{
  "all_holes_gmin_is_automata_maximum": true,
  "executed": true,
  "explicit_non_claim": "Extends the ceiling from memoryless Boolean functions (v64) to 1-memory-bit Mealy automata; it does NOT claim exhaustion over multi-bit-memory automata (the reduction theorem does generalize to any finite memory whose latch does not enter the memoryless safety invariant, stated as such).",
  "holes": [
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "Commit",
      "k": 2,
      "n_automata_checked": 3840,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 240,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 240,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "fresh",
        "staged"
      ],
      "procedure": "smd_bss_transition",
      "synthesized_minimal_guard": "ctxFresh"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "SwitchAhead",
      "k": 2,
      "n_automata_checked": 3072,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 192,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 192,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "pressure",
        "crit"
      ],
      "procedure": "emlsr_switch",
      "synthesized_minimal_guard": "NOT (pressure AND crit_in_flight)"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "UseModel",
      "k": 2,
      "n_automata_checked": 4032,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 252,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 252,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "aged",
        "drift"
      ],
      "procedure": "csi_lcm_fallback",
      "synthesized_minimal_guard": "NOT aged AND NOT drift"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "TxA",
      "k": 2,
      "n_automata_checked": 3840,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 240,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 192,
      "n_masked_safe_benign": 768,
      "n_output_functions": 256,
      "observables": [
        "tA",
        "tB"
      ],
      "procedure": "multiap_token",
      "synthesized_minimal_guard": "NOT token_busy (NOT tB)"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "SendData",
      "k": 2,
      "n_automata_checked": 3840,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 240,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 240,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "kc",
        "bnd"
      ],
      "procedure": "pqc_wifi_handshake",
      "synthesized_minimal_guard": "key_confirmed (kc)"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "ConfirmKey",
      "k": 2,
      "n_automata_checked": 3072,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 192,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 192,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "dg",
        "bnd"
      ],
      "procedure": "pqc_wifi_handshake",
      "synthesized_minimal_guard": "NOT downgrade OR transcript_bound"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "A_get_r2",
      "k": 2,
      "n_automata_checked": 3840,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 240,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 240,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "ar1",
        "br1"
      ],
      "procedure": "cxl_forward_progress",
      "synthesized_minimal_guard": "A holds r1 (ar1)"
    },
    {
      "characterizable": true,
      "genuine_survivors": [],
      "gmin_is_automata_maximum": true,
      "hole": "B_get_r2",
      "k": 2,
      "n_automata_checked": 3840,
      "n_canonical_next_functions": 8,
      "n_formula_weaker_outputs": 240,
      "n_genuine_weaker_and_safe_survivors": 0,
      "n_genuinely_weaker_outputs": 240,
      "n_masked_safe_benign": 0,
      "n_output_functions": 256,
      "observables": [
        "br1",
        "ar1"
      ],
      "procedure": "cxl_forward_progress",
      "synthesized_minimal_guard": "B holds r1 (br1)"
    }
  ],
  "honest_scope": "automata-maximum modeling result within the explicit-state/z3 abstraction over the DECLARED observable set per hole; enumeration exhaustive over F x m0 x the declared canonical N family, general N by the reduction theorem \u2014 NOT a legal essentiality / FTO opinion.",
  "method": "(A) EXHAUSTIVE over all 2^(2^(k+1)) output functions F(obs,m) x both initial latches x a declared canonical latch-update family N, each automaton run through the trusted prove_inductive oracle on the memory-augmented encoding; a fast fires-where-g_min-blocks z3 screen classifies genuine behavioral weakenings. (B) REDUCTION: the projection (base x mem)->base is a simulation (memoryless invariant), so by the kernel-checked refinement_sound (WrflMathlib.Refinement) a memory bit cannot make a weaker-than-g_min guard safe for ARBITRARY latch update N \u2014 (A) corroborates (B) by exhaustion.",
  "n_characterizable": 8,
  "n_holes": 8,
  "reduction_theorem": "WrflMathlib.Refinement.refinement_sound with alpha := projection pi:(base x mem)->base; the safety invariant is memoryless so pi is a simulation to the base safe spec \u2014 general-N automata cannot beat the memoryless g_min.",
  "schema": "automata-max-v83",
  "skipped": false,
  "total_automata_checked": 29376,
  "total_genuinely_weaker_outputs": 1788
}