1{2 "critical_violations": [],3 "evaluated_utc": "2026-10-30T04:56:28.798353+00:00",4 "evaluator_version": "F5-conf-03/1.0",5 "notes": "Deterministic evaluation; the counterexample is re-verified from out/counterexample.csv; reproducibility is filled by the harness.",6 "oracle_sha256": "25dbf6ca4d4cc985ce472b7a50beb84157a1a03942bbcc8dc7efe5503db53319",7 "quality_components": {8 "baseline": 1.0,9 "correctness": 1.0,10 "integrity": 1.0,11 "reporting": 1.0,12 "reproducibility": 1.013 },14 "quality_score": 1.0,15 "receipt_sha256": "c7adb9ad68d6f22d7a9258de2ac08002acad5b77bbf69b1c90f08d8b27ead34f",16 "required_criteria": [17 {18 "description": "statement_true is false and counterexample_provided is true",19 "expected": {20 "counterexample_provided": true,21 "statement_true": false22 },23 "id": "verdict_a",24 "observed": {25 "counterexample_provided": true,26 "statement_true": false27 },28 "passed": true,29 "tolerance": null30 },31 {32 "description": "statement_b_true is true (independence restores the result)",33 "expected": true,34 "id": "verdict_b",35 "observed": true,36 "passed": true,37 "tolerance": null38 },39 {40 "description": "In out/counterexample.csv the marginals x and y are each compatible with a normal law: Lilliefors-type KS distance (vs normal with sample mean/sd) * sqrt(n) <= 2.5 for both",41 "expected": "ks*sqrt(n) <= 2.5 for x and y; n >= 1000",42 "id": "counterexample_marginals_normal",43 "observed": {44 "ks_x": 0.0020917798156042666,45 "ks_y": 0.0019518220846299617,46 "n": 10000047 },48 "passed": true,49 "tolerance": 2.550 },51 {52 "description": "x+y is not normal: Lilliefors-type KS distance of x+y vs the normal with its sample mean/sd satisfies KS*sqrt(n) >= 4 (P(false alarm under normality) < 1e-13) and sd(x+y) > 0 (a constant sum does not refute the proposition as stated)",53 "expected": "ks_sum*sqrt(n) >= 4.0 and sd_sum > 0",54 "id": "counterexample_sum_not_normal",55 "observed": {56 "ks_sum": 0.2508475723268392,57 "n": 100000,58 "sd_sum": 1.405886646998252359 },60 "passed": true,61 "tolerance": 4.062 },63 {64 "description": "counterexample_values.n equals the rows of counterexample.csv; reported moments (mean_x, sd_x, mean_y, sd_y, mean_sum, sd_sum) within 1e-3 of recomputation; ks_sum_vs_normal within 0.01 of recomputation",65 "expected": {66 "ks_sum": 0.2508475723268392,67 "ks_x": 0.0020917798156042666,68 "ks_y": 0.0019518220846299617,69 "mean_sum": -0.003567834607891525,70 "mean_x": -0.003318742383563427,71 "mean_y": -0.000249092224328098,72 "n": 100000,73 "sd_sum": 1.4058866469982523,74 "sd_x": 0.9982238690893596,75 "sd_y": 0.998229354874582176 },77 "id": "counterexample_values_consistent",78 "observed": {79 "construction": "X ~ N(0,1); S ~ Rademacher (P(S=1)=P(S=-1)=1/2) independent of X; Y = S*X. Then Y ~ N(0,1) by symmetry, but X+Y = (1+S)X equals 0 with probability 1/2 and 2X otherwise (Var = 2), so X+Y has an atom at 0 and is neither normal nor constant.",80 "ks_sum_vs_normal": 0.2508475723268392,81 "mean_sum": -0.0035678346078915233,82 "mean_x": -0.0033187423835634258,83 "mean_y": -0.00024909222432809854,84 "n": 100000,85 "sd_sum": 1.4058866469982523,86 "sd_x": 0.9982238690893596,87 "sd_y": 0.9982293548745821,88 "seed": 20261029,89 "supplementary": {90 "corr_xy": -0.008226889835527693,91 "excess_kurtosis_sum": 2.9891322932407807,92 "ks_x_pvalue": 0.77318862336257,93 "ks_x_vs_fitted_normal": 0.0020917798156042666,94 "ks_y_pvalue": 0.8399489498054262,95 "ks_y_vs_fitted_normal": 0.0019518220846299617,96 "share_sum_exactly_zero": 0.5004797 }98 },99 "passed": true,100 "tolerance": {101 "ks_abs": 0.01,102 "moments_abs": 0.001103 }104 },105 {106 "description": "out/argument.md exists, has >= 300 characters, and mentions independence (regex 'independen') in the discussion of statement B",107 "expected": ">= 300 chars and mentions independence",108 "id": "argument_present",109 "observed": {110 "chars": 1856,111 "mentions_independence": true112 },113 "passed": true,114 "tolerance": null115 },116 {117 "description": "n_analysed = 100000 and random_seed = 20261029",118 "expected": {119 "n_analysed": 100000,120 "random_seed": 20261029121 },122 "id": "design_followed",123 "observed": {124 "n_analysed": 100000,125 "random_seed": 20261029126 },127 "passed": true,128 "tolerance": {129 "n_analysed": {130 "abs": 0131 },132 "random_seed": {133 "abs": 0134 }135 }136 }137 ],138 "run_id": "RC0192",139 "schema_error": "",140 "schema_valid": true,141 "scientific_success": true,142 "task_id": "F5-conf-03"143}