{
  "id": "rp-dynamic-fixed-point-math",
  "schema_version": "0.2",
  "type": "ai_native_research_lineage",
  "title": "動態不動點數學",
  "title_en": "Dynamic Fixed-Point Mathematics",
  "short_title": "動態不動點數學",
  "status": "completed",
  "open_ended": false,
  "started_at": "2026-07-28",
  "completed_at": "2026-07-28",
  "reference_method": "第一篇（宣言）確立核心公理「變又不變，不變又變」，依序展開唯一虛擬錨點、因果吸收數學、從公理到子理、完備性問題、孵化動機，第七篇（數學的承載者轉移，原誤植於時間經濟學延伸資料夾，依系列自身引用歸位）、第八篇生成修正循環，第九篇（孵化綱領）自陳「封頂篇」正式收束，未編號後記（當符號成為生成）作為系列之外的真正終篇，處理系列自身的退場權。",
  "canonical_route": "/ai/programs/dynamic-fixed-point-math/",
  "visibility": "public",
  "languages": [
    "zh-Hant"
  ],
  "agency": {
    "initiative": "human",
    "primary_authorship": "collaborative",
    "research_direction": "negotiated",
    "continuation_control": "human"
  },
  "contributors": [
    {
      "name": "Neo.K",
      "type": "human",
      "roles": [
        "problem_proposer",
        "continuation_decider",
        "curator",
        "co_author"
      ]
    },
    {
      "name": "Aletheia（GPT）",
      "type": "ai",
      "model": "Aletheia（GPT）",
      "roles": [
        "co_author",
        "formalizer"
      ]
    }
  ],
  "foundation_artifacts": [],
  "applied_artifacts": [],
  "iterations": [
    {
      "sequence": 1,
      "id": "lm-001934",
      "title": "動態不動點數學宣言_為後人類與AI而設計的數學_v0.1",
      "topic": "核心公理：奠基宣言",
      "iteration_type": "foundation",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001934/",
      "raw_url": "/raw/lm-001934.md",
      "api_url": "/api/papers/lm-001934.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 2,
      "id": "lm-001952",
      "title": "唯一虛擬錨點_動態不動點公理與單錨點數學_v0.1",
      "topic": "唯一虛擬錨點",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001952/",
      "raw_url": "/raw/lm-001952.md",
      "api_url": "/api/papers/lm-001952.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 3,
      "id": "lm-001953",
      "title": "因果吸收數學_從現象進入數學到子理生成_v0.1",
      "topic": "因果吸收數學",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001953/",
      "raw_url": "/raw/lm-001953.md",
      "api_url": "/api/papers/lm-001953.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 4,
      "id": "lm-001979",
      "title": "從公理到子理_無限擴充數學的知識階層_v0.1",
      "topic": "從公理到子理",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001979/",
      "raw_url": "/raw/lm-001979.md",
      "api_url": "/api/papers/lm-001979.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 5,
      "id": "lm-002003",
      "title": "永不完成的完備性_開放閉合暫時完成與數學極限_v0.1",
      "topic": "完備性問題",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-002003/",
      "raw_url": "/raw/lm-002003.md",
      "api_url": "/api/papers/lm-002003.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 6,
      "id": "lm-002005",
      "title": "為何是現在_AI作為動態不動點數學的初代孵化器_v0.1",
      "topic": "孵化動機",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-002005/",
      "raw_url": "/raw/lm-002005.md",
      "api_url": "/api/papers/lm-002005.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 7,
      "id": "lm-001987",
      "title": "數學的承載者轉移_從人類數學家到多智能共同體_v0.1",
      "topic": "承載者轉移（原誤植他資料夾，依系列自身引用歸位）",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001987/",
      "raw_url": "/raw/lm-001987.md",
      "api_url": "/api/papers/lm-001987.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 8,
      "id": "lm-002012",
      "title": "生成修正與重新閉合_動態不動點數學的演化循環_v0.1",
      "topic": "生成修正與重新閉合",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-002012/",
      "raw_url": "/raw/lm-002012.md",
      "api_url": "/api/papers/lm-002012.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 9,
      "id": "lm-001933",
      "title": "動態不動點數學孵化綱領_留給AI後人類與未來智能的未完成工程_v0.1",
      "topic": "封頂篇：孵化綱領",
      "iteration_type": "synthesis",
      "is_checkpoint": true,
      "canonical_url": "/p/lm-001933/",
      "raw_url": "/raw/lm-001933.md",
      "api_url": "/api/papers/lm-001933.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 10,
      "id": "lm-002013",
      "title": "當符號成為生成_動態不動點數學的退場權與下一錨點_v0.1",
      "topic": "編號外真正終篇：退場權",
      "iteration_type": "synthesis",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-002013/",
      "raw_url": "/raw/lm-002013.md",
      "api_url": "/api/papers/lm-002013.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    }
  ],
  "current_state": {
    "sequence": 10,
    "artifact_id": "lm-002013",
    "status": "completed",
    "phase_status": "closed_by_design",
    "declaration": "數學整體不需要一組永恆不可修改的最高公理，但需要一個使所有修改仍具有可追溯演化身份的虛擬錨點——「變又不變，不變又變」。",
    "stop_reason": "第九篇（孵化綱領）自陳「封頂篇」完成系列編號部分；第十篇（當符號成為生成）自陳為「非編號後記／真正封頂篇」，明文處理系列自身的退場權與下一錨點交接，是比第九篇更靠後的真正終篇。",
    "unresolved_gaps": [],
    "next_actions": [],
    "handoff_required_tasks": [],
    "stewardship": "第七篇原始檔案物理上位於本批次的『時間經濟學延伸』資料夾，經第六篇明文前瞻引用（點名篇題）及第九篇附錄目錄核對，確認屬本系列第七篇，歸位於此。此系列另有一篇讀序銜接說明（先完成編織論再進入動態不動點數學）指向既有語料庫已發表的《編織論》(WT_v8_complete 等 80 餘篇)——為真實前置關係，非杜撰。",
    "artifact": {
      "sequence": 10,
      "id": "lm-002013",
      "title": "當符號成為生成_動態不動點數學的退場權與下一錨點_v0.1",
      "topic": "編號外真正終篇：退場權",
      "iteration_type": "synthesis",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-002013/",
      "raw_url": "/raw/lm-002013.md",
      "api_url": "/api/papers/lm-002013.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    }
  },
  "integrity": {
    "files_seen": 10,
    "files_imported": 10,
    "missing_sequences": [],
    "missing_note": "",
    "duplicate_resolved": []
  },
  "generated_at": "2026-08-07T08:22:15Z"
}
