{
  "asset": "B3 \u2014 AI-Discovery Soundness Theorem, measured: a benchmark/test-fitness discovery engine admits FALSE discoveries at a quantified rate; proof-as-fitness admits ZERO.",
  "domain": "binary linear code [40,16] minimum distance",
  "witness_code": {
    "n": 40,
    "k": 16,
    "exact_min_distance_d": 7,
    "min_weight_codeword_count_A_d": 2,
    "nonzero_codewords": 65535
  },
  "benchmark_fitness": {
    "method": "sample M=3000 random codewords, take min weight (AlphaEvolve/FunSearch-style)",
    "trials": 400,
    "false_discovery_rate": 0.9075,
    "false_discovery_rate_closed_form": 0.9125,
    "median_overstatement": 3,
    "note": "each false discovery = benchmark reports distance > d, so it would CERTIFY this code as beating incumbent d when its true distance is exactly d \u2014 a hallucinated record."
  },
  "proof_fitness": {
    "method": "exhaustive exact minimum-distance enumeration (the certified-discovery oracle)",
    "reported_distance": 7,
    "false_discovery_rate": 0.0,
    "false_over_reports_in_sample": 0,
    "note": "exact => always returns d => never over-reports => zero false discoveries by construction."
  },
  "separation": {
    "benchmark_fdr": 0.9075,
    "proof_fdr": 0.0,
    "verdict": "QUANTIFIED SOUNDNESS SEPARATION: the sampled/benchmark fitness (the AlphaEvolve / FunSearch discovery paradigm) falsely 'discovers' a record on this code with probability ~0.907 (closed form 0.913), while the proof-as-fitness oracle used by this engine has false-discovery rate exactly 0. Benchmark-fitness AI discovery is unsound-by-construction; certified discovery is not."
  },
  "sweep_over_sample_budget": [
    {
      "sample_budget_M": 500,
      "benchmark_fdr_closed_form": 0.9849,
      "proof_fdr": 0.0
    },
    {
      "sample_budget_M": 1000,
      "benchmark_fdr_closed_form": 0.9699,
      "proof_fdr": 0.0
    },
    {
      "sample_budget_M": 3000,
      "benchmark_fdr_closed_form": 0.9125,
      "proof_fdr": 0.0
    },
    {
      "sample_budget_M": 10000,
      "benchmark_fdr_closed_form": 0.737,
      "proof_fdr": 0.0
    }
  ],
  "honest_scope": "a measured instantiation on one code domain (the same blind-spot mechanism as the impossibility theorem, GATE 22); the benchmark model is uniform codeword sampling. The point is the STRUCTURAL separation (sampled fitness has a nonzero false-accept region; the exact oracle's is measure-zero), quantified here, not a claim about any specific competitor's exact sampler."
}