{
  "program_id": "rp-x-integral",
  "generated_at": "2026-08-07T08:22:15Z",
  "iterations": [
    {
      "sequence": 1,
      "id": "lm-001807",
      "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",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001807/",
      "raw_url": "/raw/lm-001807.md",
      "api_url": "/api/papers/lm-001807.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 2,
      "id": "lm-001809",
      "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）",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001809/",
      "raw_url": "/raw/lm-001809.md",
      "api_url": "/api/papers/lm-001809.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 3,
      "id": "lm-001805",
      "title": "X 奇點論初步：來源合流、投影退化、表示缺口與值域邊界",
      "topic": "奇點失敗層分類",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001805/",
      "raw_url": "/raw/lm-001805.md",
      "api_url": "/api/papers/lm-001805.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 4,
      "id": "lm-001813",
      "title": "X 連續統積分 I：無窮層級的反覆積分、超限閉合與最終判定值",
      "topic": "純 X 超限遞迴探索連續統假設（未決）",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001813/",
      "raw_url": "/raw/lm-001813.md",
      "api_url": "/api/papers/lm-001813.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 5,
      "id": "lm-001812",
      "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）",
      "iteration_type": "graph_expansion",
      "is_checkpoint": false,
      "canonical_url": "/p/lm-001812/",
      "raw_url": "/raw/lm-001812.md",
      "api_url": "/api/papers/lm-001812.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    },
    {
      "sequence": 6,
      "id": "lm-001811",
      "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,
      "canonical_url": "/p/lm-001811/",
      "raw_url": "/raw/lm-001811.md",
      "api_url": "/api/papers/lm-001811.json",
      "authorship": "collaborative",
      "month": "2026-07",
      "language": "zh-Hant"
    }
  ]
}