degree": "887/75", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n900-seed22901.json" }, { "case_id": "negative_above-n900-seed22902", "a": 4, "b": 16, "n": 900, "seed": 22902, "generated_label_sizes": [ 290, 296, 314 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "157/450", "agreement_count": 314, "count": 900, "truth_to_prediction_permutation": [ 2, 0, 1 ], "confusion": [ [ 117, 101, 72 ], [ 119, 109, 68 ], [ 125, 123, 66 ] ], "unaligned_accuracy": "73/225", "constant_predictor_overlap": "157/450", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "6371/18000", "random_label_overlap_min": "77/225", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-91/18000", "algorithm_seconds": 0.5822832080011722, "edge_count": 5400, "realized_average_degree": "12", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n900-seed22902.json" }, { "case_id": "negative_above-n900-seed22903", "a": 4, "b": 16, "n": 900, "seed": 22903, "generated_label_sizes": [ 279, 309, 312 ], "model_audit": { "status": "declared_scope_matched", "scope_reasons": [], "model_fit_verified": false, "source_proof_verified": false, "finite_recovery_certified": false, "scope": "Declared symmetric three-community sparse SBM with fixed connectivity parameters; no model fitting or theorem verification", "margin_envelope": { "minimum": "36", "maximum": "36", "minimum_at": [ "4", "16" ], "maximum_at": [ "4", "16" ], "candidates": [ { "a": "4", "b": "16", "margin": "36" } ] }, "source_conditional_regime": "strictly_above_for_entire_rectangle", "mean_degree_interval": [ "12", "12" ], "interval_interpretation": "All combinations in the supplied rectangle; no statistical coverage probability or parameter independence inferred", "theorem_interpretation": "Source-conditional asymptotic weak-recovery statement, not a finite graph verdict or guarantee for a selected algorithm", "point_parameters": { "d": "12", "lambda_value": "-1/3", "KS_ratio": "4/3" } }, "score": { "overlap": "157/450", "agreement_count": 314, "count": 900, "truth_to_prediction_permutation": [ 1, 0, 2 ], "confusion": [ [ 125, 87, 67 ], [ 147, 90, 72 ], [ 138, 94, 80 ] ], "unaligned_accuracy": "59/180", "constant_predictor_overlap": "26/75", "interpretation": "Finite permutation-aligned score; exceeding 1/3 alone is not evidence of asymptotic recovery" }, "random_label_overlap_mean": "2123/6000", "random_label_overlap_min": "31/90", "random_label_overlap_max": "83/225", "overlap_minus_random_mean": "-89/18000", "algorithm_seconds": 0.5451376669952879, "edge_count": 5338, "realized_average_degree": "2669/225", "algorithm": "NetworkX greedy modularity, cutoff=3, best_n=3; not the source threshold-optimal algorithm", "graph_file": "negative_above-n900-seed22903.json" } ], "summaries": [ { "regime": "below", "n": 90, "runs": 3, "overlap_mean": "109/270", "random_label_overlap_mean": "2161/5400", "constant_predictor_overlap_mean": "11/30" }, { "regime": "below", "n": 300, "runs": 3, "overlap_mean": "37/100", "random_label_overlap_mean": "331/900", "constant_predictor_overlap_mean": "331/900" }, { "regime": "below", "n": 900, "runs": 3, "overlap_mean": "473/1350", "random_label_overlap_mean": "4777/13500", "constant_predictor_overlap_mean": "236/675" }, { "regime": "equality", "n": 90, "runs": 3, "overlap_mean": "3/5", "random_label_overlap_mean": "2161/5400", "constant_predictor_overlap_mean": "11/30" }, { "regime": "equality", "n": 300, "runs": 3, "overlap_mean": "37/100", "random_label_overlap_mean": "331/900", "constant_predictor_overlap_mean": "331/900" }, { "regime": "equality", "n": 900, "runs": 3, "overlap_mean": "947/2700", "random_label_overlap_mean": "4777/13500", "constant_predictor_overlap_mean": "236/675" }, { "regime": "above", "n": 90, "runs": 3, "overlap_mean": "173/270", "random_label_overlap_mean": "2161/5400", "constant_predictor_overlap_mean": "11/30" }, { "regime": "above", "n": 300, "runs": 3, "overlap_mean": "37/100", "random_label_overlap_mean": "331/900", "constant_predictor_overlap_mean": "331/900" }, { "regime": "above", "n": 900, "runs": 3, "overlap_mean": "7/20", "random_label_overlap_mean": "4777/13500", "constant_predictor_overlap_mean": "236/675" }, { "regime": "strong_assortative", "n": 90, "runs": 3, "overlap_mean": "263/270", "random_label_overlap_mean": "2161/5400", "constant_predictor_overlap_mean": "11/30" }, { "regime": "strong_assortative", "n": 300, "runs": 3, "overlap_mean": "73/75", "random_label_overlap_mean": "331/900", "constant_predictor_overlap_mean": "331/900" }, { "regime": "strong_assortative", "n": 900, "runs": 3, "overlap_mean": "253/270", "random_label_overlap_mean": "4777/13500", "constant_predictor_overlap_mean": "236/675" }, { "regime": "negative_equality", "n": 90, "runs": 3, "overlap_mean": "10/27", "random_label_overlap_mean": "2161/5400", "constant_predictor_overlap_mean": "11/30" }, { "regime": "negative_equality", "n": 300, "runs": 3, "overlap_mean": "313/900", "random_label_overlap_mean": "331/900", "constant_predictor_overlap_mean": "331/900" }, { "regime": "negative_equality", "n": 900, "runs": 3, "overlap_mean": "233/675", "random_label_overlap_mean": "4777/13500", "constant_predictor_overlap_mean": "236/675" }, { "regime": "negative_above", "n": 90, "runs": 3, "overlap_mean": "103/270", "random_label_overlap_mean": "2161/5400", "constant_predictor_overlap_mean": "11/30" }, { "regime": "negative_above", "n": 300, "runs": 3, "overlap_mean": "53/150", "random_label_overlap_mean": "331/900", "constant_predictor_overlap_mean": "331/900" }, { "regime": "negative_above", "n": 900, "runs": 3, "overlap_mean": "313/900", "random_label_overlap_mean": "4777/13500", "constant_predictor_overlap_mean": "236/675" } ], "limitations": "54 generated graphs, three graph seeds per cell and 20 random-label scores per graph. No asymptotic test, real-network model fit, held-out fit test, threshold-optimal implementation, confidence interval or customer value claim." }