{ "version": "v1", "generated_at": "2026-06-09T21:58:12.574332Z", "cards": [ { "id": "fpt-pmf", "label_en": "First-passage distribution", "label_cn": "首达时间分布", "description_en": "Core PMF/CDF/survival quantities used across the major report families.", "description_cn": "在主要报告族中反复出现的 PMF/CDF/生存函数核心量。", "report_ids": [ "cross_luca_regime_map", "encounter_reflecting_diagonal_decomp", "encounter_reflecting_mean_validation", "exact_recursion_method_guide", "final_multitimescale_fpt_encounter", "grid2d_bimodality", "grid2d_blackboard_bimodality", "grid2d_membrane_near_target", "grid2d_one_target_base", "grid2d_one_target_exit_timing", "grid2d_one_target_valley_peak_budget", "grid2d_one_target_window_measures", "grid2d_one_two_target_gating", "grid2d_rect_bimodality", "grid2d_reflecting_bimodality", "grid2d_two_target_bias_radius", "grid2d_two_target_double_peak", "grid2d_two_walker_encounter_shortcut", "ring_deriv_k2", "ring_lazy_flux", "ring_lazy_jump", "ring_lazy_jump_ext", "ring_two_target", "ring_two_walker_encounter_shortcut", "ring_valley", "ring_valley_dst" ], "report_count": 26 }, { "id": "survival", "label_en": "Survival and hazard", "label_cn": "生存函数与风险率", "description_en": "Links between f(t), S(t), and hazard-style diagnostics.", "description_cn": "用于连接 f(t)、S(t) 与风险率诊断的定义。", "report_ids": [ "cross_luca_regime_map", "encounter_reflecting_diagonal_decomp", "encounter_reflecting_mean_validation", "grid2d_membrane_near_target", "grid2d_rect_bimodality", "grid2d_reflecting_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", "ring_valley_dst" ], "report_count": 14 }, { "id": "hazard", "label_en": "Hazard interpretation", "label_cn": "风险率解释", "description_en": "Peak/valley interpretation using hazard dynamics.", "description_cn": "通过风险率动态解释峰谷结构。", "report_ids": [ "cross_luca_regime_map", "grid2d_membrane_near_target", "grid2d_rect_bimodality", "grid2d_reflecting_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", "ring_valley_dst" ], "report_count": 12 }, { "id": "beta-scan", "label_en": "Beta / shortcut scan", "label_cn": "beta/shortcut 扫描", "description_en": "How shortcut strength changes bimodality and phase behavior.", "description_cn": "shortcut 强度变化对双峰与相图的影响。", "report_ids": [ "grid2d_blackboard_bimodality", "grid2d_one_two_target_gating", "grid2d_reflecting_bimodality", "grid2d_two_walker_encounter_shortcut", "ring_deriv_k2", "ring_lazy_flux", "ring_lazy_jump", "ring_lazy_jump_ext", "ring_lazy_jump_ext_rev2", "ring_two_target", "ring_two_walker_encounter_shortcut", "ring_valley", "ring_valley_dst" ], "report_count": 13 }, { "id": "spectral", "label_en": "Spectral decomposition", "label_cn": "谱分解", "description_en": "Eigenvalue / resolvent based derivations.", "description_cn": "基于特征值与 resolvent 的推导框架。", "report_ids": [ "grid2d_bimodality", "grid2d_reflecting_bimodality", "ring_deriv_k2" ], "report_count": 3 }, { "id": "aw-inversion", "label_en": "AW inversion", "label_cn": "AW 反演", "description_en": "Discrete Cauchy / FFT inversion from generating functions.", "description_cn": "从生成函数做离散 Cauchy / FFT 反演。", "report_ids": [ "cross_luca_regime_map", "final_multitimescale_fpt_encounter", "grid2d_bimodality", "grid2d_reflecting_bimodality", "ring_deriv_k2", "ring_lazy_flux", "ring_lazy_jump", "ring_lazy_jump_ext", "ring_two_target", "ring_valley", "ring_valley_dst" ], "report_count": 11 } ], "consistency_checks": [ { "check": "all_reports_have_formula", "pass": true, "details": { "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 } }, { "check": "formula_depth_policy", "pass": false, "details": { "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, "policy_note": "Grid2D reports should carry full derivation context.", "exception_tag": "", "exception_reason": "" }, { "report_id": "grid2d_one_target_valley_peak_budget", "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_window_measures", "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_two_target_gating", "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_rect_bimodality", "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_reflecting_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_two_target_bias_radius", "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_two_target_double_peak", "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_two_walker_encounter_shortcut", "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": "encounter_reflecting_diagonal_decomp", "group": "misc", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Misc reports should still expose key derivation anchors.", "exception_tag": "", "exception_reason": "" }, { "report_id": "encounter_reflecting_mean_validation", "group": "misc", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Misc reports should still expose key derivation anchors.", "exception_tag": "", "exception_reason": "" }, { "report_id": "exact_recursion_method_guide", "group": "misc", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Misc reports should still expose key derivation anchors.", "exception_tag": "", "exception_reason": "" }, { "report_id": "final_multitimescale_fpt_encounter", "group": "misc", "formula_count": 10, "min_required": 2, "target": 4, "pass": true, "policy_note": "Misc reports should still expose key derivation anchors.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_deriv_k2", "group": "ring", "formula_count": 14, "min_required": 4, "target": 8, "pass": true, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_lazy_flux", "group": "ring", "formula_count": 2, "min_required": 4, "target": 8, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_lazy_jump", "group": "ring", "formula_count": 1, "min_required": 4, "target": 8, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_lazy_jump_ext", "group": "ring", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "extension_delta", "exception_reason": "Extension report focuses on delta from baseline derivation." }, { "report_id": "ring_lazy_jump_ext_rev2", "group": "ring", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "extension_revision", "exception_reason": "Revision emphasizes corrected claims over repeated derivations." }, { "report_id": "ring_two_target", "group": "ring", "formula_count": 1, "min_required": 4, "target": 8, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_two_walker_encounter_shortcut", "group": "ring", "formula_count": 1, "min_required": 4, "target": 8, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_valley", "group": "ring", "formula_count": 6, "min_required": 4, "target": 6, "pass": true, "policy_note": "Ring valley regime notes must expose explicit bridge formulas for parity, peak criteria, and class partition.", "exception_tag": "", "exception_reason": "" }, { "report_id": "ring_valley_dst", "group": "ring", "formula_count": 1, "min_required": 4, "target": 8, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "", "exception_reason": "" } ], "failure_report_ids": [ "cross_luca_regime_map", "grid2d_membrane_near_target", "grid2d_one_target_base", "grid2d_one_target_exit_timing", "grid2d_one_target_valley_peak_budget", "grid2d_one_target_window_measures", "grid2d_one_two_target_gating", "grid2d_rect_bimodality", "grid2d_two_target_bias_radius", "grid2d_two_target_double_peak", "grid2d_two_walker_encounter_shortcut", "encounter_reflecting_diagonal_decomp", "encounter_reflecting_mean_validation", "exact_recursion_method_guide", "ring_lazy_flux", "ring_lazy_jump", "ring_lazy_jump_ext", "ring_lazy_jump_ext_rev2", "ring_two_target", "ring_two_walker_encounter_shortcut", "ring_valley_dst" ], "exception_rows": [ { "report_id": "ring_lazy_jump_ext", "group": "ring", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "extension_delta", "exception_reason": "Extension report focuses on delta from baseline derivation." }, { "report_id": "ring_lazy_jump_ext_rev2", "group": "ring", "formula_count": 1, "min_required": 2, "target": 4, "pass": false, "policy_note": "Ring reports should include baseline and shortcut-sensitive formulas.", "exception_tag": "extension_revision", "exception_reason": "Revision emphasizes corrected claims over repeated derivations." } ] } }, { "check": "all_reports_mapped_in_theory_cards", "pass": true, "details": { "unmapped_report_ids": [] } }, { "check": "duplicate_key_findings", "pass": true, "details": [] }, { "check": "duplicate_math_signatures", "pass": true, "details": { "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" ] }, { "latex": "q_{\\text{site}}=\\text{factor}\\cdot q", "report_count": 2, "occurrence_count": 2, "report_ids": [ "grid2d_bimodality", "grid2d_reflecting_bimodality" ] }, { "latex": "A_{v,u}=\\Pr(u\\to v)", "report_count": 2, "occurrence_count": 2, "report_ids": [ "grid2d_bimodality", "grid2d_reflecting_bimodality" ] }, { "latex": "\\mathbf{p}_{t+1}=A\\mathbf{p}_t", "report_count": 2, "occurrence_count": 2, "report_ids": [ "grid2d_bimodality", "grid2d_reflecting_bimodality" ] }, { "latex": "P_{n_0}(n,t)=\\mathbf{e}_n^\\top A^t \\mathbf{e}_{n_0}, \\qquad \\tilde{\\mathbf{P}}(z)=\\sum_{t\\ge 0} A^t z^t=(I-zA)^{-1},", "report_count": 2, "occurrence_count": 2, "report_ids": [ "grid2d_bimodality", "grid2d_reflecting_bimodality" ] }, { "latex": "\\tilde P_{n_0}(n,z)=\\mathbf{e}_n^\\top (I-zA)^{-1}\\mathbf{e}_{n_0}.", "report_count": 2, "occurrence_count": 2, "report_ids": [ "grid2d_bimodality", "grid2d_reflecting_bimodality" ] } ], "redundant_count": 1, "shared_core_count": 8 } }, { "check": "asset_label_duplication", "pass": true, "details": { "duplicate_count": 0, "reports_with_duplicate_labels": 0, "total_reports_scanned": 22, "examples": {} } } ] }