{
  "schema": "fprd.result-review.audit-certificate.v1",
  "reviewed_at": "2026-09-01",
  "status": "pass_with_scope_corrections",
  "supersedes": "audit-certificate.json",
  "units": [
    {
      "claims": ["FPRD-SH-T33", "FPRD-SH-B10", "FPRD-SH-C18"],
      "title": "Optimal intersecting-core decomposition",
      "mathematical_result": "confirmed",
      "corrections": [
        "The vertex-cover quantity is optimal among decompositions formed from one pairwise-intersecting core; it is not asserted to lower-bound every exact-overhead algorithm.",
        "The displayed parameterized running times assume that a cover is supplied; finding a minimum cover has a separate cost.",
        "The projective-plane family is stated for prime-power orders."
      ]
    },
    {
      "claims": ["FPRD-SH-T02", "FPRD-SH-X01"],
      "title": "Incoming-label obstruction and occurrence minimum",
      "mathematical_result": "confirmed",
      "corrections": [
        "For trimmed or nested automata, the mixed-loop product location must be reachable.",
        "The sharp boundary is occurrence-minimal, not alphabetically minimal: the witness has two total letter occurrences."
      ]
    }
  ],
  "independent_verification": {
    "checker": "kernel_and_minimal_shuffle_review.py",
    "checker_sha256": "9b6ad6cb02727d2de5af6fecda46727d4164372e2058e6b80dfad91fae3720cc",
    "output": "independent-output.json",
    "output_sha256": "93367cfd73be05d98eac1c57c4ef950f12d49e2cfbbb3e40664d97c6872e50d3",
    "coverage": {
      "support_families": 16384,
      "matching_states": 181196,
      "strict_improvements_over_diversity": 1776,
      "projective_plane_orders": [2, 3, 5],
      "surjective_initial_preserving_shuffle_maps": 12,
      "exact_shuffle_quotient_maps": 0
    }
  },
  "preserved_source_verification": {
    "scope": "The original intersecting-core verifier was inspected independently of the public checker.",
    "families": 1088,
    "larger_policies": 2600,
    "target_systems": 1200,
    "output_sha256": "df28f0a2cdda408942876bfabc552c57c5439b7dac747be3da60c621c65e2d08"
  },
  "primary_sources": [
    {
      "authors": "David G. Harris and N. S. Narayanaswamy",
      "title": "A Faster Algorithm for Vertex Cover Parameterized by Solution Size",
      "venue": "STACS 2024, LIPIcs 289, article 40, 40:1-40:18",
      "doi": "10.4230/LIPIcs.STACS.2024.40",
      "arxiv": "2205.08022"
    },
    {
      "author": "Peter Dembowski",
      "title": "Finite Geometries",
      "venue": "Ergebnisse der Mathematik und ihrer Grenzgebiete 44, Springer",
      "year": 1968,
      "doi": "10.1007/978-3-642-62012-6"
    },
    {
      "authors": "Sabine Broda, António Machiavelo, Nelma Moreira, and Rogério Reis",
      "title": "Location based automata for expressions with shuffle and intersection",
      "venue": "Information and Computation 295, part B, article 104917",
      "year": 2023,
      "doi": "10.1016/j.ic.2022.104917"
    }
  ],
  "maturity_changes": [],
  "remaining_limitations": [
    "No general lower bound for exact-overhead evaluation is proved.",
    "The finite checks corroborate but do not replace the arbitrary-size proofs.",
    "No literature-priority claim is made for the two-occurrence witness."
  ]
}