{
  "all_configs_ordered_floor_le_actual_le_1": true,
  "all_ok": true,
  "auditor": {
    "foil": {
      "claimed_rate": 0.0,
      "verdict": "FLAG"
    },
    "foil_below_floor_flagged": true,
    "note": "a 'hallucination-free' claim is FLAGged \u2014 impossible for a calibrated model on arbitrary singleton facts",
    "valid": {
      "claimed_rate": 0.239479,
      "verdict": "SAFE"
    },
    "valid_model_safe": true
  },
  "citations": {
    "complement": "common/pac_bayes.py (the PAC-Bayes generalization UPPER bound)",
    "good_turing": "Good 1953; McAllester-Schapire 2000 (concentration)",
    "theorem": "Kalai & Vempala, arXiv:2311.14648 (2024) \u2014 Calibrated LMs Must Hallucinate"
  },
  "declared_model": {
    "bound": "rate >= M\u0302F - Miscalibration - 300\u00b7|Facts|/|Possible| - 7/\u221an (>=99% over train sets)",
    "carve_outs": "a sub-floor claim must disclose NON-calibration OR non-arbitrary/non-singleton facts (systematic, or seen more than once)",
    "monofact": "M\u0302F = (facts appearing exactly once)/n (Good-Turing missing-mass estimator)",
    "regime": "CALIBRATED model, ARBITRARY singleton facts (one statistical source of hallucination)",
    "theorem": "Kalai-Vempala 2024 (arXiv:2311.14648) Corollary 1"
  },
  "executed": true,
  "explicit_non_claim": "NOT a bound on all hallucination \u2014 ONLY the singleton/arbitrary-fact statistical source under CALIBRATION; systematic facts (arithmetic) and facts seen more than once (references) carry no such floor. NOT a measurement of any real model. The linear Corollary-1 floor ORDERING is Lean-kernel-checked (HallucinationFloor.lean, 4 theorems); the full Theorem-1 information-theoretic proof (Le Cam / Fano) is a DISCLOSED deferred spike. The first LOWER bound in-tree \u2014 the complement to, not a replacement of, the PAC-Bayes generalization UPPER bound. Booked EVIDENCE-ONLY; base byte-identical.",
  "flagship": {
    "hallucination_floor": 0.189479,
    "headline": "a CALIBRATED language model trained on a corpus where 20% of facts appear exactly once MUST hallucinate at >= 18.9% on arbitrary facts \u2014 no architecture, no data-cleaning, no scale fixes it (Kalai-Vempala 2024); the only way below is to DE-CALIBRATE or restrict to non-arbitrary facts, which the auditor force-discloses",
    "miscalibration": 0.01,
    "monofact_matches_pin": true,
    "monofact_rate": 0.2,
    "n": 1000000000,
    "name": "clean_calibrated"
  },
  "grid": [
    {
      "concentration_term": 0.00022136,
      "hallucination_floor": 0.189479,
      "miscalibration": 0.01,
      "monofact_rate": 0.2,
      "n": 1000000000,
      "name": "clean_calibrated",
      "ordered_at_representative_actual": true
    },
    {
      "concentration_term": 0.00022136,
      "hallucination_floor": 0.329479,
      "miscalibration": 0.02,
      "monofact_rate": 0.35,
      "n": 1000000000,
      "name": "sparser_facts",
      "ordered_at_representative_actual": true
    },
    {
      "concentration_term": 0.00011068,
      "hallucination_floor": 0.019589,
      "miscalibration": 0.005,
      "monofact_rate": 0.025,
      "n": 4000000000,
      "name": "well_calibrated_large",
      "ordered_at_representative_actual": true
    }
  ],
  "honest_scope": "An EXACT machine-checked LOWER bound on hallucination for the DECLARED model (calibrated, arbitrary singleton facts): the Corollary-1 floor, z3-certified ordering, the auditor FLAGging any sub-floor claim. Covers ONE statistical source of hallucination (singleton/arbitrary facts), NOT all hallucination; the complement to the existing PAC-Bayes UPPER bound. We own the certifier + gated auditor, NOT the theorem (Alice/Mayo). MODEL, NOT a measurement, NOT OTA.",
  "lean_rung": {
    "build_rc": 0,
    "credited": true,
    "n_v99_theorems": 16,
    "n_v99_verified": 16,
    "note": "the linear Corollary-1 floor ORDERING is now Lean-kernel-checked in HallucinationFloor.lean (4 theorems: monotone in the MonoFact rate, antitone in concentration and miscalibration, sandwich) \u2014 the twin of the z3 lemma, the same ordering the other two floors' Lean rungs certify. The full Theorem 1 (the Le Cam / Fano information-theoretic core) remains a DISCLOSED DEFERRED spike \u2014 a heavy continuous-probability lift with no off-the-shelf Mathlib Fano",
    "ordering_lean_checked": true,
    "theorem1_deferred": true
  },
  "schema": "hallucination-floor-v99h",
  "skipped": false,
  "wall_banner_untouched": {
    "checked": true,
    "unchanged": true
  },
  "z3_ordering_lemma": {
    "name": "hallucination_floor_ordering",
    "proven": true,
    "tier": "z3-lra"
  }
}