{
  "artifact_schema": "fprd.result-review-certificate.v1",
  "review_date": "2026-09-01",
  "review_units": [
    {
      "title": "universal prefix-product agreement criterion",
      "claims": ["FPRD-SH-T12", "FPRD-SH-T13", "FPRD-SH-T14", "FPRD-SH-C07"]
    },
    {
      "title": "componentwise left quotients for Boolean products",
      "claims": ["FPRD-SH-T11", "FPRD-SH-B02", "FPRD-SH-C06"]
    }
  ],
  "mathematical_decisions": [
    {
      "claims": ["FPRD-SH-T12", "FPRD-SH-T13", "FPRD-SH-T14"],
      "decision": "confirmed with boundary clarification",
      "detail": "The marked event-signature expansion and the universal rigidity proof are coherent. The public proof now states why overlapping or nested same-letter supports remain distinct after unmarking and why the positive quotient is the identity-block quotient."
    },
    {
      "claim": "FPRD-SH-C06",
      "decision": "audit-scope correction",
      "detail": "The original 8,192-case checker enumerated transition structures and partitions but did not enumerate initial or final sets. Public wording no longer calls those objects complete NFAs; a separate implementation now checks every saturated initial-set pair and every final-set pair for all 5,408 predecessor-compatible structural cases."
    },
    {
      "claim": "FPRD-SH-T11",
      "decision": "confirmed",
      "detail": "The direct predecessor proof handles advancing and stuttering coordinates separately. Initial saturation and final-block commutation were checked independently, and quotienting before or after the product gives the same transition, initial, and final block data."
    }
  ],
  "independent_audit": {
    "checker": "transfer_rigidity_independent_review.py",
    "checker_sha256": "acde869ad666299b00eb1ebe070ff085506fbfa7906e736d695fa175176877f2",
    "output": "independent-output.json",
    "output_sha256": "b7b48a0417cd752861126503b0f24f67d25c84bd02facc286be5e532add0e0b9",
    "result": "pass",
    "coverage": {
      "transfer_transition_partition_cases": 8192,
      "transfer_predecessor_compatible_cases": 5408,
      "saturated_initial_set_pairs": 56448,
      "final_set_pairs": 86528,
      "two_letter_support_policies": 16452,
      "nonrigid_target_witnesses": 16382,
      "same_letter_unmarked_support_pair_occurrences": 172128
    },
    "hostile_controls": [
      "empty policy and one active support",
      "nested same-letter supports",
      "disjoint distinct-letter supports",
      "pairwise-intersecting three-support triangle with empty global core",
      "arbitrary unsaturated initial sets rejected before left-invariance testing"
    ]
  },
  "source_artifacts_inspected": [
    "fprd-boolean-product-left-quotient-hunt-2026-09-01.md",
    "boolean_product_left_quotient_audit.py",
    "boolean_product_left_quotient_verification.json",
    "fprd-boolean-product-prefix-rigidity-attack-2026-09-01.md",
    "boolean_product_prefix_rigidity_attack.py",
    "fprd-boolean-product-prefix-rigidity-verification.json"
  ],
  "primary_sources": [
    {
      "citation": "Sabine Broda, Markus Holzer, Eva Maia, Nelma Moreira, and Rogério Reis, A Mesh of Automata, Information and Computation 265 (2019), 94–111",
      "doi": "10.1016/j.ic.2019.01.003"
    },
    {
      "citation": "Sabine Broda, Eva Maia, Nelma Moreira, and Rogério Reis, The Prefix Automaton, Journal of Automata, Languages and Combinatorics 26(1–2) (2021), 17–53",
      "doi": "10.25596/jalc-2021-017"
    },
    {
      "citation": "Sabine Broda, António Machiavelo, Nelma Moreira, and Rogério Reis, Boolean Products of Languages, CIAA 2026, LNCS 16695, 16–31",
      "doi": "10.1007/978-3-032-31176-4_2"
    }
  ],
  "maturity_changes": [],
  "unresolved_items": [
    "The event-signature expansion is stated only for flat Boolean-product expressions.",
    "No literature-priority claim is made for the universal signature-rigidity classification."
  ]
}