统一数学映射

下列卡片展示跨报告共享的数学概念，并映射到具体报告页面。

目标：把符号、推导、证据和跨报告核对串成一条连续数学链。

阅读协议

1. 先从 Book 第0/1章进入，统一符号和核心 FPT 对象。 /book
2. 使用下方概念卡，把每个理论概念定位到具体报告。
3. 查看阶段覆盖矩阵与 claim 账本，核对 model/method/result/finding 的连续性。
4. 通过重复治理区分“共享基础公式”与“有害重复”。

理论卡片 6 Claim 数 130 Book 章节 8

主线脊柱

幕结构定义整本论证骨架，章节脊柱过渡说明“上一段已验证结论”如何进入下一段推导。

概念卡片

符号与术语锁表

这些锁定术语用于保持中英文语义一致，并提供公式锚点便于快速查阅。

阶段覆盖矩阵

每行跟踪单个报告是否完整覆盖从假设到结论的链条。

公式深度治理

按报告族设置公式阈值，轻量文档必须通过显式例外标注，而不是隐性缺口。

概念 → Claim → 证据

重复治理

一致性检查

• all_reports_have_formula: PASS
  详情

  • ring_lazy_jump: 1
  • ring_lazy_jump_ext: 1
  • ring_lazy_jump_ext_rev2: 1
  • ring_lazy_flux: 2
  • ring_valley: 6
  • 其余 22 个字段见原始 JSON。

  展开原始检查载荷

  {
    "ring_lazy_jump": 1,
    "ring_lazy_jump_ext": 1,
    "ring_lazy_jump_ext_rev2": 1,
    "ring_lazy_flux": 2,
    "ring_valley": 6,
    "ring_valley_dst": 1,
    "ring_deriv_k2": 14,
    "ring_two_target": 1,
    "ring_two_walker_encounter_shortcut": 1,
    "grid2d_bimodality": 14,
    "grid2d_reflecting_bimodality": 14,
    "grid2d_blackboard_bimodality": 8,
    "grid2d_two_target_double_peak": 1,
    "grid2d_two_walker_encounter_shortcut": 1,
    "grid2d_rect_bimodality": 1,
    "grid2d_membrane_near_target": 1,
    "cross_luca_regime_map": 1,
    "final_multitimescale_fpt_encounter": 10,
    "grid2d_one_target_base": 1,
    "grid2d_one_target_exit_timing": 1,
    "grid2d_one_target_valley_peak_budget": 1,
    "grid2d_one_target_window_measures": 1,
    "grid2d_one_two_target_gating": 1,
    "exact_recursion_method_guide": 1,
    "encounter_reflecting_diagonal_decomp": 1,
    "encounter_reflecting_mean_validation": 1,
    "grid2d_two_target_bias_radius": 1
  }

  原始数据可在此查看 /data/v1/theory_map.json

• formula_depth_policy: FAIL
  详情

  • rows: 27
  • failure_report_ids: 21
  • exception_rows: 2

  展开原始检查载荷

  {
    "rows": [
      {
        "report_id": "cross_luca_regime_map",
        "group": "cross",
        "formula_count": 1,
        "min_required": 2,
        "target": 4,
        "pass": false,
        "policy_note": "Cross synthesis can be concise if it cites upstream derivations.",
        "exception_tag": "",
        "exception_reason": ""
      },
      {
        "report_id": "grid2d_bimodality",
        "group": "grid2d",
        "formula_count": 14,
        "min_required": 8,
        "target": 12,
        "pass": true,
        "policy_note": "Grid2D reports should carry full derivation context.",
        "exception_tag": "",
        "exception_reason": ""
      },
      {
        "report_id": "grid2d_blackboard_bimodality",
        "group": "grid2d",
        "formula_count": 8,
        "min_required": 8,
        "target": 12,
        "pass": true,
        "policy_note": "Grid2D reports should carry full derivation context.",
        "exception_tag": "",
        "exception_reason": ""
      },
      {
        "report_id": "grid2d_membrane_near_target",
        "group": "grid2d",
        "formula_count": 1,
        "min_required": 8,
        "target": 12,
        "pass": false,
        "policy_note": "Grid2D reports should carry full derivation context.",
        "exception_tag": "",
        "exception_reason": ""
      },
      {
        "report_id": "grid2d_one_target_base",
        "group": "grid2d",
        "formula_count": 1,
        "min_required": 8,
        "target": 12,
        "pass": false,
        "policy_note": "Grid2D reports should carry full derivation context.",
        "exception_tag": "",
        "exception_reason": ""
      },
      {
        "report_id": "grid2d_one_target_exit_timing",
        "group": "grid2d",
        "formula_count": 1,
        "min_required": 8,
        "target": 12,
        "pass": false,
  
  ... 已截断 8572 个字符。完整内容请查看 /data/v1/theory_map.json。

  原始数据可在此查看 /data/v1/theory_map.json

• all_reports_mapped_in_theory_cards: PASS
  详情

  • unmapped_report_ids:

  展开原始检查载荷

  {
    "unmapped_report_ids": []
  }

  原始数据可在此查看 /data/v1/theory_map.json

• duplicate_key_findings: PASS
  详情

  • 未发现问题。

  展开原始检查载荷

  []

  原始数据可在此查看 /data/v1/theory_map.json

• duplicate_math_signatures: PASS
  详情

  • redundant_count: 1
  • shared_core_count: 8

  展开原始检查载荷

  {
    "redundant_signatures": [
      {
        "latex": "f(t)=\\Pr[T=t]",
        "report_count": 8,
        "occurrence_count": 8,
        "report_ids": [
          "encounter_reflecting_diagonal_decomp",
          "encounter_reflecting_mean_validation",
          "exact_recursion_method_guide",
          "grid2d_one_target_base",
          "grid2d_one_target_exit_timing",
          "grid2d_one_target_window_measures",
          "grid2d_one_two_target_gating",
          "grid2d_two_target_bias_radius"
        ]
      }
    ],
    "shared_core_signatures": [
      {
        "latex": "f(t)=\\Pr[T=t],\\quad S(t)=\\Pr[T>t],\\quad h(t)=\\frac{f(t)}{S(t-1)}",
        "report_count": 10,
        "occurrence_count": 10,
        "report_ids": [
          "cross_luca_regime_map",
          "grid2d_membrane_near_target",
          "grid2d_rect_bimodality",
          "grid2d_two_target_double_peak",
          "grid2d_two_walker_encounter_shortcut",
          "ring_lazy_jump",
          "ring_lazy_jump_ext",
          "ring_two_target",
          "ring_two_walker_encounter_shortcut",
          "ring_valley_dst"
        ]
      },
      {
        "latex": "\\begin{aligned} p_{\\text{left}} &= \\frac{q}{4}(1+g_x),\\quad p_{\\text{right}} = \\frac{q}{4}(1-g_x),\\\\ p_{\\text{down}} &= \\frac{q}{4}(1+g_y),\\quad p_{\\text{up}} = \\frac{q}{4}(1-g_y),\\\\ p_{\\text{stay}} &= 1-q. \\end{aligned}",
        "report_count": 3,
        "occurrence_count": 3,
        "report_ids": [
          "grid2d_bimodality",
          "grid2d_blackboard_bimodality",
          "grid2d_reflecting_bimodality"
        ]
      },
      {
        "latex": "\\Delta=\\delta p_{\\text{stay}}",
        "report_count": 3,
        "occurrence_count": 3,
        "report_ids": [
          "grid2d_bimodality",
          "grid2d_blackboard_bimodality",
          "grid2d_reflecting_bimodality"
        ]
      },
      {
  
  ... 已截断 1255 个字符。完整内容请查看 /data/v1/theory_map.json。

  原始数据可在此查看 /data/v1/theory_map.json

• asset_label_duplication: PASS
  详情

  • duplicate_count: 0

  展开原始检查载荷

  {
    "duplicate_count": 0,
    "reports_with_duplicate_labels": 0,
    "total_reports_scanned": 22,
    "examples": {}
  }

  原始数据可在此查看 /data/v1/theory_map.json

跨报告路线图

这些路线把报告串成连续轨道，而不是孤立页面。

内容层叙事弧线