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  "title": "X 積分系列",
  "title_en": "X-Integral Program",
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  "started_at": "2026-07-24",
  "reference_method": "核心形成（導論／六大基本律／代數實作）之後，展開為前測度結構判定、兩個真實數學問題的案例應用（掛谷猜想的前測度重述、連續統假設的模型纖維重述）、奇點失敗層分類，以及超限積分與模型語義探索，最終由統一綱領收束為單一分層框架並逐篇標註認識論標籤（DEF/AXIOM/ENC/EQV/THM/CASE/CONJ/PROG/OPEN）。排序取自統一綱領自身的參考文件列表（其論文本身的權威排序），非單純依檔名。",
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    "research_direction": "negotiated",
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      "name": "Neo.K",
      "type": "human",
      "roles": [
        "problem_proposer",
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    },
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      "title": "X 積分作為前測度結構判定：零測度、無窮小、奇點與量化合法性的統一框架",
      "topic": "前測度結構判定",
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      "title": "X 積分對掛谷問題的前測度重述：方向完備性、投影重數與多尺度非坍縮",
      "topic": "案例應用：掛谷猜想的前測度重述（非新證明，CASE + STRUCTURAL REINTERPRETATION）",
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      "topic": "奇點失敗層分類",
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      "title": "X 積分與連續統假設 I：中間基數形成證書、模型纖維與公理相對合法性",
      "topic": "案例應用：連續統假設的模型纖維重述（Gödel–Cohen 獨立性的 X 語言重述，非繞過）",
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      "month": "2026-07",
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      "title": "X 積分統一綱領：合法結構生成、失敗診斷、前測度投影與超限模型判定",
      "topic": "統一綱領（分層收束＋認識論標籤稽核）",
      "iteration_type": "graph_expansion",
      "is_checkpoint": true,
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      "raw_url": "/raw/lm-001811.md",
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  "current_state": {
    "sequence": 6,
    "artifact_id": "lm-001811",
    "status": "ongoing",
    "phase_status": "synthesis_checkpoint_not_final_result",
    "declaration": "X 積分系列已形成一個可被明確分層的研究綱領。其最穩定核心，是一種帶有型別、來源、邊界、守衛、失敗診斷與合法性證書的部分結構建構演算；其數學價值必須由形式語義、可失敗規則、實現等價、案例區辨力與機器驗證逐步確立。",
    "stop_reason": null,
    "unresolved_gaps": [
      "連續統假設（CH）狀態明示為 J_CH^X = ⟨ 開放 ↑, BranchDependent_ZFC ⟩ ——本系列未證明、未否證 CH，也未宣稱繞過 Gödel–Cohen 獨立性",
      "掛谷猜想僅作為前測度結構判定的案例重述，明確聲明不構成、不簡化、不補強 Wang–Zahl 的原始證明",
      "X 奇點論尚未形成一般奇點的完備分類（本質奇點、分支點、分布奇點、PDE 動態奇點等仍未處理）",
      "統一綱領本身承認：目前多數內容的認識論標籤是 ENC（既有數學的重新編碼）或 PROG／CONJ（方法論／猜想），不是 THM（已證定理）",
      "尚無獨立形式語義、機器驗證或可失敗規則集確立 X 積分本身的數學新穎性"
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      "逐步以形式語義、可失敗規則、實現等價與案例區辨力確立 X 積分的數學價值，而非僅止於記號重述",
      "若後續要追加案例研究（如其他既有數學問題的前測度重述），可作為新的 applied_artifacts 或新一輪 iterations 追加"
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    "handoff_required_tasks": [],
    "stewardship": "本綱領明確、反覆自我聲明八項不主張事項（不取代既有數學基礎、記號重寫不產生新定理、未證明或否證 CH／掛谷、未繞過獨立性結果等），且掛谷與連續統假設兩案例均只是「前測度結構判定」的示範應用；判斷是否繼續、追加案例或封存，由 Neo.K 決定。",
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