{
  "moduleInfo": {
    "name": "d8-canonical-tables",
    "version": "1.0.0",
    "step": 1872,
    "purpose": "Canonical D-FUMT₈ 二代数 (seven-logic Dfumt8Truth + Verilog dfumt8_alu.v Dfumt8InfoHybrid) 真理値表 dump の canonical schema (STEP 1676 contract 準拠)。 β canonical JSON path 実装 = 却下率エンジン artifact algebra toggle consumer-ification の 前提。 chat-Claude 2026-09-07 提案 「今は 2 表とも 埋め込みなので、β の canonical JSON が出た時点で consumer 化するのが筋」 の 応答実装。",
    "publicApi": [
      "d8_names: 8 値 canonical 順序 array (index 0-7 が 名前対応)",
      "seven.and[a][b] / seven.or[a][b]: 8x8 二項 truth table (index in 0-7)",
      "seven.not[a]: 8-entry 単項",
      "verilog.and[a][b] / verilog.or[a][b] / verilog.not[a]: 同 shape",
      "diff_summary: total_entries + diff_entries + four_value_subset_diff",
      "role_swap: and_identity / and_absorber / or_absorber × 2 algebras (chat-Claude 2026-09-07 discovery)",
      "audit_refs: STEP 1772-1866 arc trail",
      "cross_flow_ban: consumer 側 の 意図判定 禁止 line"
    ],
    "keyConcepts": [
      "D-FUMT₈ 二代数 併存 (Route C, STEP 1773 決定、code 変更ゼロ)",
      "Dfumt8Truth = seven-logic.ts (classical Boolean truth-order edition, MCP d8_table source)",
      "Dfumt8InfoHybrid = Verilog dfumt8_alu.v (Belnap knowledge order + T×F pair 4/32 classical Boolean carve-out)",
      "Diff 78/136 (57.4%), 4-value subset 12/32 (37.5%) — STEP 1772 実測、chat-Claude 2026-09-07 独立 verify 全一致",
      "Role-swap: seven ∧-identity=⊤ / verilog ∧-identity=∞ (chat-Claude 2026-09-07 artifact 更新で 発見)"
    ],
    "relatedModules": [
      "src/axiom-os/seven-logic.ts",
      "data/verilog/dfumt8_alu.v",
      "data/lean4-mathlib/CollatzRei/PhaseC/Dfumt8Binary64Refinement.lean",
      "data/tabs/rei-aios-f4/d8-algebra-corrigendum/scratch/d8_table_dump.json",
      "data/tabs/rei-aios-f4/d8-algebra-corrigendum/scratch/verilog_table_dump.json"
    ],
    "honestScope": [
      "本 JSON は 実装通り の 表 dump、意図 判定材料 として 使用禁止 (Cross-flow ban、STEP 1866 で T×F carve-out 意図 = UNDETERMINED、γ 採択)",
      "diff 78 は STEP 1772 rei-aios-f4/a6 tab audit で 実測、本 JSON で 独立 verify 可能 (equality check script は STEP 1875 comparator tool 予定)",
      "Role-swap mapping は chat-Claude 2026-09-07 artifact 更新で 独立到達、我々 STEP 1859-1866 arc と 齟齬なし",
      "Schema version 1.0.0、後方互換性は 1.x.x 内で 保証、breaking change は 2.0.0 で (moduleInfo.version 参照)",
      "consumer 側 は d8_names の 順序に 依存 (index 0-7 が 名前と 対応)、変更禁止",
      "tables-latest.json は 追跡型 URL (mutable、常に 最新)、tables-<version>.json は 凍結型 (immutable、引用用)、consumer は 使い分け明示"
    ]
  },
  "d8_names": ["TRUE", "FALSE", "BOTH", "NEITHER", "INFINITY", "ZERO", "FLOWING", "SELF"],
  "d8_symbols": ["⊤", "⊥", "B", "N", "∞", "〇", "～", "⟲"],
  "seven": {
    "label": "seven-logic.ts (Dfumt8Truth = classical Boolean truth-order)",
    "provenance": "src/axiom-os/seven-logic.ts, STEP 406 8 値化 + STEP 1773 Route C, MCP d8_table",
    "and": [[0,1,2,3,4,5,6,7],[1,1,1,1,1,5,1,1],[2,1,2,1,4,5,6,7],[3,1,1,3,4,5,6,7],[4,1,4,4,4,5,6,7],[5,5,5,5,5,5,5,5],[6,1,6,6,6,5,6,7],[7,1,7,7,7,5,7,7]],
    "or":  [[0,0,0,0,0,5,0,0],[0,1,2,3,4,5,6,7],[0,2,2,0,4,5,6,7],[0,3,0,3,4,5,6,7],[0,4,4,4,4,5,6,7],[5,5,5,5,5,5,5,5],[0,6,6,6,6,5,6,7],[0,7,7,7,7,5,7,7]],
    "not": [1,0,2,3,4,5,6,7]
  },
  "verilog": {
    "label": "dfumt8_alu.v (Dfumt8InfoHybrid = Belnap knowledge order + T×F classical Boolean carve-out)",
    "provenance": "data/verilog/dfumt8_alu.v, STEP 1006 R-1 (feef2e6825), Paper 145 silicon 一次 (Tang Nano 9K + Tang Console 138K + IBM Heron r2 4-substrate)",
    "and": [[0,1,0,3,0,0,0,0],[1,1,1,3,1,1,1,1],[0,1,2,3,2,2,2,2],[3,3,3,3,3,3,3,3],[0,1,2,3,4,5,6,7],[0,1,2,3,5,5,5,5],[0,1,2,3,6,5,6,5],[0,1,2,3,7,5,5,7]],
    "or":  [[0,0,2,0,0,0,0,0],[0,1,2,1,1,1,1,1],[2,2,2,2,2,2,2,2],[0,1,2,3,3,3,3,3],[0,1,2,3,4,4,4,4],[0,1,2,3,4,5,6,7],[0,1,2,3,4,6,6,4],[0,1,2,3,4,7,4,7]],
    "not": [1,0,2,3,4,5,6,7]
  },
  "diff_summary": {
    "total_entries": 136,
    "diff_entries": 78,
    "diff_ratio": 0.5735,
    "four_value_subset_total": 32,
    "four_value_subset_diff": 12,
    "four_value_subset_ratio": 0.375,
    "computed_by": "STEP 1772 rei-aios-f4/a6 tab audit + independent re-verify chat-Claude 2026-09-07 (all match)"
  },
  "role_swap": {
    "and_identity": {"seven": "TRUE", "verilog": "INFINITY"},
    "and_absorber": {"seven": "ZERO", "verilog": "NEITHER"},
    "or_absorber":  {"seven": "ZERO", "verilog": "BOTH"},
    "notes": "seven-logic の 〇 (ZERO) は universal absorber、Verilog では 〇 は 吸収元ですらない。 chat-Claude 2026-09-07 artifact 更新で 独立走査 発見。 詳細 memory: reference_dfumt8_two_algebras_role_swap_table.md"
  },
  "algebraic_laws": {
    "note": "各 code は 「破れ count / 全 case count」 形式。 seven-logic と Verilog で 法則の 成否 パターンが 総取っ替え。",
    "seven": {
      "commutativity_and": "0/64",
      "commutativity_or": "0/64",
      "double_negation": "0/8",
      "de_morgan_and": "0/64",
      "de_morgan_or": "0/64",
      "associativity_and": "12/512",
      "associativity_or": "12/512",
      "absorption_and_over_or": "16/64",
      "absorption_or_over_and": "16/64",
      "distributivity_and_over_or": "18/512",
      "distributivity_or_over_and": "18/512"
    },
    "verilog": {
      "commutativity_and": "0/64",
      "commutativity_or": "0/64",
      "double_negation": "0/8",
      "de_morgan_and": "22/64",
      "de_morgan_or": "22/64",
      "associativity_and": "0/512",
      "associativity_or": "0/512",
      "absorption_and_over_or": "16/64",
      "absorption_or_over_and": "16/64",
      "distributivity_and_over_or": "48/512",
      "distributivity_or_over_and": "48/512"
    }
  },
  "audit_refs": {
    "route_d_1772": "一次資料 audit 前段、rei-aios-f4 tab 2026-09-04",
    "route_c_1773": "2 algebra 併存 決定、code 変更ゼロ",
    "hybrid_finding_1775": "Dfumt8InfoHybrid 命名 + T×F carve-out 4/32 発見",
    "d8_verify_1779": "cross-impl-drift claim 追加、fail 固定 (実装 drift 検出器)",
    "force_diff_1859": "力学差検定 STABLE_NEITHER (5 seed × 2000 attempts、m1 verilog 4.3× / m3 seven 11.2×)",
    "survival_bias_1865": "MIXED verdict、higher-tier attractor は pure_higher initial ではなく mixed initial から convergence",
    "txf_intent_audit_1866": "T×F carve-out 意図 = UNDETERMINED、bug 寄り 傾向 evidence あり、γ 採択 documentation-only",
    "chat_claude_artifact_2026_09_07": "https://claude.ai/code/artifact/c587e04c-5020-4f32-ae8d-4144e647ab1c (2 代数 toggle 版 + 反証の記録 section + 2 表 埋め込み走査、我々 audit 記録と 全一致)"
  },
  "cross_flow_ban": "本 canonical JSON は 実装通り の 表 dump のみ。 T×F carve-out 意図 (silicon 互換性 vs 実装 bug) は 一次資料 audit で UNDETERMINED (STEP 1866 γ 採択、bug 寄り 傾向 evidence あり 但し 断定不能)。 力学差 実測結果 (STEP 1859 STABLE_NEITHER、m1/m3 opposite direction sig 有意) は 意図判定 の 根拠に **使用禁止** — 意図的な pass-through でも 実装 bug でも 同じ像が 出る。 consumer 側 も この Cross-flow ban を 継承する 責任。"
}