{
  "scope": "Finite Boolean and literal TM model checks. No proof assistant, no arbitrary-heap verification, no claim that Python data-structure costs satisfy record bounds.",
  "bounds": {
    "type_counts_and_pins": "all Boolean relations at b=0,1,2,3",
    "gadgets": "all literal sign patterns at lengths 4 through 7, plus all Horn positive-literal positions",
    "retained_dags": "1000 seeded attempts, w=2, at most 9 decoded variables and 45 postfix operations; seed 20261001",
    "postfix_words": "all words through length 4 over the seven listed test opcodes",
    "postfix_test_alphabet": [
      "Empty_empty",
      "Empty_slot0",
      "Introduce0",
      "Forget0",
      "Add_x0",
      "Add_not_x0",
      "Join"
    ],
    "tm": "one scanned cell and one move at most per encoded symbol; every tested prefix; initially all blank",
    "record_model": "two pointer fields, two fresh records, old endpoint paths of length at most two; all earlier tested stacks remain intact",
    "single_edge_model": "one finite-control stack evaluator and the push/keep/pop scaffold rows, one appended node per unpadded opcode; prefix decoding and acceptance checked",
    "shared_implementation": "TM and record transitions share finite relation-update tables with the abstract stack; independent CNF enumeration checks table semantics on the stated samples",
    "omitted": "arbitrary widths/heaps/histories, simultaneous-record compiler execution, generic TM-to-scaffold instantiation, proof-assistant verification and optimality"
  },
  "all_relation_syntheses_b_0_to_3": 278,
  "renaming_checks_all_partial_sorts_w_0_to_3": 1968,
  "exhaustive_clause_gadgets_lengths_4_to_7": 266,
  "exhaustive_small_type_counts": [
    {
      "b": 0,
      "all": 2,
      "2cnf": 2,
      "affine": 2,
      "horn": 2
    },
    {
      "b": 1,
      "all": 4,
      "2cnf": 4,
      "affine": 4,
      "horn": 4
    },
    {
      "b": 2,
      "all": 16,
      "2cnf": 16,
      "affine": 12,
      "horn": 14
    },
    {
      "b": 3,
      "all": 256,
      "2cnf": 166,
      "affine": 52,
      "horn": 122
    }
  ],
  "horn_protocol_all_relation_pairs_b_0_to_3": [
    {
      "b": 0,
      "pairs": 4,
      "max_turns": 2,
      "max_communicated_bits": 4
    },
    {
      "b": 1,
      "pairs": 16,
      "max_turns": 4,
      "max_communicated_bits": 10
    },
    {
      "b": 2,
      "pairs": 196,
      "max_turns": 5,
      "max_communicated_bits": 16
    },
    {
      "b": 3,
      "pairs": 14884,
      "max_turns": 6,
      "max_communicated_bits": 24
    }
  ],
  "horn_middle_layer_families": [
    {
      "b": 2,
      "distinct": 4
    },
    {
      "b": 3,
      "distinct": 8
    },
    {
      "b": 4,
      "distinct": 64
    }
  ],
  "distinguishing_pin_pairs": 32767,
  "disjointness_fooling_pair_checks": 32767,
  "retained_dag_new_checks": 997,
  "retained_old_version_checks": 997,
  "negative_controls": [
    "private-name capture changes SAT",
    "positive-only observations omit a pin distinction"
  ],
  "clocked_programs_exhaustive_through_4_operations": 2801,
  "clock_mutations": 900,
  "literal_tape_transitions_checked": 48736,
  "literal_record_programs_checked": 3798,
  "single_edge_scaffold_appends_checked": 19664,
  "maximum_old_endpoint_radius_observed": 2,
  "maximum_fresh_records_observed": 2,
  "universal_status": "Theorems, view inequality and resource bounds are written proofs. The single-edge compiler has finite instances checked here and a prior Lean proof. This program does not certify unrestricted theorems, generic compiler correctness, or optimality.",
  "source_sha256": {
    "public/research-artifacts/foundations/sat-boundary-dynamics.md": "dda59c078468c21a6a7e0a7cbd46f26814fa0ba025424565d19db46404b2eda3",
    "public/research-artifacts/foundations/verify_sat_boundary.py": "c6a71ac0940b22dc3e333ba5c5cbca77a4106965b423ac8416ee0eb6e74309e3",
    "public/research-artifacts/foundations/foundational-contracts.md": "3686e6105a371e879cadbc92d676ca9fd451e26a9a4998a09088aa1deec91896",
    "public/formal/persistent-stacks/lean/FPRDTransfer/RealtimeTransfer.lean": "567e1f7b1d166a2699bb8383cd742b8f116822f3a51a4f0c7103850efa9bf3aa",
    "public/formal/persistent-stacks/lean/FPRDTransfer/TapeZipper.lean": "29f3aa81175570cabad03d728a5fb8159e2c9dceedf1d898af4472d1ca75e3c4",
    "public/formal/persistent-stacks/lean/FPRDTransfer/StackMachine.lean": "dce34cd921bc8e9a40b475d3d4c8bacc9e07af08256573402c7802136b59ee14",
    "public/formal/persistent-stacks/lean/FPRDTransfer/Compile.lean": "e6861b5f072bde0a56174cdb912d78f4e8501441b9fb5195066f71a5e0ad3338"
  }
}