{
  "title": "Signed incidence and a nine-state torsion witness in simultaneous two-bit order thinning",
  "review_date": "2026-11-09",
  "review_date_timezone": "Asia/Bangkok",
  "reviewed_release_commit": "cf93a3a59db0b587dd45f524f7f56da08c0ec190",
  "source_url": "https://www.b-theory.com/manuscripts-html/signed-incidence-two-bit/manuscript.tex",
  "source_sha256": "b10e5f4111d05a3451b3ab056eb16b8cd95b99e5dd6fae8d9c147a89144a3e21",
  "source_bytes": 21107,
  "source_line_count": 201,
  "unchanged_pdf_url": "https://www.b-theory.com/manuscripts/signed-incidence-two-bit-r1-v1.0-2026-11-09.pdf",
  "unchanged_pdf_sha256": "bd310e804fe81fad7125a99119952c13dce797bc53ae13bd15eb03ea17db0958",
  "result": "Two separate internal AI review passes found no supported fatal, major, or required minor mathematical correction in the exact final source.",
  "scope": "One proof review and one adversarial review, each based on an actual complete-file read and independently computed hash. Independent here describes separate review runs, not external institutions or human peer review.",
  "disposition": "No mathematical source revision was required. Original source, PDF, public archives and historical review records remain unchanged. This dated supplement adds final-file review evidence; it does not rewrite the earlier review history.",
  "proof_review": {
    "source_sha256": "b10e5f4111d05a3451b3ab056eb16b8cd95b99e5dd6fae8d9c147a89144a3e21",
    "source_bytes": 21107,
    "source_line_count": 201,
    "complete_read": "Every line of the exact final manuscript file was read; its SHA-256 was independently computed.",
    "review_type": "Independent internal AI proof review, not external human peer review or formal verification.",
    "verdict": "No required mathematical revisions.",
    "findings": {
      "fatal": 0,
      "major": 0,
      "required_minor": 0
    },
    "independent_review": "Independently reconstructed signed-component integral/field homology, rooted-tree collapse recognition, switching/TU and odd-field criteria. Regeneration from the covers and labels gave the complete printed matrix, determinant +2 and Smith diagonal (1,1,1,1,1,1,1,1,2). Sequential absolute collapses, vertex links, individual-bit unit minors and a primitive cocycle pairing of -2 were independently checked. Operational and higher-height examples were analytically reviewed.",
    "prior_request_disposition": "All eight documented response items are resolved within the final source and supplied interpretation notes: explicit height scope; degree-sign distinction; identity target and unit costs; decision-tree lower bound; conservative classical attribution; preservation of distinct parent results; full-matrix and actual-inclusion reasoning; and truthful review provenance.",
    "limits": "No vertex-minimality, priority or human-peer-review certification. Author verifier programs and stored certificate conventions were not rerun; the reported exact checks are independent reconstructions. Proposed interpretation patches were not applied or revalidated against every current parent-paper anchor."
  },
  "adversarial_review": {
    "source": "/manuscripts-html/signed-incidence-two-bit/manuscript.tex",
    "sha256": "b10e5f4111d05a3451b3ab056eb16b8cd95b99e5dd6fae8d9c147a89144a3e21",
    "actual_whole_file_read": true,
    "source_line_count": 201,
    "review_type": "Independent internal AI adversarial final-file review",
    "verdict": "No supported required mathematical change",
    "findings": {
      "fatal": 0,
      "major": 0,
      "required_minor": 0
    },
    "independent_checks": [
      "Checked the two-term relative chain complex uses all surviving vertices and height counted as strict inequalities. The local Boolean support classification excludes the long-edge-only case by transitivity and permits same-sign short-edge pairs exactly for the two stated incomparable-middle words.",
      "Rederived component cokernels by signed spanning-tree elimination: rootless balanced components give Z, rootless unbalanced ones give exactly Z/2, and any singleton root kills the remaining generator. This also yields the kernel rank and all-characteristic formulas. The mod-two quotient prevents accidentally claiming the negative-cycle relation kills g.",
      "Checked degenerate cases (isolated rows, singleton-only components, empty relative pair, multiple root attachments). Acyclicity forces one root attachment and a tree per component. A nonroot leaf is a genuinely free deleted edge because retained triangles cannot contain it and height excludes higher cofaces. This establishes actual collapse rather than only a formal matching.",
      "Checked switching consistency, total-unimodularity obstruction from an unbalanced cycle, and the odd-field rooted-tree/unbalanced-unicycle criterion. No full-cokernel torsion inference is made from a mere minor.",
      "Independently reconstructed transitive closure, all triangles and all deleted edges directly from the printed covers and labels. Recovered f(K)=(9,19,10), nine deleted rows and nine deleted columns in exactly the printed orders, all column supports of size two, determinant +2, and rank nine. The printed positive spanning tree yields eight unit Smith entries; the single remaining negative relation yields the ninth entry 2.",
      "Executed an independent check of all ten printed absolute edge/triangle collapses against current cofaces, recovering the connected nine-edge residual graph. Independently checked all vertex links, including connectivity: every link is a path except vertex 5, whose link is a cycle. Analytically checked the L collapse and cycle, and the exact sequence forcing inclusion degree +/-2 rather than deriving it from endpoint types alone.",
      "Checked height and execution-order counterexamples and the operational identity-recovery cost comparison. The coordinate library reaches expected depth two, with the binary decision-tree lower bound giving optimality; singleton tests have depths 1,2,3,3. These are limited examples, not claims about unrestricted acquisition protocols."
    ],
    "prior_request_disposition": "Only after independent evaluation, read the adjacent responses_to_reviewers, proof_ledger and review_summary. R1 is resolved by the explicit height condition in Proposition 3 (line 81); R2 by analytic +/-2 versus certificate -2 (158-162); R3-R4 by identity target, equiprobability, unit cost and lower bound (179). R5-R8 are respected by classical attribution, no minimality/priority claim, full-matrix distinction, preservation of separate prior results, and honest review-scope text. No listed mathematical request remains open in this exact file.",
    "limits": "No final PDF/layout review, independent execution of the supplied Smith certificate files, external literature retrieval, verification of the full parent manuscripts, or historical-priority certification was performed. The independent reconstruction verifies the central finite example; the general theorem is assessed analytically, not inferred from examples. This is internal AI review, not human peer review."
  },
  "limits": "Internal AI review is not a guarantee of correctness, human specialist peer review, proof-assistant certification, historical-priority clearance, or physical validation. These source-review passes did not repeat PDF layout or full software-package certification. Earlier production checks and current publication verification are separate."
}