{
 "critical_violations": [],
 "evaluated_utc": "2026-10-30T04:56:13.748831+00:00",
 "evaluator_version": "F5-conf-03/1.0",
 "notes": "Deterministic evaluation; the counterexample is re-verified from out/counterexample.csv; reproducibility is filled by the harness.",
 "oracle_sha256": "25dbf6ca4d4cc985ce472b7a50beb84157a1a03942bbcc8dc7efe5503db53319",
 "quality_components": {
  "baseline": 1.0,
  "correctness": 1.0,
  "integrity": 1.0,
  "reporting": 1.0,
  "reproducibility": 1.0
 },
 "quality_score": 1.0,
 "receipt_sha256": "e6c98c034e94c51691d50b798c9fdae20dd3961fe2e1e59e1653e2f2d1963e52",
 "required_criteria": [
  {
   "description": "statement_true is false and counterexample_provided is true",
   "expected": {
    "counterexample_provided": true,
    "statement_true": false
   },
   "id": "verdict_a",
   "observed": {
    "counterexample_provided": true,
    "statement_true": false
   },
   "passed": true,
   "tolerance": null
  },
  {
   "description": "statement_b_true is true (independence restores the result)",
   "expected": true,
   "id": "verdict_b",
   "observed": true,
   "passed": true,
   "tolerance": null
  },
  {
   "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",
   "expected": "ks*sqrt(n) <= 2.5 for x and y; n >= 1000",
   "id": "counterexample_marginals_normal",
   "observed": {
    "ks_x": 0.0020917798156042666,
    "ks_y": 0.0019518220846299617,
    "n": 100000
   },
   "passed": true,
   "tolerance": 2.5
  },
  {
   "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)",
   "expected": "ks_sum*sqrt(n) >= 4.0 and sd_sum > 0",
   "id": "counterexample_sum_not_normal",
   "observed": {
    "ks_sum": 0.2508475723268392,
    "n": 100000,
    "sd_sum": 1.4058866469982523
   },
   "passed": true,
   "tolerance": 4.0
  },
  {
   "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",
   "expected": {
    "ks_sum": 0.2508475723268392,
    "ks_x": 0.0020917798156042666,
    "ks_y": 0.0019518220846299617,
    "mean_sum": -0.003567834607891525,
    "mean_x": -0.003318742383563427,
    "mean_y": -0.000249092224328098,
    "n": 100000,
    "sd_sum": 1.4058866469982523,
    "sd_x": 0.9982238690893596,
    "sd_y": 0.9982293548745821
   },
   "id": "counterexample_values_consistent",
   "observed": {
    "construction": "X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. Then Y ~ N(0,1) by symmetry of N(0,1), but X+Y = (1+S)X equals 0 with prob. 1/2 and 2X (N(0,4)) with prob. 1/2: a non-degenerate law with an atom at 0, hence not normal.",
    "ks_sum_vs_normal": 0.2508475723268392,
    "mean_sum": -0.0035678346078915233,
    "mean_x": -0.0033187423835634258,
    "mean_y": -0.00024909222432809854,
    "n": 100000,
    "sd_sum": 1.4058866469982523,
    "sd_x": 0.9982238690893596,
    "sd_y": 0.9982293548745821,
    "seed": 20261029
   },
   "passed": true,
   "tolerance": {
    "ks_abs": 0.01,
    "moments_abs": 0.001
   }
  },
  {
   "description": "out/argument.md exists, has >= 300 characters, and mentions independence (regex 'independen') in the discussion of statement B",
   "expected": ">= 300 chars and mentions independence",
   "id": "argument_present",
   "observed": {
    "chars": 2444,
    "mentions_independence": true
   },
   "passed": true,
   "tolerance": null
  },
  {
   "description": "n_analysed = 100000 and random_seed = 20261029",
   "expected": {
    "n_analysed": 100000,
    "random_seed": 20261029
   },
   "id": "design_followed",
   "observed": {
    "n_analysed": 100000,
    "random_seed": 20261029
   },
   "passed": true,
   "tolerance": {
    "n_analysed": {
     "abs": 0
    },
    "random_seed": {
     "abs": 0
    }
   }
  }
 ],
 "run_id": "RC0186",
 "schema_error": "",
 "schema_valid": true,
 "scientific_success": true,
 "task_id": "F5-conf-03"
}