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    },
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      "preview": "# Platform `platform/` 放置“不是研究正文本身，但支撑研究交付、自动化和 agent handoff”的能力层。 ## Subtrees - `platform/web/`: Next.js 站点与 `public/data/v1` 预计算数据 - `platform/tools/repo/`: 注册表、归档、文档检查、摘要刷新、仓库维护 - `platform/tools/web/`: web payload、b"
    },
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    },
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    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/skills/valley-k-small-continuation/SKILL.md",
      "preview": "--- name: valley-k-small-continuation description: Operational playbook for continuing report work, repo maintenance, web payload generation, and agent handoff tasks in valley-k-small."
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/skills/valley-k-small-continuation/references/core-checklist.md",
      "preview": "# Core Checklist ## Session Start - Confirm repo root: `pwd` should end with `valley-k-small` - Scan active report IDs: `python3 scripts/reportctl.py list` - Read `AGENTS.md` and the target report `README.md` ## Report T"
    },
    {
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      "sha256": "b0f6a1b1d6467c424ecf9ea4edd9f3d3ca9526015472a3b43900cfda87d7ab39",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/skills/valley-k-small-continuation/references/report-map.md",
      "preview": "# Report Map Use this map to jump directly to the correct entry script and build command family. | report_id | folder | primary entry | build notes | | --- | --- | --- | --- | | `ring_valley` | `research/reports/ring_val"
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/skills/valley-k-small-continuation/references/research-conventions.md",
      "preview": "# Research Conventions ## Model-rule disambiguation (always state explicitly) - Random walk type: `lazy` (`q < 1`) or `non-lazy` (`q = 1`). - Shortcut rule: `selfloop`, `renormalize`, or `equal4`."
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/tools/automation/keepalive_ctl.py"
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    {
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/tools/repo/audit_reports.py"
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    {
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    {
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/platform/tools/web/validate_web_data.py"
    },
    {
      "path": "pyproject.toml",
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      "size": 572,
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/pyproject.toml"
    },
    {
      "path": "requirements.txt",
      "category": "root",
      "size": 266,
      "sha256": "a3491033861a23bc5d7afb2b18cca47db63db4460ad103804ee158e82218ecea",
      "updated_at": "2026-06-09T21:57:41.589445Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/requirements.txt",
      "preview": "contourpy==1.3.0 cycler==0.12.1 fonttools==4.60.1 importlib_resources==6.5.2 joblib==1.5.2 kiwisolver==1.4.7 matplotlib==3.9.4 numpy==2.0.2 packaging==25.0 pandas>=2.2 pillow==11.3.0 pyparsing==3.2.5 python-dateutil==2.9"
    },
    {
      "path": "research/docs/DELIVERABLES.md",
      "category": "docs",
      "size": 1284,
      "sha256": "aabe676c709bb35b7f4103a3d5d4657c555ca63839f8ac77adde27f112161119",
      "updated_at": "2026-06-09T21:57:41.698446Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/docs/DELIVERABLES.md",
      "preview": "# Valley-K Small Deliverables 仓库当前的三类主要交付物： 1. Website - `https://zhouyi-xiaoxiao.github.io/valley-k-small/` 2. Publication PDF - `.local/deliverables/publication/valley_k_small_compendium_en.pdf` - `.local/deliverables/"
    },
    {
      "path": "research/docs/README.md",
      "category": "docs",
      "size": 792,
      "sha256": "bd69430a56ff19b0fc422d6c81b562d4a18890ce6e6204d87ec1458b90d6df54",
      "updated_at": "2026-06-09T21:57:41.698808Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/docs/README.md",
      "preview": "# Research Docs 跨报告研究文档的主入口只保留当前有效材料。 ## Active Documents - `research/docs/RESEARCH_SUMMARY.md`: 单文件研究简报，给人和 LLM 快速上手 - `research/docs/research_log/`: 阶段日志与迁移记录 - `research/docs/submission/`: 提交材料 PDF ## Archived Materia"
    },
    {
      "path": "research/docs/RESEARCH_SUMMARY.md",
      "category": "docs",
      "size": 10768,
      "sha256": "d9796fb8f5b9f110f3e4058f4581d4858d255470821dfffe00cbe8ac1dc3ab25",
      "updated_at": "2026-06-09T21:57:41.698808Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/docs/RESEARCH_SUMMARY.md",
      "preview": "# RESEARCH SUMMARY 最后更新: 2026-06-09 ## 仓库定位 - 本仓库研究随机游走首达时间分布中的双峰、谷值、shortcut 机制与跨模型对比。 - `research/` 是研究主树，包含报告、研究文档与历史归档。 - `platform/` 承载网站、schema、自动化与 agent handoff 工具。 - `scripts/reportctl.py` 是唯一 Python CLI 入口"
    },
    {
      "path": "research/docs/research_log/P1-function-split-baseline-20260217T004027Z.md",
      "category": "docs",
      "size": 8233,
      "sha256": "64d237d0cff6cd06235b98f91548a0c80b2c73305be7c60b52061ebfdf2995d3",
      "updated_at": "2026-06-09T21:57:41.698808Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/docs/research_log/P1-function-split-baseline-20260217T004027Z.md",
      "preview": "# P1 Function Split Baseline (20260217T004027Z) ## Help Snapshots ### .venv/bin/python reports/grid2d_reflecting_bimodality/code/reflecting_bimodality_pipeline.py --help ```text usage: reflecting_bimodality_pipeline.py ["
    },
    {
      "path": "research/docs/research_log/P1-split-baseline-20260217T000835Z.md",
      "category": "docs",
      "size": 40059,
      "sha256": "776e443c14f6b85c60a588f409521be08e719f6b97c2414c68f11af4165465be",
      "updated_at": "2026-06-09T21:57:41.698993Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/docs/research_log/P1-split-baseline-20260217T000835Z.md",
      "preview": "# P1 Split Baseline (20260217T000835Z) ## ring_valley_dst --help snapshots ### bimodality_flux_scan.py ```text usage: bimodality_flux_scan.py [-h] [--N N] [--K K] [--n0 N0] [--target TARGET] --sc-src SC_SRC [--rho RHO] ["
    },
    {
      "path": "research/docs/research_log/RESEARCH_PROGRESS_ARCHIVE.md",
      "category": "docs",
      "size": 86927,
      "sha256": "5a589ce3b934dbbc27f896243082c041981c574343c9baf064907b6b9fd1bf59",
      "updated_at": "2026-06-09T21:57:41.698993Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/docs/research_log/RESEARCH_PROGRESS_ARCHIVE.md",
      "preview": "# RESEARCH Progress Archive ## Archived on 2026-02-16 - 2026-02-16: 再次核查并修正 `reports/grid2d_rect_bimodality/`：图9/10改为更有区分度的 two-target 代表热图（A=`TT_W05_X10`，B=`TT_W06_X12`）；图12首峰/峰点与平滑曲线对齐并复核为无锯齿假峰"
    },
    {
      "path": "research/reports/README.md",
      "category": "report_docs",
      "size": 2554,
      "sha256": "aed5cd6a96f5974a37e4d296e802479038fe1fdc142fcdeb32c5c6458ba660ba",
      "updated_at": "2026-06-09T21:57:41.704076Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/README.md",
      "preview": "# Research Reports 所有报告统一遵循同一 v2 骨架： ```text research/reports/<report_id>/ README.md code/ notes/ manuscript/ <report_id>_cn.tex | <report_id>_en.tex | <report_id>.tex <report_id>_cn.pdf | <report_id>_en.pdf | <report_id"
    },
    {
      "path": "research/reports/cross_luca_regime_map/README.md",
      "category": "report_docs",
      "size": 1905,
      "sha256": "34c63b15c5e696d8b67f01d5f6b6087665451d3f0aadc4a8e80e6d8ab33f9e3d",
      "updated_at": "2026-06-09T21:57:41.705310Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/README.md",
      "preview": "# Luca Regime Map Standalone cross-report benchmark for fixed-horizon full-FPT fairness. This is the **canonical Luca-vs-recursion comparison** for the project"
    },
    {
      "path": "research/reports/cross_luca_regime_map/artifacts/tables/regime_anchor_baselines.tex",
      "category": "report_docs",
      "size": 331,
      "sha256": "9cc48899306e713f69880d83ba2c3dc361cf2d6543e52eb596dda6c93efb2aad",
      "updated_at": "2026-06-09T21:57:41.707763Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/artifacts/tables/regime_anchor_baselines.tex",
      "preview": "\\begin{tabular}{lcccccc} \\toprule Anchor & Defects & Sparse(s) & Dense(s) & Full AW(s) & Luca(s) & Linear(s) \\\\ \\midrule low\\_defect (TT\\_SYN\\_B1\\_K1\\_T300) & 4 & 0.0029 & 0.0050 & 22.9998 & 0.0416 & 0.0147 \\\\ high\\_defe"
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    {
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      "category": "report_docs",
      "size": 1167,
      "sha256": "559244072793c7b37385d09e9cdf8cafed298e9081fc5fbf77459453ff049e97",
      "updated_at": "2026-06-09T21:57:41.708201Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/artifacts/tables/regime_summary_by_bin.tex",
      "preview": "\\begin{tabular}{lccccc} \\toprule Defect bin & T & n & Median $R$ & Mean $R$ & $P(R>1)$ \\\\ \\midrule \\texttt{[0,20]} & 300 & 13 & 0.0734 & 0.0919 & 0.000 \\\\ \\texttt{[0,20]} & 600 & 8 & 0.0705 & 0.0628 & 0.000 \\\\ \\texttt{[0"
    },
    {
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      "sha256": "b31db2ddbfb5cf93a8aca0bd23f468097a32aea3c856799cab12dd54e52b9240",
      "updated_at": "2026-06-09T21:57:41.708201Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/artifacts/tables/smoke/regime_anchor_baselines.tex",
      "preview": "\\begin{tabular}{lcccccc} \\toprule Anchor & Defects & Sparse(s) & Dense(s) & Full AW(s) & Luca(s) & Linear(s) \\ \\midrule \\bottomrule \\end{tabular}"
    },
    {
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      "category": "report_docs",
      "size": 324,
      "sha256": "53ddcf810e68cb316a482de56e43280eed698587961f1ad500564dfc32124cdd",
      "updated_at": "2026-06-09T21:57:41.708303Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/artifacts/tables/smoke/regime_summary_by_bin.tex",
      "preview": "\\begin{tabular}{lccccc} \\toprule Defect bin & T & n & Median $R$ & Mean $R$ & $P(R>1)$ \\ \\midrule [301,700] & 300 & 1 & 0.0006 & 0.0006 & 0.000 \\\" [301,700] & 1200 & 1 & 0.0004 & 0.0004 & 0.000 \\\" [701,+inf) & 300 & 2 &"
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/code/build_manifest.py"
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    {
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/code/plot_regime_figures.py"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/code/run_regime_scan.py"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/code/write_regime_report.py"
    },
    {
      "path": "research/reports/cross_luca_regime_map/manuscript/cross_luca_regime_map_cn.tex",
      "category": "report_docs",
      "size": 3490,
      "sha256": "17ee199fc1df305d624763bbbfa5c125ec8d661f59fa867ec47d9085557d3599",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/manuscript/cross_luca_regime_map_cn.tex",
      "preview": "\\documentclass[11pt]{ctexart} \\usepackage[margin=1in]{geometry} \\usepackage{amsmath,amssymb,booktabs,graphicx,float,xurl} \\usepackage[hypertexnames=false]{hyperref} \\setlength{\\emergencystretch}{6em} \\title{Luca 缺陷技术速度分区"
    },
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      "path": "research/reports/cross_luca_regime_map/manuscript/cross_luca_regime_map_en.tex",
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      "updated_at": "2026-06-09T21:57:41.709462Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/manuscript/cross_luca_regime_map_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[margin=1in]{geometry} \\usepackage{amsmath,amssymb,booktabs,graphicx,float,xurl,array} \\usepackage[hypertexnames=false]{hyperref} \\setlength{\\emergencystretch}{6em} \\title{Luca De"
    },
    {
      "path": "research/reports/cross_luca_regime_map/manuscript/extras/cross_luca_regime_map_cn_smoke.tex",
      "category": "report_docs",
      "size": 3490,
      "sha256": "d5d85c9975ec05b9dcee845a07d6681032ae7bbb4bec509f27f2fb1bdd44d9b3",
      "updated_at": "2026-06-09T21:57:41.710377Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/manuscript/extras/cross_luca_regime_map_cn_smoke.tex",
      "preview": "\\documentclass[11pt]{ctexart} \\usepackage[margin=1in]{geometry} \\usepackage{amsmath,amssymb,booktabs,graphicx,float,xurl} \\usepackage[hypertexnames=false]{hyperref} \\setlength{\\emergencystretch}{6em} \\title{Luca 缺陷技术速度分区"
    },
    {
      "path": "research/reports/cross_luca_regime_map/manuscript/extras/cross_luca_regime_map_en_smoke.tex",
      "category": "report_docs",
      "size": 3556,
      "sha256": "3142abcd78a08b520b8e44f7decd98e4bf3262e9a70434143b7133ed5aeb593b",
      "updated_at": "2026-06-09T21:57:41.710377Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/manuscript/extras/cross_luca_regime_map_en_smoke.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[margin=1in]{geometry} \\usepackage{amsmath,amssymb,booktabs,graphicx,float,xurl,array} \\usepackage[hypertexnames=false]{hyperref} \\setlength{\\emergencystretch}{6em} \\title{Luca De"
    },
    {
      "path": "research/reports/cross_luca_regime_map/notes/readme_smoke.md",
      "category": "report_docs",
      "size": 1665,
      "sha256": "26bf34e9ef1e8fc9899e9586653366a28e188591ca9c8f0bbd786a6da427a19a",
      "updated_at": "2026-06-09T21:57:41.710377Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/cross_luca_regime_map/notes/readme_smoke.md",
      "preview": "# Luca Regime Map Standalone cross-report benchmark for fixed-horizon full-FPT fairness. ## Key policy - Main full-FPT winner metric: `Sparse exact` vs `Luca defect-reduced`. - `Linear MFPT` is reference only."
    },
    {
      "path": "research/reports/encounter_reflecting_diagonal_decomp/README.md",
      "category": "report_docs",
      "size": 1208,
      "sha256": "6b289a70115fe9cfb95941165be07fe008cc5466991930c05bda9735aa666ffc",
      "updated_at": "2026-06-09T21:57:41.710377Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_diagonal_decomp/README.md",
      "preview": "# Reflecting Encounter Diagonal Decomposition This report runs a bounded mobility-ratio scan for the reflecting-boundary two-walker encounter model using diagonal-position contributions."
    },
    {
      "path": "research/reports/encounter_reflecting_diagonal_decomp/code/compare_green_formula.py",
      "category": "report_code",
      "size": 11991,
      "sha256": "081963bbdcae652a800dc54fdc4e4e969d5541dab5f79f91a95705db9e6cf38d",
      "updated_at": "2026-06-09T21:57:41.745076Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_diagonal_decomp/code/compare_green_formula.py"
    },
    {
      "path": "research/reports/encounter_reflecting_diagonal_decomp/code/run_ratio_scan.py",
      "category": "report_code",
      "size": 14906,
      "sha256": "9e27d9d7af00f3041eaa3d3ab65866be3fd39dc8f462ddde5c1d7eacdd73463d",
      "updated_at": "2026-06-09T21:57:41.747076Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_diagonal_decomp/code/run_ratio_scan.py"
    },
    {
      "path": "research/reports/encounter_reflecting_diagonal_decomp/notes/SUMMARY.md",
      "category": "report_docs",
      "size": 1670,
      "sha256": "b2807ec8c470802122e877ff0cecc65317322e361b6428a52320ff95c6efbd17",
      "updated_at": "2026-06-09T21:57:41.747299Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_diagonal_decomp/notes/SUMMARY.md",
      "preview": "# Reflecting Encounter Diagonal Decomposition Ratio Scan This bounded scan uses the fixed-total-mobility convention `Q1 = 2*q0*rho/(1+rho)` and `Q2 = 2*q0/(1+rho)`."
    },
    {
      "path": "research/reports/encounter_reflecting_diagonal_decomp/notes/green_formula_comparison.md",
      "category": "report_docs",
      "size": 2950,
      "sha256": "32da6a41f7299dbdb66ea5bf49972774c2cb2d1f115de46feffb572652585be3",
      "updated_at": "2026-06-09T21:57:41.747299Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_diagonal_decomp/notes/green_formula_comparison.md",
      "preview": "# Encounter Green Formula Comparison ## Literature Formula and Conventions The comparison uses the finite-state Green/renewal identity behind the multi-target first-passage formalism."
    },
    {
      "path": "research/reports/encounter_reflecting_mean_validation/README.md",
      "category": "report_docs",
      "size": 3316,
      "sha256": "024860cd96f1834eb08cf83642c56cca6ea4feaf95650412e56150adfea861cf",
      "updated_at": "2026-06-09T21:57:41.747299Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_mean_validation/README.md",
      "preview": "# Reflecting Encounter Mean Validation This report validates the first exact-computation step for a one-dimensional two-walker encounter process with reflecting boundaries. ## Model - Interval: `{0, , L-1}`."
    },
    {
      "path": "research/reports/encounter_reflecting_mean_validation/code/reflecting_encounter.py",
      "category": "report_code",
      "size": 21682,
      "sha256": "1268d096f98c8f61514a6d3e2428d59e9d8d20b1a54c87b95c7ef789b03c83cb",
      "updated_at": "2026-06-09T21:57:41.749698Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_mean_validation/code/reflecting_encounter.py"
    },
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      "size": 6250,
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      "updated_at": "2026-06-09T21:57:41.749935Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_mean_validation/code/run_diagonal_smoke.py"
    },
    {
      "path": "research/reports/encounter_reflecting_mean_validation/code/run_smoke.py",
      "category": "report_code",
      "size": 5008,
      "sha256": "010a4a2dfd7edac563fcdb65f6d38686940ea3ee6876b17eed4ab34a92c7e3ab",
      "updated_at": "2026-06-09T21:57:41.749935Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/encounter_reflecting_mean_validation/code/run_smoke.py"
    },
    {
      "path": "research/reports/exact_recursion_method_guide/README.md",
      "category": "report_docs",
      "size": 1074,
      "sha256": "85ee5cb544ceda65fd2394b332314ce0914d153cc05fe747cbdb7ed30dcefe33",
      "updated_at": "2026-06-09T21:57:41.749935Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/exact_recursion_method_guide/README.md",
      "preview": "# Exact Recursion — Method Guide **Status: WIP scaffold (not yet started).** Tracking: [#9](https://github.com/zhouyi-xiaoxiao/valley-k-small/issues/9) Directory layout is in place"
    },
    {
      "path": "research/reports/final_multitimescale_fpt_encounter/README.md",
      "category": "report_docs",
      "size": 5113,
      "sha256": "72ad75d62f961d07cbe4118b80dd8afda1dab0e93a0ab7d3c4f680af1a38d7cc",
      "updated_at": "2026-06-09T21:57:41.750278Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/final_multitimescale_fpt_encounter/README.md",
      "preview": "# Final Multitimescale FPT and Encounter Report **Status: consistency layer.** This report indexes the accepted outputs for the multi-timescale first-passage and two-walker encounter project without regenerating raw scie"
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/final_multitimescale_fpt_encounter/artifacts/encounter_search/results/final_report.tex",
      "preview": "\\documentclass[10pt]{article} \\usepackage[a4paper,margin=0.72in]{geometry} \\usepackage{amsmath,amssymb} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage[hidelinks]{hyperref} \\usepackage{microtype} \\usepackage{enum"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/final_multitimescale_fpt_encounter/code/build_consistency_layer.py"
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      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=0.75in]{geometry} \\usepackage{amsmath,amssymb} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage[hidelinks]{hyperref} \\usepackage{enumitem} \\usepackage{tikz}"
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      "preview": "\\begin{tabular}{p{0.21\\linewidth}p{0.26\\linewidth}p{0.20\\linewidth}p{0.25\\linewidth}} \\toprule Setting & Observed range & Reference case & Mechanism/criterion \\\\ \\midrule Luca email configuration & \\(N=100\\), \\(n_0=1\\)"
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      "preview": "\\begin{tabular}{p{0.18\\linewidth}p{0.16\\linewidth}p{0.18\\linewidth}p{0.40\\linewidth}} \\toprule Module & Output & Mechanism & Supported claim \\\\ \\midrule luca\\_shortcut & K2\\_K4\\_beta001 & budget decomposition & In the Lu"
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      "preview": "\\begin{tabular}{p{0.18\\linewidth}p{0.16\\linewidth}p{0.18\\linewidth}p{0.40\\linewidth}} \\toprule Setting & Scan result & Configuration & Condition/claim \\\\ \\midrule 1D two-target ring scan & 34 double\\_peak cases in 240 ca"
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      "preview": "\\begin{tabular}{p{0.19\\linewidth}p{0.16\\linewidth}p{0.16\\linewidth}p{0.16\\linewidth}p{0.21\\linewidth}} \\toprule Module & Row max & Mass max & Decomp max & Status \\\\ \\midrule ring\\_two\\_target & 0.000000e+00 & 4.544976e-1"
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      "preview": "# 2D Two-Target Local-Bias Basin Experiment Plan Purpose: test whether a plain 2D reflecting rectangle, without corridor geometry, can produce a smoother near/far double-peak first-passage distribution by adding a local"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_bimodality/README.md",
      "preview": "# 2D Bimodality Report ## Quick reproduce From repo root: ``` MPLCONFIGDIR=research/reports/grid2d_bimodality/.mplcache \\ python3 research/reports/grid2d_bimodality/code/bimodality_2d_pipeline.py \\ --cases-json research/"
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    {
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_bimodality/manuscript/grid2d_bimodality_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{caption} \\usepackage{enumitem} \\usepack"
    },
    {
      "path": "research/reports/grid2d_bimodality/manuscript/grid2d_bimodality_en.tex",
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      "size": 32433,
      "sha256": "e721dc8428ae479a91ab62931c6c484b07290b5fe1fdd5d2bbaadeebab0dae63",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_bimodality/manuscript/grid2d_bimodality_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[hidelinks]{"
    },
    {
      "path": "research/reports/grid2d_bimodality/notes/repro_notes_v6.md",
      "category": "report_docs",
      "size": 1916,
      "sha256": "4d7535c3b8b2025916765f1b50e1bf030d54cab92317925d2af894faa9201000",
      "updated_at": "2026-06-09T21:57:41.847077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_bimodality/notes/repro_notes_v6.md",
      "preview": "# v6 Repro Notes (2D bimodality) This note is historical context for the v6 plotting pass. The active public interface is still: - `python3 scripts/reportctl.py run --report grid2d_bimodality -- ` - `python3 scripts/repo"
    },
    {
      "path": "research/reports/grid2d_blackboard_bimodality/README.md",
      "category": "report_docs",
      "size": 3163,
      "sha256": "cde54c6de5f2d5626930ecff0d4e8e1b7f5a47826198a0ff2c25c2cd4d377bea",
      "updated_at": "2026-06-09T21:57:41.847077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/README.md",
      "preview": "# 2D Blackboard-Style Bimodality Report This report follows the figure/layout style of `research/reports/grid2d_bimodality/` and `research/reports/grid2d_reflecting_bimodality/`, and currently focuses on the single case"
    },
    {
      "path": "research/reports/grid2d_blackboard_bimodality/code/blackboard_bimodality_pipeline.py",
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      "size": 404,
      "sha256": "a3fbef7d0d2d9d333062f18699c5cc1e291fe67a8cd140d15ed167b600054d1f",
      "updated_at": "2026-06-09T21:57:41.864077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/code/blackboard_bimodality_pipeline.py"
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      "size": 365,
      "sha256": "e670e95b35f50749d647e1ba83e072a451252fb2de4abae20a64a810e00df84e",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/code/model_core.py"
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/code/screenshot_scan.py"
    },
    {
      "path": "research/reports/grid2d_blackboard_bimodality/code/z_scan.py",
      "category": "report_code",
      "size": 418,
      "sha256": "869382efb1be1dfeb892cf5853f6f753df493650ff453d25006e0179c4f726d5",
      "updated_at": "2026-06-09T21:57:41.866135Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/code/z_scan.py"
    },
    {
      "path": "research/reports/grid2d_blackboard_bimodality/manuscript/grid2d_blackboard_bimodality_cn.tex",
      "category": "report_docs",
      "size": 12856,
      "sha256": "664d13c8b319b074fc77a7d663f2a860e5d17c3286d377e81595452ecd286fbf",
      "updated_at": "2026-06-09T21:57:41.868077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/manuscript/grid2d_blackboard_bimodality_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{caption} \\usepackage{enumitem} \\usepack"
    },
    {
      "path": "research/reports/grid2d_blackboard_bimodality/manuscript/grid2d_blackboard_bimodality_en.tex",
      "category": "report_docs",
      "size": 12843,
      "sha256": "e43c2307a808c56767baba002bdb962ca20915421e9e3eb606be78d0c6e82129",
      "updated_at": "2026-06-09T21:57:41.869077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_blackboard_bimodality/manuscript/grid2d_blackboard_bimodality_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[hidelinks]{"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/README.md",
      "category": "report_docs",
      "size": 914,
      "sha256": "27c5f3f2ae8d24ce2f3a293cd6205d2db6623a4d84d3540c5407c70a7060e4cb",
      "updated_at": "2026-06-09T21:57:41.869077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/README.md",
      "preview": "# grid2d_membrane_near_target New 2D extension report covering: - one-target corridor with symmetric/asymmetric semi-permeable membranes; - no-corridor two-target setting with one target near the start."
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_asymmetric_topcases.tex",
      "category": "report_docs",
      "size": 551,
      "sha256": "73e76bb5350b8ad71bc6bd10723befa189cbeb3d8a05b646e6dd3c5af312c769",
      "updated_at": "2026-06-09T21:57:41.875077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_asymmetric_topcases.tex",
      "preview": "\\begin{tabular}{@{}cccccc@{}} \\toprule $\\kappa_{\\uparrow}$ & $\\kappa_{\\downarrow}$ & phase & $t_{p1}$ & $t_{p2}$ & sep-score \\\\ \\midrule 0 & 0.0003 & 2 & 395 & 1711 & 1.85 \\\\ 0.0003 & 0 & 2 & 395 & 1710 & 1.85 \\\\ 0.0005"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_qstar_sensitivity.tex",
      "category": "report_docs",
      "size": 801,
      "sha256": "7683cdfaa7c04076507350656d7266ca5020b539fef4b24b8e3b3143b8fa9b17",
      "updated_at": "2026-06-09T21:57:41.876563Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_qstar_sensitivity.tex",
      "preview": "\\begin{tabular}{@{}lllc c@{}} \\toprule Case & $q^*$ & Window & dominant class & $w_{\\mathrm{L1R1}}$ \\\\ \\midrule sym & 0.4 & peak1 & L0R0 & 0.000 \\\\ sym & 0.4 & valley & L0R0 & 0.197 \\\\ sym & 0.4 & peak2 & L0R1 & 0.104 \\\\"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_symmetric_w16.tex",
      "category": "report_docs",
      "size": 1255,
      "sha256": "a1b1ab667a8cda60ec4c66089f5dc1fedf6177101e01141d678ccf31b5381865",
      "updated_at": "2026-06-09T21:57:41.876563Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_symmetric_w16.tex",
      "preview": "\\begin{tabular}{@{}cccccc@{}} \\toprule $\\kappa$ & phase & $t_{p1}$ & $t_{p2}$ & valley/max & sep-score \\\\ \\midrule 0 & 2 & 395 & 1711 & 0.058 & 1.87 \\\\ 0.0003 & 2 & 395 & 1710 & 0.061 & 1.84 \\\\ 0.0005 & 2 & 395 & 1708 &"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_window_classes.tex",
      "category": "report_docs",
      "size": 406,
      "sha256": "16af578532b02dd92aadc45eb9a3f08523bb6098867966f18e81455d3d1cb254",
      "updated_at": "2026-06-09T21:57:41.876563Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/membrane_window_classes.tex",
      "preview": "\\begin{tabular}{@{}lccccc@{}} \\toprule Window & Case & L0R0 & L0R1 & L1R0 & L1R1 \\\\ \\midrule peak1 & sym & 0.996 & 0.000 & 0.004 & 0.000 \\\\ peak1 & asym & 0.998 & 0.000 & 0.002 & 0.000 \\\\ valley & sym & 0.581 & 0.116 & 0"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/artifacts/tables/two_target_nearstart_summary.tex",
      "category": "report_docs",
      "size": 683,
      "sha256": "94ff3132e515008d9a3a3d9264dbcd3b49c7107753374219ce5520406d6d3a74",
      "updated_at": "2026-06-09T21:57:41.876563Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/two_target_nearstart_summary.tex",
      "preview": "\\begin{tabular}{@{}cccccc@{}} \\toprule $b_x$ & clear $d$ interval & best $d$ & phase(best) & $P(\\mathrm{near})$ & $P(\\mathrm{far})$ \\\\ \\midrule +0.00 & - & 3 & 0 & 0.867 & 0.087 \\\\ +0.02 & - & 2 & 0 & 0.603 & 0.383 \\\\ +0"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/artifacts/tables/two_target_no_corridor_clear_instance.tex",
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      "size": 426,
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/two_target_no_corridor_clear_instance.tex",
      "preview": "\\begin{tabular}{@{}cccccccccccccccc@{}} \\toprule spec & $b_x$ & $d$ & $\\Delta y$ & phase & sep-score & valley/max & $p_{\\min}$ & peak-ratio & peak-margin & min-margin & gate-pass & gate-slack & clear-score & showcase & $"
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      "size": 262,
      "sha256": "d4a07d721fa419961102f322cf1d8937ec66907964ee44111ac2bb5cdb7ec9db",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/artifacts/tables/two_target_rep_case.tex",
      "preview": "\\begin{tabular}{@{}cccccccccc@{}} \\toprule $b_x$ & $d$ & phase & $t_{p1}$ & $t_v$ & $t_{p2}$ & $P(\\mathrm{near})$ & $P(\\mathrm{far})$ & sep-score & clear-score \\\\ \\midrule +0.07 & 2 & 2 & 11 & 307 & 739 & 0.326 & 0.674 &"
    },
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      "preview": "\\begin{tabular}{@{}lcccccc@{}} \\toprule case & $q_{\\mathrm{far}}(x_s)$ & $P_{\\mathrm{far}}$ & $\\varepsilon_{\\mathrm{split}}$ & $\\|r_{\\mathrm{int}}\\|_\\infty$ & $\\|r_{\\mathrm{near}}\\|_\\infty$ & $\\|r_{\\mathrm{far}}\\|_\\infty"
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    {
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      "category": "report_code",
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      "updated_at": "2026-06-09T21:57:41.876563Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/code/membrane_near_target_report.py"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/manuscript/grid2d_membrane_near_target_cn.tex",
      "category": "report_docs",
      "size": 25379,
      "sha256": "a2bb80539a2969792e51f2acfb5dd0ca8841ad424b69b7c2becc5736831eacf0",
      "updated_at": "2026-06-09T21:57:41.878077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/manuscript/grid2d_membrane_near_target_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepack"
    },
    {
      "path": "research/reports/grid2d_membrane_near_target/manuscript/grid2d_membrane_near_target_en.tex",
      "category": "report_docs",
      "size": 25790,
      "sha256": "473bebaecff15790165e3784ce5ff82e2fd3442c2058a9c67b4e06aeedbae707",
      "updated_at": "2026-06-09T21:57:41.880077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_membrane_near_target/manuscript/grid2d_membrane_near_target_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[table]{xcol"
    },
    {
      "path": "research/reports/grid2d_one_target_base/README.md",
      "category": "report_docs",
      "size": 2178,
      "sha256": "93e0b7b28419b0a27ffe3aa423f7927f956875e8df83fd760e9565efec3fffe6",
      "updated_at": "2026-06-09T21:57:41.880077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_base/README.md",
      "preview": "# Grid2D One Target — Base **Status: WIP scaffold (not yet started).** Tracking: [#4](https://github.com/zhouyi-xiaoxiao/valley-k-small/issues/4) This is the **mother report** for the `grid2d_one_target_*` sub-series."
    },
    {
      "path": "research/reports/grid2d_one_target_exit_timing/README.md",
      "category": "report_docs",
      "size": 1153,
      "sha256": "7e1425c5b4be00a4e25156cdab99522d4ab8b03af944a798dd2a9080c0ffee85",
      "updated_at": "2026-06-09T21:57:41.881431Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_exit_timing/README.md",
      "preview": "# Grid2D One Target — Exit Timing **Status: WIP scaffold (not yet started).** Tracking: [#5](https://github.com/zhouyi-xiaoxiao/valley-k-small/issues/5) Directory layout is in place"
    },
    {
      "path": "research/reports/grid2d_one_target_valley_peak_budget/README.md",
      "category": "report_docs",
      "size": 2685,
      "sha256": "9f239b94389c5bfda3bae01fa24f8f399a847f559fe841901f2ff7b67690b484",
      "updated_at": "2026-06-09T21:57:41.881722Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_valley_peak_budget/README.md",
      "preview": "# Grid2D One Target — Valley/Peak Budget **Status: 3-page short report. Manuscript landed; code and notes still pending.** Tracking: [#6](https://github.com/zhouyi-xiaoxiao/valley-k-small/issues/6)."
    },
    {
      "path": "research/reports/grid2d_one_target_valley_peak_budget/code/build_budget_bar_figures.py",
      "category": "report_code",
      "size": 13651,
      "sha256": "b43942152ed692c5fb7313b0d642d4a725a8ae0ed69978b1922ef7cbecd55c3c",
      "updated_at": "2026-06-09T21:57:41.882576Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_valley_peak_budget/code/build_budget_bar_figures.py"
    },
    {
      "path": "research/reports/grid2d_one_target_valley_peak_budget/manuscript/grid2d_one_target_valley_peak_budget_cn.tex",
      "category": "report_docs",
      "size": 5797,
      "sha256": "499b8761fb9d42e2a5107574aed24cb05a0dbb5196483546ef3cc53a2343e561",
      "updated_at": "2026-06-09T21:57:41.882719Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_valley_peak_budget/manuscript/grid2d_one_target_valley_peak_budget_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{caption} \\usepackage[hidelinks]{hyperref} \\usepackage{microty"
    },
    {
      "path": "research/reports/grid2d_one_target_valley_peak_budget/manuscript/grid2d_one_target_valley_peak_budget_en.tex",
      "category": "report_docs",
      "size": 6750,
      "sha256": "c8025aea2380ffbdcb3903fb54d04d317588170e15bba9089fa63a030078d694",
      "updated_at": "2026-06-09T21:57:41.882719Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_valley_peak_budget/manuscript/grid2d_one_target_valley_peak_budget_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{caption} \\usepackage[hidelinks]{hyperref} \\usepackage{microtype} \\setlength{"
    },
    {
      "path": "research/reports/grid2d_one_target_window_measures/README.md",
      "category": "report_docs",
      "size": 1170,
      "sha256": "bfebee19a99e8a387704bf6c5f7c72a1afd9e09e9931fff83a2b3cbbe7ee4fa1",
      "updated_at": "2026-06-09T21:57:41.882719Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_target_window_measures/README.md",
      "preview": "# Grid2D One Target — Window Measures **Status: WIP scaffold (not yet started).** Tracking: [#7](https://github.com/zhouyi-xiaoxiao/valley-k-small/issues/7) Directory layout is in place"
    },
    {
      "path": "research/reports/grid2d_one_two_target_gating/README.md",
      "category": "report_docs",
      "size": 1230,
      "sha256": "983b6f857ef164e857961c881659945bd31faba67f18eab274f4b69c97dcb6da",
      "updated_at": "2026-06-09T21:57:41.883077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_one_two_target_gating/README.md",
      "preview": "# Grid2D One vs Two Target — Gating **Status: WIP scaffold (not yet started).** Tracking: [#8](https://github.com/zhouyi-xiaoxiao/valley-k-small/issues/8) Directory layout is in place"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/README.md",
      "category": "report_docs",
      "size": 1452,
      "sha256": "95478c55eb51c98905c6f7823b52032cabce755139ab583d596b560be2acedda",
      "updated_at": "2026-06-09T21:57:41.884409Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/README.md",
      "preview": "# 2D Rectangle Bimodality (Two-Target + One-Target Corridor) This report studies when **non-square rectangular** 2D domains can produce a visible **double peak** in first-passage time (FPT) distributions, in two settings"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/ot_anchor_selection.tex",
      "category": "report_docs",
      "size": 215,
      "sha256": "b907f703300e642c3e04bbafc8a610edd9a3db6d0ce00d35bc0433e9bfb853ea",
      "updated_at": "2026-06-09T21:57:41.925077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/ot_anchor_selection.tex",
      "preview": "\\begin{tabular}{rrrrccc} \\toprule $x_s$ & $x_t$ & $b_x^{*}$ & $W_y^{\\mathrm{ref}}$ & phase(ref) & clear interval(s) & first loss \\\\ \\midrule 7 & 58 & -0.080 & 12 & 2 & 8-16 (step=2) & 18 \\\\ \\bottomrule \\end{tabular}"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/ot_bias2d_phase_overview.tex",
      "category": "report_docs",
      "size": 286,
      "sha256": "fd9260bad72fe6b8f11b63c0e6fc0818c33284fd08ca7ed09c6447afb77066c1",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/ot_bias2d_phase_overview.tex",
      "preview": "\\begin{tabular}{rccccc} \\toprule $b_y$ & $b_x=-0.12$ & $b_x=-0.08$ & $b_x=-0.04$ & $b_x=0.00$ & $b_x=0.08$ \\\\ \\midrule -0.08 & 1 & 1 & 1 & 0 & 0 \\\\ -0.04 & 1 & 2 & 1 & 0 & 0 \\\\ 0.00 & 1 & 2 & 0 & 0 & 0 \\\\ 0.04 & 1 & 2 &"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/ot_corridor_width_summary.tex",
      "category": "report_docs",
      "size": 304,
      "sha256": "392d4369c53270288e99a3bc91ba147282ad1d2eb1803865a727634ba4aa83b2",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/ot_corridor_width_summary.tex",
      "preview": "\\begin{tabular}{rccccc} \\toprule $h$ & band width & phase2 @ $b_x=-0.08$ & first loss & phase$\\ge1$ @ $b_x=-0.12$ & phase$\\ge1$ @ $b_x=+0.00$ \\\\ \\midrule 0 & 1 & - & - & 8-28 & - \\\\ 1 & 3 & 8-16 & 18 & 8-28 & - \\\\ 2 & 5"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/ot_representative_metrics.tex",
      "category": "report_docs",
      "size": 331,
      "sha256": "a5751f6953f46aa154f38de6f095448ccd91d90accdaf42cdaf34c0f9be4b95c",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/ot_representative_metrics.tex",
      "preview": "\\begin{tabular}{lrrrrr} \\toprule ID & $W_y$ & $b_x$ & phase & valley/max & sep-score \\\\ \\midrule OT\\_W16\\_bxm0p080 & 16 & -0.080 & 2 & 0.081 & 1.05 \\\\ OT\\_W28\\_bxm0p080 & 28 & -0.080 & 1 & 0.056 & 0.77 \\\\ OT\\_W28\\_bxm0p1"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/ot_scan_overview.tex",
      "category": "report_docs",
      "size": 431,
      "sha256": "75ec230ee17ece851c5591ecc0f79e7fb9a312b84cee105b40aeae84d30b175b",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/ot_scan_overview.tex",
      "preview": "\\begin{tabular}{rccccc} \\toprule $W_y$ & $b_x=-0.12$ & $b_x=-0.08$ & $b_x=-0.04$ & $b_x=0.00$ & $b_x=0.08$ \\\\ \\midrule 8 & 1 & 2 & 0 & 0 & 0 \\\\ 10 & 1 & 2 & 0 & 0 & 0 \\\\ 12 & 1 & 2 & 0 & 0 & 0 \\\\ 14 & 1 & 2 & 0 & 0 & 0 \\"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/tt_critical_width_by_xstart.tex",
      "category": "report_docs",
      "size": 220,
      "sha256": "9c75ff64ab30a9388b5c5005878f6204e80ecab3fb19255ed6c87e995761b8de",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/tt_critical_width_by_xstart.tex",
      "preview": "\\begin{tabular}{rcccc} \\toprule $x_0$ & clear interval(s) & upper clear branch & first loss width & phase at loss \\\\ \\midrule 8 & - & - & - & - \\\\ 10 & 5-6 & 5-6 & 7 & 1 \\\\ 12 & 5 & 5 & 6 & 1 \\\\ \\bottomrule \\end{tabular}"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/tt_representative_metrics.tex",
      "category": "report_docs",
      "size": 288,
      "sha256": "82a6b95ba6ec5d504f0ce66a67f8a5fa9b712da4460831da1bf548429ca30f3b",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/tt_representative_metrics.tex",
      "preview": "\\begin{tabular}{lrrrrrr} \\toprule ID & $W_y$ & $x_0$ & phase & $P(m_1)$ & $P(m_2)$ & sep-score \\\\ \\midrule TT\\_W05\\_X10 & 5 & 10 & 2 & 0.561 & 0.439 & 1.42 \\\\ TT\\_W05\\_X12 & 5 & 12 & 2 & 0.544 & 0.456 & 1.29 \\\\ TT\\_W06\\_"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/tt_scan_overview.tex",
      "category": "report_docs",
      "size": 674,
      "sha256": "6fc1e86c4b895b9f73defe49764099d7c9233caf4d1db3037c1aec41b1940daf",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/tt_scan_overview.tex",
      "preview": "\\begin{tabular}{rcccc} \\toprule $W_y$ & n(single) & n(weak) & n(clear) & best $\\min(p_1,p_2)$ \\\\ \\midrule 5 & 6 & 0 & 3 & 0.456 \\\\ 6 & 6 & 0 & 3 & 0.444 \\\\ 7 & 7 & 0 & 2 & 0.411 \\\\ 8 & 8 & 0 & 1 & 0.374 \\\\ 9 & 8 & 0 & 1"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/artifacts/tables/tt_width_sweep_metrics.tex",
      "category": "report_docs",
      "size": 461,
      "sha256": "02e5aa2b5c7a087681dfa5c311108bed71ecf5e2d0e1dc4048e5e20741015f89",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/artifacts/tables/tt_width_sweep_metrics.tex",
      "preview": "\\begin{tabular}{lrrrrrrr} \\toprule ID & $W_y$ & $x_0$ & phase & $t_{p1}$ & $t_{p2}$ & $p_{\\min}/p_{\\max}$ & valley/max \\\\ \\midrule TT\\_W05\\_X10 & 5 & 10 & 2 & 67 & 798 & 0.148 & 0.114 \\\\ TT\\_W06\\_X10 & 6 & 10 & 2 & 72 &"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/code/rect_bimodality_report.py",
      "category": "report_code",
      "size": 572,
      "sha256": "dd90a97f530044ce13ce6346c9257acbf27a823b98d933ef2de6d9f1e1db28d0",
      "updated_at": "2026-06-09T21:57:41.926544Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/code/rect_bimodality_report.py"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/manuscript/grid2d_rect_bimodality_cn.tex",
      "category": "report_docs",
      "size": 21861,
      "sha256": "e6b9a9f8eb6081cb29e19748d1be01672a77f4966931753517fca71895246a79",
      "updated_at": "2026-06-09T21:57:41.928077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/manuscript/grid2d_rect_bimodality_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepack"
    },
    {
      "path": "research/reports/grid2d_rect_bimodality/manuscript/grid2d_rect_bimodality_en.tex",
      "category": "report_docs",
      "size": 20935,
      "sha256": "2daf12484471c0134c4e0efb69a7bb784d77c45a3d15d25161139dc51358d1d1",
      "updated_at": "2026-06-09T21:57:41.928077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_rect_bimodality/manuscript/grid2d_rect_bimodality_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[table]{xcol"
    },
    {
      "path": "research/reports/grid2d_reflecting_bimodality/README.md",
      "category": "report_docs",
      "size": 2929,
      "sha256": "72ff6be5972f6da991bb465b5197d32f2ee214c3e21b7ad47c6e2a06bed8c92f",
      "updated_at": "2026-06-09T21:57:41.928077Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_reflecting_bimodality/README.md",
      "preview": "# 2D Reflecting-Boundary Bimodality Report This report mirrors `research/reports/grid2d_bimodality/` but replaces all periodic boundaries with reflecting boundaries and adds reflecting-boundary constructions (R1--R7 plus"
    },
    {
      "path": "research/reports/grid2d_reflecting_bimodality/code/benchmark_aw_exact.py",
      "category": "report_code",
      "size": 9011,
      "sha256": "18c98ea0051986db712a5b34840b2b1dc32dbe655f6e83cd08194d3fca0313f5",
      "updated_at": "2026-06-09T21:57:41.964078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_reflecting_bimodality/code/benchmark_aw_exact.py"
    },
    {
      "path": "research/reports/grid2d_reflecting_bimodality/code/model_core.py",
      "category": "report_code",
      "size": 365,
      "sha256": "59c3d75ef6dc8ec8d11208bcbd1b6df56084f9c494f5b98cdb692fa8855e667f",
      "updated_at": "2026-06-09T21:57:41.965492Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_reflecting_bimodality/code/model_core.py"
    },
    {
      "path": "research/reports/grid2d_reflecting_bimodality/code/reflecting_bimodality_pipeline.py",
      "category": "report_code",
      "size": 404,
      "sha256": "c0233f2ad9c929c82617dae78da60c0006cdd232759b92585431394eada87893",
      "updated_at": "2026-06-09T21:57:41.965492Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_reflecting_bimodality/code/reflecting_bimodality_pipeline.py"
    },
    {
      "path": "research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_cn.tex",
      "category": "report_docs",
      "size": 48307,
      "sha256": "6c0aca26a24e9445da637b3e5fb5114585ec86d8cf2b9b73ffe55fc40b93e937",
      "updated_at": "2026-06-09T21:57:41.981078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{caption} \\usepackage{enumitem} \\usepack"
    },
    {
      "path": "research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_en.tex",
      "category": "report_docs",
      "size": 48015,
      "sha256": "01449b76efa81b14ae479ea222c6b71a8a6f0c6906f150c0f9092ee9494f362e",
      "updated_at": "2026-06-09T21:57:41.983078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[hidelinks]{"
    },
    {
      "path": "research/reports/grid2d_two_target_bias_radius/README.md",
      "category": "report_docs",
      "size": 3037,
      "sha256": "bbf92981585087a96fa885ea4618f0e977536963d0682a61d9925af72c7c1e7b",
      "updated_at": "2026-06-09T21:57:41.983078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_bias_radius/README.md",
      "preview": "# Grid2D Two-Target Bias-Radius Scaffold This WIP report prepares the 2D two-target scan where the start and far target are fixed and the near target is placed by radius and angle relative to a bias direction."
    },
    {
      "path": "research/reports/grid2d_two_target_bias_radius/code/run_small_heatmap.py",
      "category": "report_code",
      "size": 17871,
      "sha256": "dc2f3497cf2fd40cfc353a3d48ad404b080551bf12e178c857ceffcc16816bdc",
      "updated_at": "2026-06-09T21:57:41.985016Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_bias_radius/code/run_small_heatmap.py"
    },
    {
      "path": "research/reports/grid2d_two_target_bias_radius/code/run_smoke.py",
      "category": "report_code",
      "size": 5017,
      "sha256": "914d66564de3b7567c48bbec62df7c90e2d2a0a61dd76bfb3ecbaf81474aed55",
      "updated_at": "2026-06-09T21:57:41.985519Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_bias_radius/code/run_smoke.py"
    },
    {
      "path": "research/reports/grid2d_two_target_bias_radius/notes/SUMMARY.md",
      "category": "report_docs",
      "size": 1808,
      "sha256": "03677f5e7ee4beb71e2c26bcfc612292422d9e21ca1bf77a519470cb3d0904df",
      "updated_at": "2026-06-09T21:57:41.985519Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_bias_radius/notes/SUMMARY.md",
      "preview": "# Grid2D Bias-Radius Small Heatmap Summary This bounded scan fixes `theta=0`, so near targets lie along the global eastward bias direction."
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/README.md",
      "category": "report_docs",
      "size": 4508,
      "sha256": "d87b565e76a02c3d83e613632e4f10cb1562be3008b8a3b33fc6d5521550af0d",
      "updated_at": "2026-06-09T21:57:41.985519Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/README.md",
      "preview": "# 2D Two-Target Double-Peak (Reflecting Boundary) This report studies when a 2D lazy random walk with **two absorbing targets** can produce a visible double peak in \\(F_{n_0\\to(m_1;m_2)}(t)\\), under reflecting boundaries"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/artifacts/tables/case_mechanism.tex",
      "category": "report_docs",
      "size": 349,
      "sha256": "fc8345434925fe95de80c3f36dd25ab9aa709c836bc601ca3b93f8430fb6c4c9",
      "updated_at": "2026-06-09T21:57:42.019078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/artifacts/tables/case_mechanism.tex",
      "preview": "\\begin{tabular}{lcccccc} \\toprule Case & $t^*_{m_1|m_2}$ & $t^*_{m_2|m_1}$ & $t_v$ & valley/max & absorbed@6000 & tail@6000 \\\\ \\midrule C1 & 35 & 287 & 143 & 0.194 & 0.851 & 0.149 \\\\ C2 & 36 & 316 & 152 & 0.176 & 0.949 &"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/artifacts/tables/case_metrics.tex",
      "category": "report_docs",
      "size": 406,
      "sha256": "fcb565b2d927cdf006c140cc0f16e08221201e81743f77201acafd34c78fce19",
      "updated_at": "2026-06-09T21:57:42.020578Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/artifacts/tables/case_metrics.tex",
      "preview": "\\begin{tabular}{lcccccccc} \\toprule Case & $w_2$ & skip2 & $t_{p1}$ & $t_{p2}$ & $h_1$ & $h_2$ & $P(m_1)$ & $P(m_2)$ \\\\ \\midrule C1 & 3 & 2 & 35 & 284 & 7.77e-04 & 6.46e-04 & 0.363 & 0.488 \\\\ C2 & 2 & 1 & 36 & 313 & 7.94"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/artifacts/tables/case_separation.tex",
      "category": "report_docs",
      "size": 354,
      "sha256": "13b017d5bc04628d33e1a4ace71b0a30b1953abd2338b500ad85525f25fc9bc2",
      "updated_at": "2026-06-09T21:57:42.020578Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/artifacts/tables/case_separation.tex",
      "preview": "\\begin{tabular}{lccccc} \\toprule Case & $t^*_{m_1|m_2}$ & $t^*_{m_2|m_1}$ & $w_{1/2}^{(1)}$ & $w_{1/2}^{(2)}$ & $|\\Delta t^*|/(w_{1/2}^{(1)}+w_{1/2}^{(2)})$ \\\\ \\midrule C1 & 35 & 287 & 25.0 & 141.5 & 1.514 \\\\ C2 & 36 & 3"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/artifacts/tables/sparse_testset_configs.tex",
      "category": "report_docs",
      "size": 305,
      "sha256": "d35993c1699c2cc0cd6bce3b676308f2999c90aef5e177f0204af22252366c05",
      "updated_at": "2026-06-09T21:57:42.020578Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/artifacts/tables/sparse_testset_configs.tex",
      "preview": "\\begin{tabular}{lp{0.35\\linewidth}lcccc} \\toprule ID & Name & Type & local-bias & sticky & barriers & shortcuts \\\\ \\midrule S02 & corridor thin w2 1 skip2 0 & corridor\\_model & 160 & 0 & 0 & 0 \\\\ S03 & centerline only bi"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/artifacts/tables/sparse_testset_metrics.tex",
      "category": "report_docs",
      "size": 258,
      "sha256": "7214cc8ff0badaee5d03d8e62662b2da1435c9f96f8795f66aea8791dcd10410",
      "updated_at": "2026-06-09T21:57:42.020578Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/artifacts/tables/sparse_testset_metrics.tex",
      "preview": "\\begin{tabular}{lccccccc} \\toprule ID & $t_{p1}$ & $t_{p2}$ & valley/max & $P(m_1)$ & $P(m_2)$ & sep-score & phase \\\\ \\midrule S02 & 38 & 436 & 0.235 & 0.233 & 0.740 & 1.17 & 2 \\\\ S03 & 38 & 925 & 0.217 & 0.411 & 0.511 &"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/code/compare_numeric_methods.py",
      "category": "report_code",
      "size": 30820,
      "sha256": "322b7275f11c6ea82931c99c8d14eb912a97aca25d3e1f7ee275895b7d5e6fb4",
      "updated_at": "2026-06-09T21:57:42.020578Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/code/compare_numeric_methods.py"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/code/luca_fast_case.py",
      "category": "report_code",
      "size": 12328,
      "sha256": "d746c34ceec5299d5afb3365efd6c071931fc64a3a34bf5314c264bc9c937c71",
      "updated_at": "2026-06-09T21:57:42.020900Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/code/luca_fast_case.py"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/code/two_target_2d_report.py",
      "category": "report_code",
      "size": 85312,
      "sha256": "efda4988aa6659b3f4fc844eafb37f5b64902df01d3fd8e13feabd1f6b4fbfe2",
      "updated_at": "2026-06-09T21:57:42.020900Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/code/two_target_2d_report.py"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/manuscript/extras/method_comparison_cn.tex",
      "category": "report_docs",
      "size": 15430,
      "sha256": "f8c5e474b6f67a454bb96344bd2ccd725aaa351c09bebaf721acd6626ea62374",
      "updated_at": "2026-06-09T21:57:42.022206Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/manuscript/extras/method_comparison_cn.tex",
      "preview": "\\documentclass[11pt,a4paper]{ctexart} \\usepackage{geometry} \\geometry{margin=2.2cm} \\usepackage{amsmath,amssymb} \\usepackage{booktabs} \\usepackage{siunitx} \\usepackage{graphicx} \\usepackage{array} \\usepackage[hypertexnam"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/manuscript/extras/method_comparison_en.tex",
      "category": "report_docs",
      "size": 15030,
      "sha256": "e8a3f31444e2247a0e0d42d46b45f91019c38fd7d1dac79a6928788ea5e13a56",
      "updated_at": "2026-06-09T21:57:42.022206Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/manuscript/extras/method_comparison_en.tex",
      "preview": "\\documentclass[11pt,a4paper]{article} \\usepackage[margin=2.2cm]{geometry} \\usepackage{amsmath,amssymb} \\usepackage{booktabs} \\usepackage{array} \\usepackage{siunitx} \\usepackage{graphicx} \\usepackage[hypertexnames=false]{"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/manuscript/grid2d_two_target_double_peak_cn.tex",
      "category": "report_docs",
      "size": 20854,
      "sha256": "89cf713548a8d4c360367dd694d7a9cf89da7529666f01a66ef6a74ed09e8ecd",
      "updated_at": "2026-06-09T21:57:42.025079Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/manuscript/grid2d_two_target_double_peak_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepack"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/manuscript/grid2d_two_target_double_peak_en.tex",
      "category": "report_docs",
      "size": 11806,
      "sha256": "f49ac6981904967ec5d0d43db4159b5e93baecd1cb3e0d93c02de01dd8a65515",
      "updated_at": "2026-06-09T21:57:42.025079Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/manuscript/grid2d_two_target_double_peak_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[table]{xcol"
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/notes/luca_fast_case_cn.md",
      "category": "report_docs",
      "size": 1583,
      "sha256": "ffe237b728858a1c88913ad5345313b5bc823211fb321272f87d4791766c807d",
      "updated_at": "2026-06-09T21:57:42.025079Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/notes/luca_fast_case_cn.md",
      "preview": "# Luca Fast Case (Constructed Benchmark) ## 1. Goal Construct a reproducible setup where Luca/Giuggioli defect-reduced inversion is faster than all comparison methods in this benchmark file. ## 2."
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/notes/method_comparison_cn.md",
      "category": "report_docs",
      "size": 4966,
      "sha256": "220555cea0b0d4d791629086cf96cd18327ea0e7390ecaf843f5dae44c3f940d",
      "updated_at": "2026-06-09T21:57:42.026792Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/notes/method_comparison_cn.md",
      "preview": "# 2D Two-Target 数值方法比较报告（C1 配置） ## 1. 研究目标 在 `2d_two_target_double_peak` 的同一模型设定下，对比五种常用数值路线： 1. 时间域 sparse exact 递推（当前主脚本用法） 2. 时间域 dense 递推（显式 transient 矩阵 Q） 3. 生成函数 AW/Cauchy-FFT 反演（离散 PGF 反演） 4."
    },
    {
      "path": "research/reports/grid2d_two_target_double_peak/notes/method_comparison_en.md",
      "category": "report_docs",
      "size": 6543,
      "sha256": "d64742c9ec5bee4b70c2f3952e10fe60c975f1893fbdddc081639df8909f909f",
      "updated_at": "2026-06-09T21:57:42.026792Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_target_double_peak/notes/method_comparison_en.md",
      "preview": "# 2D Two-Target Numerical Method Comparison (C1 Configuration) ## 1. Objective Under the same `2d_two_target_double_peak` model setup, compare five numerical approaches: 1."
    },
    {
      "path": "research/reports/grid2d_two_walker_encounter_shortcut/README.md",
      "category": "report_docs",
      "size": 1437,
      "sha256": "87950ca50b6133c8f05a7f210ef7e69d8f9cb14868b8f1201938871dec0cee36",
      "updated_at": "2026-06-09T21:57:42.026792Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_walker_encounter_shortcut/README.md",
      "preview": "# 2D Two-Walker Encounter With Shortcut This report extends the existing bimodality workflow to **two walkers** on a 2D reflecting lattice with directed shortcuts."
    },
    {
      "path": "research/reports/grid2d_two_walker_encounter_shortcut/artifacts/tables/a1a8_test_table.tex",
      "category": "report_docs",
      "size": 444,
      "sha256": "ec368bc6c39a4db0a9518612476acebd3125c40cc8306fc456ba18328e816170",
      "updated_at": "2026-06-09T21:57:42.028922Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_walker_encounter_shortcut/artifacts/tables/a1a8_test_table.tex",
      "preview": "\\begin{tabular}{lcccccc} \\toprule Case & $(N,q)$ & $z$ & $M$ & $r$ & $|LHS-RHS|$ & rel.err \\\\ \\midrule R1\\_real\\_small & (16,0.30) & $0.40+0.00i$ & 128 & 0.632 & 8.13e-18 & 8.13e-18 \\\\ R2\\_complex & (12,0.35) & $0.30+0.1"
    },
    {
      "path": "research/reports/grid2d_two_walker_encounter_shortcut/artifacts/tables/encounter_scan_table.tex",
      "category": "report_docs",
      "size": 668,
      "sha256": "05ce4382e4c598d754f5620a10f2cbbc01172901aed416d5859d01b430176b4d",
      "updated_at": "2026-06-09T21:57:42.029023Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_walker_encounter_shortcut/artifacts/tables/encounter_scan_table.tex",
      "preview": "\\begin{tabular}{ccccccc} \\toprule $\\beta$ & phase & $t_1$ & $t_2$ & peak ratio & valley ratio & bimodal \\\\ \\midrule 0.00 & 0 & - & - & 0.000 & 1.000 & 0 \\\\ 0.05 & 0 & - & - & 0.000 & 1.000 & 0 \\\\ 0.10 & 0 & - & - & 0.000"
    },
    {
      "path": "research/reports/grid2d_two_walker_encounter_shortcut/code/two_walker_encounter_report.py",
      "category": "report_code",
      "size": 31558,
      "sha256": "4d76914d2efd5161ee097a31d5844cc78030ae97c96073e520056af07757cc1e",
      "updated_at": "2026-06-09T21:57:42.029023Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_walker_encounter_shortcut/code/two_walker_encounter_report.py"
    },
    {
      "path": "research/reports/grid2d_two_walker_encounter_shortcut/manuscript/grid2d_two_walker_encounter_shortcut_cn.tex",
      "category": "report_docs",
      "size": 6147,
      "sha256": "db802df374a203cef1ebd110ec41e325073b00ab4925e16cab11fcc3113b41cd",
      "updated_at": "2026-06-09T21:57:42.029629Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_walker_encounter_shortcut/manuscript/grid2d_two_walker_encounter_shortcut_cn.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,mathtools} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{float} \\usepackage{xcolor} \\usepackage{hyperref} \\use"
    },
    {
      "path": "research/reports/grid2d_two_walker_encounter_shortcut/manuscript/grid2d_two_walker_encounter_shortcut_en.tex",
      "category": "report_docs",
      "size": 7646,
      "sha256": "c92493994e8856b75bf0cc05ff22001359c0c8663fdfad8deca307460bfb4023",
      "updated_at": "2026-06-09T21:57:42.030078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/grid2d_two_walker_encounter_shortcut/manuscript/grid2d_two_walker_encounter_shortcut_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,mathtools} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{float} \\usepackage{xcolor} \\usepackage{hyperref} \\use"
    },
    {
      "path": "research/reports/ring_deriv_k2/README.md",
      "category": "report_docs",
      "size": 467,
      "sha256": "819362d37c813fe27d465ecb2a6fd38aa576c8ac8038a9f6d8acaddb7a8e6147",
      "updated_at": "2026-06-09T21:57:42.030078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_deriv_k2/README.md",
      "preview": "# ring_deriv_k2 K=2 derivation notes for the ring lattice, plus companion PDFs. ## Manuscript - `manuscript/ring_deriv_k2_en.tex` (+ `.pdf`) — primary derivation - `manuscript/extras/note_k2.tex`, `manuscript/extras/note"
    },
    {
      "path": "research/reports/ring_deriv_k2/manuscript/extras/note_k2.tex",
      "category": "report_docs",
      "size": 20211,
      "sha256": "5a1347203bb9c85f4b5567d45d58a70600816942e871fa280258bb39f4ef6f2e",
      "updated_at": "2026-06-09T21:57:42.032881Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_deriv_k2/manuscript/extras/note_k2.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage{amsmath,amssymb,amsfonts,bm} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{mathtools} \\usepackage{hyperref} % Chebyshev \\newcommand{\\T}{\\mathcal{T}} \\newcommand{\\U}{\\math"
    },
    {
      "path": "research/reports/ring_deriv_k2/manuscript/extras/note_rewire_lazy.tex",
      "category": "report_docs",
      "size": 30806,
      "sha256": "c9107fb7c765b7ba47b7d41f351122e85ab05b4edf0793acf23522744cd020be",
      "updated_at": "2026-06-09T21:57:42.033078Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_deriv_k2/manuscript/extras/note_rewire_lazy.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage{amsmath,amssymb,amsfonts,bm} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{mathtools} \\usepackage{hyperref} \\usepackage{physics} \\setlength{\\emergencystretch}{4em} % Cheb"
    },
    {
      "path": "research/reports/ring_deriv_k2/manuscript/ring_deriv_k2_en.tex",
      "category": "report_docs",
      "size": 30806,
      "sha256": "c9107fb7c765b7ba47b7d41f351122e85ab05b4edf0793acf23522744cd020be",
      "updated_at": "2026-06-09T21:57:42.034079Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_deriv_k2/manuscript/ring_deriv_k2_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage{amsmath,amssymb,amsfonts,bm} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{mathtools} \\usepackage{hyperref} \\usepackage{physics} \\setlength{\\emergencystretch}{4em} % Cheb"
    },
    {
      "path": "research/reports/ring_lazy_flux/README.md",
      "category": "report_docs",
      "size": 73,
      "sha256": "a9b961de9a1d14560572bd2f69a11516dd84b2c1a7f6439f33290b70c9430b9f",
      "updated_at": "2026-06-09T21:57:42.034079Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_flux/README.md",
      "preview": "# ring_lazy_flux This report studies lazy ring flux bimodality (CN/EN)."
    },
    {
      "path": "research/reports/ring_lazy_flux/artifacts/tables/lazy_K2_equal4_paper_geometry_summary_cn.tex",
      "category": "report_docs",
      "size": 545,
      "sha256": "e910bbcb9233f8234ccd1af530d008d3c6632bea2167c178de4bcaa6904a4168",
      "updated_at": "2026-06-09T21:57:42.049079Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_flux/artifacts/tables/lazy_K2_equal4_paper_geometry_summary_cn.tex",
      "preview": "\\begin{table}[!htbp] \\centering \\small \\begin{tabular}{rrrrrr} \\toprule $N$ & $u$ & $v$ & paper & macro & $t_\\mathrm{peak}$\\\\ \\midrule 20 & 6 & 11 & 0 & 0 & 34\\\\ 50 & 6 & 26 & 0 & 0 & 27\\\\ 100 & 6 & 51 & 0 & 0 & 27\\\\ 160"
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      "preview": "\\begin{longtable}{rrrrrrr} \\caption{完整扫描表（等概率基准 $q=2/3$，取 $\\beta=0.02$ 使 $p=0.006666\\ldots$，起点 $n_0=1$，shortcut 取 $u=n_0\\to v=\\mathrm{target}$）。paper/macro 为 0/1；$d$ 为 $n_0$ 到终点的环距离"
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      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs,longtable} \\usepackage{pdfpages} \\usepackage[hidelinks]{hyperref} \\"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump/README.md",
      "preview": "# ring_lazy_jump Jump-over bimodality mechanisms on the lazy ring (bilingual CN/EN). ## Lineage - **Predecessor:** none — this is the base report of the lazy-jump series."
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      "preview": "\\begin{table}[!htbp] \\centering \\small \\begin{tabular}{rrrrrr} \\toprule $\\beta$ & $p$ & paper & macro & $t_1$ & $t_2$\\\\ \\midrule 0 & 0 & 0 & 0 & -- & --\\\\ 0.0005 & 0.000166667 & 1 & 1 & 54 & 1243\\\\ 0.001 & 0.000333333 &"
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      "preview": "\\begin{table}[!htbp] \\centering \\small \\begin{tabular}{rrrrrr} \\toprule $\\beta$ & $p$ & paper & macro & $t_1$ & $t_2$\\\\ \\midrule 0 & 0 & 0 & 0 & -- & --\\\\ 0.0005 & 0.000166667 & 1 & 1 & 54 & 1243\\\\ 0.001 & 0.000333333 &"
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      "preview": "\\begin{table}[!htbp] \\centering \\small \\begin{tabular}{rrrrrr} \\toprule $\\beta$ & $p$ & paper & macro & $t_1$ & $t_2$\\\\ \\midrule 0 & 0 & 0 & 0 & -- & --\\\\ 0.0005 & 0.000166667 & 0 & 0 & -- & --\\\\ 0.001 & 0.000333333 & 1"
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      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/beta_sweep_en.tex",
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      "sha256": "c7848259078410be16d9f4e92de6186830187f2343728bc7c6dccef0c9f0fd74",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/beta_sweep_en.tex",
      "preview": "\\section{Beta-only sweep at fixed \\texorpdfstring{$N$}{N} (\\texorpdfstring{$N=100$}{N=100})} We fix $N=100$, $q=2/3$, $\\rho=1$, and the \\texttt{lazy\\_selfloop} convention, and vary only $\\beta$."
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/mc_beta_cn.tex",
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      "size": 1974,
      "sha256": "976c391af989b434b8c820e7c49a944e3a747a977706f45d401ea81563a3e305",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/mc_beta_cn.tex",
      "preview": "\\section{MC 扫描：四分类随 \\texorpdfstring{$\\beta$}{beta} 变化（\\texorpdfstring{$N=100$}{N=100}）} 使用 MC 统计窗口内的四类轨迹比例，重点关注 $J$-相关类别在 valley/第二峰窗口的集中程度。 窗口由 $(t_1,t_v,t_2)$ 与 $\\Delta=\\lfloor\\delta_{\\mathrm{frac}}(t_2-t_1)\\rfloor$ 定义"
    },
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      "sha256": "27a326d85a8bff49ce299621c413195d27778bed9682e99683f4f52069b7d2fa",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/mc_beta_en.tex",
      "preview": "\\section{MC sweep: four classes vs \\texorpdfstring{$\\beta$}{beta} (\\texorpdfstring{$N=100$}{N=100})} We use MC to estimate class probabilities within each window, defined by $(t_1,t_v,t_2)$ and $\\Delta=\\lfloor\\delta_{\\ma"
    },
    {
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      "sha256": "e7ed9faf9df061b1792ba935f1351a0bdaacd26b2553e156bbf1f2ff399484c2",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/mc_n_cn.tex",
      "preview": "\\section{MC 扫描：四分类随 \\texorpdfstring{$N$}{N} 变化（固定 \\texorpdfstring{$\\beta=0.01$}{beta=0.01}）} 保持 $\\beta=0.01$，对偶数 $N$ 做 MC 扫描并统计四类轨迹在不同窗口的比例"
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      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/mc_n_en.tex",
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      "sha256": "659064de705dc83cf54fe5bad9de015566cfbd95b69566eb910e41faa0ca825d",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/mc_n_en.tex",
      "preview": "\\section{MC sweep: four classes vs \\texorpdfstring{$N$}{N} (fixed \\texorpdfstring{$\\beta=0.01$}{beta=0.01})} With $\\beta=0.01$ fixed, we scan even $N$ and estimate class proportions within each window."
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/n_sweep_cn.tex",
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      "size": 628,
      "sha256": "5630fdceffbdfa341e24d54d5917d2e53947f770dac03c88b34b7d7b4efc3e37",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/n_sweep_cn.tex",
      "preview": "\\section{固定 \\texorpdfstring{$\\beta=0.01$}{beta=0.01} 改变 \\texorpdfstring{$N$}{N}（精确 AW）} 取自动选择的 $\\beta_\\ast=0.01$，固定 $q=2/3,\\rho=1$ 与 \\texttt{lazy\\_selfloop}，对偶数 $N$ 扫描峰高、峰位与尾部衰减指标"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/n_sweep_en.tex",
      "category": "report_docs",
      "size": 615,
      "sha256": "6fa14bd904f7eb37015cd7d18a56df288dcbed7b95a1a2273992a67d80ccfc6e",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/n_sweep_en.tex",
      "preview": "\\section{Fix \\texorpdfstring{$\\beta=0.01$}{beta=0.01} and sweep \\texorpdfstring{$N$}{N} (exact AW)} Using the automatically selected $\\beta_\\ast=0.01$ and fixing $q=2/3$, $\\rho=1$, and \\texttt{lazy\\_selfloop}, we sweep e"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/repro_cn.tex",
      "category": "report_docs",
      "size": 2759,
      "sha256": "25192a6e24ca887d84595bc00b2ea5b0529bc99e16dd0ab1a14984cd7da88a1c",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/repro_cn.tex",
      "preview": "\\section{复现指南（命令与输出）} 以下命令均在 \\texttt{reports/lazy\\_jump\\_ext/} 内执行。 \\paragraph{1. \\texorpdfstring{$\\beta$}{beta} 扫描（精确 AW）} \\begin{verbatim} python code/beta_sweep_peaks_tail.py \\ --N 100 --Ks 2 4 --q 0.6666666667 --rho"
    },
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      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/repro_en.tex",
      "category": "report_docs",
      "size": 2780,
      "sha256": "0a385a3f93c6cd8091d88a1debdebef6b9f4db79e6f40cf2c84c6b666d65debb",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/repro_en.tex",
      "preview": "\\section{Reproducibility (commands and outputs)} Run the following inside \\texttt{reports/lazy\\_jump\\_ext/}. \\paragraph{1. \\texorpdfstring{$\\beta$}{beta} sweep (exact AW)} \\begin{verbatim} python code/beta_sweep_peaks_ta"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/theory_cn.tex",
      "category": "report_docs",
      "size": 4149,
      "sha256": "bcd49bfe81ca1648c16c3e3e763e6dbdc130e8de365ce173cec1180fddb66ff7",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/theory_cn.tex",
      "preview": "\\section{理论推导：生成函数、AW 反演与尾部衰减} 本节给出本文数值计算与尾部指标所依赖的核心理论推导。我们考虑在 $N$ 点环上、每步以概率 $q$ 做 $K=2k$ 邻居环走、以概率 $1-q$ 懒惰自环的随机游走，并在源点 $\\mathrm{src}$ 增加一条到 $\\mathrm{dst}$ 的有向 shortcut"
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      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/theory_en.tex",
      "category": "report_docs",
      "size": 4388,
      "sha256": "bfff762723d4967f24c807c6f1ce403b28fd4bc299f18e2bcfb630da6c4d352e",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/theory_en.tex",
      "preview": "\\section{Theory: generating functions, AW inversion, and tail decay} This section provides the theoretical backbone for our exact pmf computation and tail diagnostics."
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/manuscript/sections/valley_cn.tex",
      "category": "report_docs",
      "size": 1562,
      "sha256": "166f22cd44c927d1b66698659fe6cc214581be250d9a9f5bdbbb9918d16b78a8",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/valley_cn.tex",
      "preview": "\\section{Valley 的可比较定义与窗口划分} 令首吸收时间的概率质量函数为 $f(t)=\\mathbb{P}(T=t)$（$t\\in\\mathbb{N}^+$）。 我们采用严格局部极大作为峰的候选： \\begin{equation} f(t)>f(t-1),\\qquad f(t)>f(t+1),\\qquad f(t)\\ge h_{\\min}."
    },
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      "sha256": "fe513895f8879bd315328855da5068a3516fea9fcea2f46342989ce4778a63d9",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/manuscript/sections/valley_en.tex",
      "preview": "\\section{Comparable definition of the valley and windowing} Let $f(t)=\\mathbb{P}(T=t)$ for $t\\in\\mathbb{N}^+$ denote the pmf of the first absorption time."
    },
    {
      "path": "research/reports/ring_lazy_jump_ext/notes/readme_ext.md",
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      "size": 3692,
      "sha256": "32482e24bd18c68fec2cea199fdf4e69a262cfe6435b1375ee1c9d88b1427c0b",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext/notes/readme_ext.md",
      "preview": "# lazy_jump_ext This extension folder is isolated from the original report. All new scripts, data, figures, and PDFs live here under `research/reports/ring_lazy_jump_ext/`."
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/README.md",
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      "size": 3616,
      "sha256": "af426069e17000d4d23980e242f4bbd64efe99bd9920bd5a4ac03b3c6c862d23",
      "updated_at": "2026-06-09T21:57:42.169399Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/README.md",
      "preview": "# ring_lazy_jump_ext_rev2 Revision v2 of the lazy jump-over extension report. ## Lineage - **Predecessor:** `ring_lazy_jump_ext` — original extension; this revision supersedes it."
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/artifacts/figures/standalone/fig2_overlap_binbars_beta0.01_x1350_description_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath} \\usepackage{microtype} \\begin{document} \\noindent Figure~1 shows two stacked panels (top $K=2$, bottom $K=4$)."
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/artifacts/tables/luca_k2_fixed_shortcut_definition_comparison.tex",
      "preview": "\\begin{tabular}{L{0.21\\linewidth} c L{0.39\\linewidth} c} \\toprule Definition & Cases with $\\beta\\geq\\beta_c$ & Maximum passing $\\beta$ & $\\rho_c$ \\\\ \\midrule two local maxima & 34 & n0=1: 0.062; n0=2: 0.060; n0=3: 0.060"
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      "preview": "\\begin{tabular}{rrrrrr} \\toprule $n_0$ & target & $\\beta_c$ & any double & max $\\beta$ double & double at/above $\\beta_c$ \\\\ \\midrule 1 & 56 & 0.040 & yes & 0.030 & 0 \\\\ 2 & 56 & 0.040 & yes & 0.030 & 0 \\\\ 3 & 56 & 0.040"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/artifacts/tables/window_params_beta0.01.tex",
      "preview": "% Auto-generated by export_window_table.py \\begin{table}[!htbp] \\centering \\scriptsize \\setlength{\\tabcolsep}{3pt} \\caption{窗口参数与样本量（$\\beta=0.01, N=100$；窗口中心来自 $K=4$ 峰谷检测）"
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      "preview": "% Auto-generated by export_window_table.py \\begin{table}[!htbp] \\centering \\scriptsize \\setlength{\\tabcolsep}{3pt} \\caption{Window parameters and sample counts ($\\beta=0.01, N=100$"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/manuscript/extras/luca_calculations_audit/updated_calculation_remaining_issues_audit.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[margin=0.78in]{geometry} \\usepackage[T1]{fontenc} \\usepackage[utf8]{inputenc} \\usepackage{amsmath,amssymb} \\usepackage{booktabs,longtable,array} \\usepackage[table]{xcolor} \\usepa"
    },
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      "path": "research/reports/ring_lazy_jump_ext_rev2/manuscript/extras/luca_k2_fixed_shortcut_meeting_report.tex",
      "category": "report_docs",
      "size": 10235,
      "sha256": "3bbe0807baac6f02bd35beb5518960a9f3bacb4106a0c4ff8aef8b1c08460060",
      "updated_at": "2026-06-09T21:57:42.265080Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/manuscript/extras/luca_k2_fixed_shortcut_meeting_report.tex",
      "preview": "\\documentclass[10pt]{article} \\usepackage[a4paper,margin=0.72in]{geometry} \\usepackage{amsmath,amssymb} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage[hidelinks]{hyperref} \\usepackage{microtype} \\usepackage{enum"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/manuscript/ring_lazy_jump_ext_rev2_cn.tex",
      "category": "report_docs",
      "size": 13905,
      "sha256": "698b5afba20ec3cfb1d88ceff3398abb86938840bc1a760e4684399ce9e20ac5",
      "updated_at": "2026-06-09T21:57:42.266081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/manuscript/ring_lazy_jump_ext_rev2_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{array} \\usepackage{caption} \\usepackage"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/manuscript/ring_lazy_jump_ext_rev2_en.tex",
      "category": "report_docs",
      "size": 13723,
      "sha256": "dd13ff31fcb235b77250c0b1fa12aac898dba2e93b3f8124d710490cf9722913",
      "updated_at": "2026-06-09T21:57:42.266081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/manuscript/ring_lazy_jump_ext_rev2_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts,amssymb} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{array} \\usepackage{caption} \\usepackage{enumitem} \\use"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/notes/changelog_v2.md",
      "category": "report_docs",
      "size": 630,
      "sha256": "6602c7f7b1193f726f1f0bed8aa9267980f16704484808b98c6fd22fad87c8ab",
      "updated_at": "2026-06-09T21:57:42.267081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/notes/changelog_v2.md",
      "preview": "# CHANGELOG_v2 - Added v2 report `ring_lazy_jump_ext_rev2_cn.tex` with front-loaded abstract, symbol quick reference, reproduction chain, and data provenance table."
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/notes/luca_k2_fixed_shortcut_sweep.md",
      "category": "report_docs",
      "size": 2748,
      "sha256": "45f8e0d993e45c8bc7d4b31461f6cfb52367020d8bad7e53af4a1ae07c0fdbe0",
      "updated_at": "2026-06-09T21:57:42.268198Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/notes/luca_k2_fixed_shortcut_sweep.md",
      "preview": "# Luca K=2 fixed-shortcut sweep ## Meeting question Check the first-passage distribution for a lazy nearest-neighbour ring with one directed shortcut: - `N = 100` - `K = 2` - `q = 2/3` - fixed directed shortcut `u = 6 ->"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/notes/readme_rev.md",
      "category": "report_docs",
      "size": 3841,
      "sha256": "adafd427c8df81b78a6ad4f6bf7817a8eae6d01919e3080c0345c6bbb3bbfb34",
      "updated_at": "2026-06-09T21:57:42.268198Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/notes/readme_rev.md",
      "preview": "# lazy_jump_ext_rev2 (v2 revision) ## Quick start Run commands from `research/reports/ring_lazy_jump_ext_rev2/`. ``` make fig2 make sensitivity make pdf ``` ## Export real inputs for Fig.1 The figure uses a standardized"
    },
    {
      "path": "research/reports/ring_lazy_jump_ext_rev2/notes/revision_notes.md",
      "category": "report_docs",
      "size": 2758,
      "sha256": "2f462699c4bfc795fd5019161fb05bb16647b40610c2855f48e7115b997d60f1",
      "updated_at": "2026-06-09T21:57:42.268198Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_lazy_jump_ext_rev2/notes/revision_notes.md",
      "preview": "# REVISION_NOTES (v2) 1) 问题：图2将 f(t) 与分类柱状拆成不同面板，窗口与比例没有在同一坐标系对齐 → 影响：读者难以判断窗内比例与峰谷位置的对应关系 → 修正：在同一主轴上用三段全宽栈叠条替代 bin 底色，并用混合变换绘制 → 验证：`figures/fig2_overlap_binbars_beta0.01_x1350.pdf` 三段 bar 覆盖各自窗口且无 inset/twin 轴"
    },
    {
      "path": "research/reports/ring_two_target/README.md",
      "category": "report_docs",
      "size": 1716,
      "sha256": "c25a8ee1eb07d5102eb5b932ad4e87aab64d6a9e9b0159db53efeccd19b4096c",
      "updated_at": "2026-06-09T21:57:42.268198Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/README.md",
      "preview": "# two_target_ring Two-target lazy ring report (Chinese + English). ## Structure - `code/`: data generation scripts - `outputs/`: FPT time series CSVs - `data/`: scan tables and model configs - `tables/`: LaTeX tables for"
    },
    {
      "path": "research/reports/ring_two_target/artifacts/tables/case_configs.tex",
      "category": "report_docs",
      "size": 407,
      "sha256": "fd7706ea2bd6acfb1db02a3c65d436d7a493265b950e9e6cc3c8eabd83d4c1d6",
      "updated_at": "2026-06-09T21:57:42.276814Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/artifacts/tables/case_configs.tex",
      "preview": "\\begin{tabular}{lllllll} \\toprule Case & $N$ & $K$ & $q$ & $g$ & $\\beta$ & targets \\\\ \\midrule A\\_no\\_sc\\_K2 & 20 & 2 & 0.667 & 0.60 & 0.000 & (18,10) \\\\ B\\_no\\_sc\\_K4 & 30 & 4 & 0.667 & 0.60 & 0.000 & (27,15) \\\\ C\\_sc\\_"
    },
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      "category": "report_docs",
      "size": 479,
      "sha256": "ed8bf7a204a7cad3501257866dd3d526cb43f41b66d025ef3680356861a53165",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/artifacts/tables/case_peaks.tex",
      "preview": "\\begin{tabular}{llllllll} \\toprule Case & $t_1$ & $h_1$ & $t_2$ & $h_2$ & $h_2/h_1$ & paper & macro \\\\ \\midrule A\\_no\\_sc\\_K2 & 2 & 1.78e-02 & 20 & 5.30e-02 & 2.98 & True & True \\\\ B\\_no\\_sc\\_K4 & 3 & 9.78e-03 & 20 & 3.7"
    },
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      "category": "report_code",
      "size": 3407,
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      "updated_at": "2026-06-09T21:57:42.277476Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/code/channel_decomposition.py"
    },
    {
      "path": "research/reports/ring_two_target/code/run_small_scan.py",
      "category": "report_code",
      "size": 14622,
      "sha256": "e513053048e8fec0d5d24ca794578f24dc2cd088737e2e8517e77c3cfeacf503",
      "updated_at": "2026-06-09T21:57:42.277591Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/code/run_small_scan.py"
    },
    {
      "path": "research/reports/ring_two_target/code/two_target_report.py",
      "category": "report_code",
      "size": 11392,
      "sha256": "ad8e4abafbea5e1186fee65ab68a854b1080350589db025264c4193003a9ed56",
      "updated_at": "2026-06-09T21:57:42.277591Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/code/two_target_report.py"
    },
    {
      "path": "research/reports/ring_two_target/manuscript/ring_two_target_cn.tex",
      "category": "report_docs",
      "size": 25203,
      "sha256": "173b64cc4c08459fc1fed74f6e7f03fdd50aaeb13e087208e52b9ca8f9d6f41a",
      "updated_at": "2026-06-09T21:57:42.277835Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/manuscript/ring_two_target_cn.tex",
      "preview": "\\documentclass[11pt]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepackage{pgfplots} \\"
    },
    {
      "path": "research/reports/ring_two_target/manuscript/ring_two_target_en.tex",
      "category": "report_docs",
      "size": 25458,
      "sha256": "a2515c624efb3f71d713bed955c916769aa49cf72f728a7e37abdefe13cf7c1d",
      "updated_at": "2026-06-09T21:57:42.279081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/manuscript/ring_two_target_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepackage{pgfplots} \\"
    },
    {
      "path": "research/reports/ring_two_target/notes/small_scan_summary.md",
      "category": "report_docs",
      "size": 1972,
      "sha256": "db952542e0259cf517384ec93a24f3421def396d377cd45ade29f866b093a8cb",
      "updated_at": "2026-06-09T21:57:42.280475Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_target/notes/small_scan_summary.md",
      "preview": "# Small Two-Target Ring Scan This bounded scan uses exact propagation on a small grid of periodic 1D ring two-target first-passage problems."
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/README.md",
      "category": "report_docs",
      "size": 4054,
      "sha256": "6da434b9ed7a9fc0d85ea0fe3eb062321724a8a3d1bb8cf2f9818dfc1a0adc5e",
      "updated_at": "2026-06-09T21:57:42.280475Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/README.md",
      "preview": "# 1D Ring Two-Walker Encounter With Shortcut This report focuses on **1D ring encounter** for two independent lazy walkers. It contains: - Robust numerical verification of appendix Eq. (A1) == Eq. (A8)."
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/a1a8_test_table.tex",
      "category": "report_docs",
      "size": 444,
      "sha256": "ec368bc6c39a4db0a9518612476acebd3125c40cc8306fc456ba18328e816170",
      "updated_at": "2026-06-09T21:57:42.282732Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/a1a8_test_table.tex",
      "preview": "\\begin{tabular}{lcccccc} \\toprule Case & $(N,q)$ & $z$ & $M$ & $r$ & $|LHS-RHS|$ & rel.err \\\\ \\midrule R1\\_real\\_small & (16,0.30) & $0.40+0.00i$ & 128 & 0.632 & 8.13e-18 & 8.13e-18 \\\\ R2\\_complex & (12,0.35) & $0.30+0.1"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_consistency_summary_cn.tex",
      "category": "report_docs",
      "size": 954,
      "sha256": "8c7a1a5082beba7447283b80badcddcc8a0f79675f1873e7d10114d3d45f2fb6",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_consistency_summary_cn.tex",
      "preview": "% Auto-generated from data/case_summary.json; do not edit by hand. \\begin{enumerate}[leftmargin=1.4em] \\item $\\beta\\le0.14$：phase=1（弱双峰/过渡）； \\item 粗扫描从 $\\beta\\approx0.16$ 起：phase=2（clear bimodal）"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_consistency_summary_en.tex",
      "category": "report_docs",
      "size": 961,
      "sha256": "33ad538b1fb3e578c529adb613d19a9899a265d8dc91c0b667c2b703f2501953",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_consistency_summary_en.tex",
      "preview": "% Auto-generated from data/case_summary.json; do not edit by hand. \\begin{enumerate}[leftmargin=1.4em] \\item $\\beta\\le0.14$: phase 1 (weak/transition double structure)"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_key_metrics.tex",
      "category": "report_docs",
      "size": 1083,
      "sha256": "2aea2893a9bb6281d39716184d55a4336a53d53c720dbd72bb6e67d6bd159717",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_key_metrics.tex",
      "preview": "\\begin{tabular}{lc} \\toprule Metric & Value \\\\ \\midrule Coarse onset $\\beta$ & 0.160 \\\\ Refined onset $\\beta$ & 0.150 \\\\ Detector onset range & [0.110, 0.160] \\\\ Detector onset median & 0.140 \\\\ Agreement crossing ($25\\%"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_n_scan_table.tex",
      "category": "report_docs",
      "size": 474,
      "sha256": "32e17cff627a4757f0aba548b6aff2f7d1c86e90a553f04638bb50926c1b8768",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_n_scan_table.tex",
      "preview": "\\begin{tabular}{cccccccc} \\toprule $N$ & onset $\\beta^\\dagger$ & onset source & $\\beta_{\\max}$ & clear frac & phase@0.20 & peak@0.20 & valley@0.20 \\\\ \\midrule 81 & 0.380\\textsuperscript{*} & \\texttt{extended} & 0.380 & 0"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_nscan_summary_cn.tex",
      "category": "report_docs",
      "size": 929,
      "sha256": "d13f4ce579efa45f38d0ff216155851d00625377b3babade4f42cd5bd07623b0",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_nscan_summary_cn.tex",
      "preview": "% Auto-generated from data/encounter_onset_n_scan.csv; do not edit by hand. 为避免结论仅依赖单一基准尺寸 $N=101$，我们额外做了 $N\\in\\{81,101,121,141\\}$ 的 ring-size 稳健性扫描，并按比例缩放 $(n_0,m_0,\\text{src},\\text{dst})$ 几何位置"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_nscan_summary_en.tex",
      "category": "report_docs",
      "size": 868,
      "sha256": "b4bae7cdc38f82d2118be9ce588b1f106e086c7c112723f061e13c8dba14a445",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_nscan_summary_en.tex",
      "preview": "% Auto-generated from data/encounter_onset_n_scan.csv; do not edit by hand. To avoid over-reliance on the single baseline size $N=101$, we additionally scan $N\\in\\{81,101,121,141\\}$ with geometry-scaled $(n_0,m_0,\\mathrm"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_scan_table.tex",
      "category": "report_docs",
      "size": 863,
      "sha256": "1a8fea0e86068ec51654d68cddbea680a29aef7b8741806cc7b5ad9972e8680f",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_scan_table.tex",
      "preview": "\\begin{tabular}{ccccccc} \\toprule $\\beta$ & phase & $t_1$ & $t_2$ & peak balance ratio (min/max) & valley ratio & bimodal \\\\ \\midrule 0.00 & 1 & 192 & 322 & 0.194 & 0.011 & 0 \\\\ 0.02 & 1 & 192 & 322 & 0.192 & 0.020 & 0 \\"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_shortcut_rep_case.tex",
      "category": "report_docs",
      "size": 518,
      "sha256": "6e68f9a895ddb916ba2191664519624939c18c422011ee1c25fb5d8fa6db98b4",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/encounter_shortcut_rep_case.tex",
      "preview": "\\begin{tabular}{ll} \\toprule Field & Value \\\\ \\midrule $N$ / $q$ & 101 / 0.70 \\\\ $(g_1,g_2)$ & (0.70, -0.40) \\\\ Starts $(n_0,m_0)$ & (5, 55) \\\\ Shortcut $(\\mathrm{src}\\to\\mathrm{dst})$ & (5 $\\to$ 70) \\\\ Representative $\\"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_example_table.tex",
      "category": "report_docs",
      "size": 407,
      "sha256": "434242fb210046a55872482318d0e5bbb95ac4c148a8f376eefe2180871171c1",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_example_table.tex",
      "preview": "\\begin{tabular}{lcccccc} \\toprule Case & $(g_1,g_2)$ & phase & $t_1\\,(=2m)$ & $t_2\\,(=2m)$ & peak balance ratio ($\\bar{\\tilde f}$, min/max) & valley ratio ($\\bar{\\tilde f}$) \\\\ \\midrule C0 & (0.00,0.00) & 0 & - & - & --"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_parity_note_cn.tex",
      "category": "report_docs",
      "size": 1214,
      "sha256": "ffc854f46d70c3567aeb4cb6a24c5511cc05ca3001bc44b26987f2f5cbc6bbbe",
      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_parity_note_cn.tex",
      "preview": "其中 clear 占比为 $159/169=0.941$（脚本自动汇总）。该 fixed-site 基准刻意选在漂移主导区；K=2 奇偶粗粒化用于抑制 odd/even 微结构，使 clear 判定反映“分离时间尺度”而非 parity 伪峰。在首遇分布中 $f(0)=0$，因此 $\\widetilde f(0)=f(0)=0$，检测从 $m\\ge1$ 开始"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_parity_note_en.tex",
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      "updated_at": "2026-06-09T21:57:42.283684Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_parity_note_en.tex",
      "preview": "The clear fraction is $159/169=0.941$ (auto-synced from generated scan data). This fixed-site benchmark is intentionally drift-dominated"
    },
    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_phase_summary.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/artifacts/tables/fixedsite_phase_summary.tex",
      "preview": "\\begin{tabular}{lcc} \\toprule Phase class & Count & Fraction \\\\ \\midrule single (0) & 7 & 0.041 \\\\ weak (1) & 3 & 0.018 \\\\ clear (2) & 159 & 0.941 \\\\ \\bottomrule \\end{tabular}"
    },
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    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/code/two_walker_ring_encounter_report.py",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/code/two_walker_ring_encounter_report.py"
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    {
      "path": "research/reports/ring_two_walker_encounter_shortcut/manuscript/ring_two_walker_encounter_shortcut_cn.tex",
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      "size": 26206,
      "sha256": "e0a42c2cf59fef3fda94ac65ad6dcecd82268ee7e95e65d3d6c5f4d881f9f0de",
      "updated_at": "2026-06-09T21:57:42.286081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/manuscript/ring_two_walker_encounter_shortcut_cn.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,mathtools} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{float} \\usepackage{xcolor} \\usepackage{hyperref} \\use"
    },
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      "path": "research/reports/ring_two_walker_encounter_shortcut/manuscript/ring_two_walker_encounter_shortcut_en.tex",
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      "size": 26922,
      "sha256": "bcafc4397d516edc7ab1067591483fad4ba6a9a9fc51a70fa11627469919343f",
      "updated_at": "2026-06-09T21:57:42.288081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_two_walker_encounter_shortcut/manuscript/ring_two_walker_encounter_shortcut_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,mathtools} \\usepackage{booktabs} \\usepackage{graphicx} \\usepackage{float} \\usepackage{xcolor} \\usepackage{hyperref} \\use"
    },
    {
      "path": "research/reports/ring_valley/README.md",
      "category": "report_docs",
      "size": 525,
      "sha256": "9e0af431009e03496aa498b512ae6c4cbe63baef8e0e2f7dfc76adb5b1f037c7",
      "updated_at": "2026-06-09T21:57:42.288081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley/README.md",
      "preview": "# ring_valley Non-lazy valley-regime notes and scans for the ring lattice. ## Manuscript - `manuscript/ring_valley_en.tex` (+ `.pdf`) ## Languages English-only (`languages: [en]` in `report_registry.yaml`)."
    },
    {
      "path": "research/reports/ring_valley/code/valley_study.py",
      "category": "report_code",
      "size": 441,
      "sha256": "8acda4243cf09e507860ab49c11189d289d5c905d61348bfb70211171e170c9f",
      "updated_at": "2026-06-09T21:57:42.290345Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley/code/valley_study.py"
    },
    {
      "path": "research/reports/ring_valley/manuscript/ring_valley_en.tex",
      "category": "report_docs",
      "size": 7768,
      "sha256": "b27b2a1bdd47e061461e29e663ad9c5940c292646529f57688d6aa04c75c06a9",
      "updated_at": "2026-06-09T21:57:42.293081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley/manuscript/ring_valley_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts} \\usepackage{graphicx} \\usepackage{caption} \\usepackage{enumitem} \\usepackage[hidelinks]{hyperref} \\setlength{\\emergenc"
    },
    {
      "path": "research/reports/ring_valley_dst/README.md",
      "category": "report_docs",
      "size": 1150,
      "sha256": "957d9e89905f6804f18d30ce7998cbebfb28c96a3f22f549ff754d9ad7c84d0f",
      "updated_at": "2026-06-09T21:57:42.293081Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/README.md",
      "preview": "# ring_valley_dst This report studies DST-driven second-peak modulation on ring lattices (CN/EN). ## Entry scripts (thin wrappers) - `research/reports/ring_valley_dst/code/bimodality_flux_scan.py` - `research/reports/rin"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K2_n0_1_target_50_src_1/latest/bimodal_table.tex",
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      "size": 5502,
      "sha256": "41678769e45e0cfa2d670350a87a6cafd4695db5f0fe16b26478cea74817b3bb",
      "updated_at": "2026-06-09T21:57:42.295180Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K2_n0_1_target_50_src_1/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 3 & 798 & 802 & 4 & 0.000383586 & 0.00038359 & 1.000 \\\\ 4 & 785 & 789 & 4 & 0.00078377 & 0.000783"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K2_n0_1_target_50_src_6/latest/bimodal_table.tex",
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      "size": 5573,
      "sha256": "f06d2b9bc0c5596ec16601ff4c028b30e88ffc6b830f4ed34448b5b7381dc93b",
      "updated_at": "2026-06-09T21:57:42.295504Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K2_n0_1_target_50_src_6/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 1 & 909 & 913 & 4 & 0.000669973 & 0.000669965 & 0.000 \\\\ 2 & 797 & 801 & 4 & 0.000388827 & 0.0003"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K6_n0_1_target_50_src_1/latest/bimodal_table.tex",
      "category": "report_docs",
      "size": 537,
      "sha256": "08b426791d5993861e93221138616b721589512dde7adaa89a555d4853fd4d33",
      "updated_at": "2026-06-09T21:57:42.295810Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K6_n0_1_target_50_src_1/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 36 & 34 & 108 & 74 & 0.00208676 & 0.00217576 & 0.988 \\\\ 37 & 28 & 104 & 76 & 0.00227434 & 0.00219"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K6_n0_1_target_50_src_6/latest/bimodal_table.tex",
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      "size": 931,
      "sha256": "71ffe92f91afa5074eb96d051e5fd0879964e8b67ac1226355487f7c0643b2e8",
      "updated_at": "2026-06-09T21:57:42.296052Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K6_n0_1_target_50_src_6/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 43 & 37 & 120 & 83 & 0.00201691 & 0.00231041 & 1.000 \\\\ 44 & 29 & 117 & 88 & 0.00219366 & 0.00232"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_30_src_1/latest/bimodal_table.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_30_src_1/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 4 & 263 & 313 & 50 & 0.00186464 & 0.00182629 & 0.000 \\\\ 6 & 243 & 293 & 50 & 0.00213414 & 0.00208"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_40_src_1/latest/bimodal_table.tex",
      "category": "report_docs",
      "size": 5364,
      "sha256": "5d5477f2293d4ca29eeb4983936103d9d83c9fb95c533e0b1ef37e244b8393e7",
      "updated_at": "2026-06-09T21:57:42.296569Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_40_src_1/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 4 & 485 & 535 & 50 & 0.00101533 & 0.00100826 & 0.038 \\\\ 6 & 459 & 509 & 50 & 0.00114188 & 0.00113"
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    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_51_src_1/latest/bimodal_table.tex",
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      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 4 & 806 & 856 & 50 & 0.000611827 & 0.000610159 & 0.240 \\\\ 6 & 772 & 822 & 50 & 0.000680594 & 0.00"
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    {
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      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 4 & 1125 & 1175 & 50 & 0.000436896 & 0.000436254 & 0.365 \\\\ 6 & 1087 & 1137 & 50 & 0.00048326 & 0"
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    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_70_src_1/latest/bimodal_table.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N101K2_n0_1_target_70_src_1/latest/bimodal_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule 4 & 326 & 376 & 50 & 0.000380702 & 0.000374958 & 0.032 \\\\ 6 & 1469 & 1519 & 50 & 0.000347269 & 0."
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    {
      "path": "research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N30K4_n0_1_target_15_src_6/runs/p1_smoke_flux/bimodal_table__p1_smoke_flux.tex",
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      "preview": "\\begin{tabular}{r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $t_2-t_1$ & $A(t_1)$ & $A(t_2)$ & $V$ \\\\ \\midrule \\bottomrule \\end{tabular}"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_1/latest/analysis_summary.tex",
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      "sha256": "0db703461d18c9fc3d002a58d7d76cfb9f5ab54a84cf06e5d3f21780064ff918",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_1/latest/analysis_summary.tex",
      "preview": "\\begin{itemize} \\item Pearson $r(R,\\;P(C\\ge1))$：-0.439（全体），-0.406（去掉 $\\mathrm{dst}=\\mathrm{target}$）。 \\item Spearman $\\rho(R,\\;P(C\\ge1))$：-0.472（全体），-0.471（去掉 $\\mathrm{dst}=\\mathrm{target}$）"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_1/latest/scope_summary.tex",
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      "sha256": "dbc9f8f2abe53ef3f9738cce02afa62decadc6959c878e97f601ea46be1c3608",
      "updated_at": "2026-06-09T21:57:42.298135Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_1/latest/scope_summary.tex",
      "preview": "\\begin{itemize} \\item 本次参数：$N=100,\\;K=6,\\;n_0=1,\\;\\mathrm{target}=50,\\;\\mathrm{src}=1$。 \\item 满足双峰判据（Fig.~3 规则）的 $\\mathrm{dst}$：共 18 个，范围 36--64"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_1/latest/selected_table.tex",
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      "updated_at": "2026-06-09T21:57:42.298135Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_1/latest/selected_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $\\Delta$ & $R$ & $A(t_1)$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 36 & 34 & 108 & 3 & 1.043 & 0.0020860594 & 0.00217576 & 0.367 & 0.633"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/latest/analysis_summary.tex",
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      "sha256": "78621203c6dad19b6c7acdc8b331d7bd50dd60af0c8257e37290eea32562f7aa",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/latest/analysis_summary.tex",
      "preview": "\\begin{itemize} \\item Pearson $r(R,\\;P(C\\ge1))$：-0.165（全体），-0.969（去掉 $\\mathrm{dst}=\\mathrm{target}$）。 \\item Spearman $\\rho(R,\\;P(C\\ge1))$：-0.843（全体），-0.965（去掉 $\\mathrm{dst}=\\mathrm{target}$）"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/latest/scope_summary.tex",
      "category": "report_docs",
      "size": 353,
      "sha256": "5b64494b53590377d83d23eb51033577fa854799fbe6ba1baed4eab5f74708e4",
      "updated_at": "2026-06-09T21:57:42.298708Z",
      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/latest/scope_summary.tex",
      "preview": "\\begin{itemize} \\item 本次参数：$N=100,\\;K=6,\\;n_0=1,\\;\\mathrm{target}=50,\\;\\mathrm{src}=6$。 \\item 满足双峰判据（Fig.~3 规则）的 $\\mathrm{dst}$：共 15 个，范围 43--57"
    },
    {
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      "preview": "\\begin{tabular}{r r r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $\\Delta$ & $R$ & $A(t_1)$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 43 & 37 & 120 & 4 & 1.146 & 0.0020160646 & 0.00231041 & 0.446 & 0.554"
    },
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      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/runs/p1_smoke_dstmc/analysis_summary__p1_smoke_dstmc.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/runs/p1_smoke_dstmc/analysis_summary__p1_smoke_dstmc.tex",
      "preview": "\\begin{itemize} \\item Pearson $r(R,\\;P(C\\ge1))$：nan（全体），nan（去掉 $\\mathrm{dst}=\\mathrm{target}$）。 \\item Spearman $\\rho(R,\\;P(C\\ge1))$：nan（全体），nan（去掉 $\\mathrm{dst}=\\mathrm{target}$）"
    },
    {
      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/runs/p1_smoke_dstmc/scope_summary__p1_smoke_dstmc.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/runs/p1_smoke_dstmc/scope_summary__p1_smoke_dstmc.tex",
      "preview": "\\begin{itemize} \\item 本次参数：$N=100,\\;K=6,\\;n_0=1,\\;\\mathrm{target}=50,\\;\\mathrm{src}=6$。 \\item 满足双峰判据（Fig.~3 规则）的 $\\mathrm{dst}$：共 15 个，范围 43--57"
    },
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      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/runs/p1_smoke_dstmc/selected_table__p1_smoke_dstmc.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/N100K6_n0_1_target_50_src_6/runs/p1_smoke_dstmc/selected_table__p1_smoke_dstmc.tex",
      "preview": "\\begin{tabular}{r r r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $\\Delta$ & $R$ & $A(t_1)$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 51 & 14 & 101 & 4 & 0.678 & 0.00345483 & 0.0023412 & 0.000 & 1.000 \\\\"
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      "path": "research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/latest/analysis_summary.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/latest/analysis_summary.tex",
      "preview": "\\begin{itemize} \\item Pearson $r(R,\\;P(C\\ge1))$：-0.439（全体），-0.406（去掉 $\\mathrm{dst}=\\mathrm{target}$）。 \\item Spearman $\\rho(R,\\;P(C\\ge1))$：-0.472（全体），-0.471（去掉 $\\mathrm{dst}=\\mathrm{target}$）"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/latest/scope_summary.tex",
      "preview": "\\begin{itemize} \\item 本次参数：$N=100,\\;K=6,\\;n_0=1,\\;\\mathrm{target}=50,\\;\\mathrm{src}=1$。 \\item 满足双峰判据（Fig.~3 规则）的 $\\mathrm{dst}$：共 18 个，范围 36--64"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/artifacts/data/second_peak_dst_shortcut_usage/latest/selected_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $\\Delta$ & $R$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 36 & 34 & 108 & 3 & 1.043 & 0.00217576 & 0.367 & 0.633 \\\\ 37 & 28 & 104 & 3 & 0.964"
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      "preview": "\\begin{tabular}{r r r r r} \\hline dst & $t_1$ & $A(t_1)$ & $t_2$ & $A(t_2)$ \\\\ \\hline \\hline \\end{tabular}"
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      "preview": "\\begin{tabular}{r r r r r r r r r} \\toprule $N$ & $K$ & $t_1$ & $t_2$ & $\\Delta$ & $A(t_1)$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 100 & 6 & 14 & 101 & 4 & 0.00345483 & 0.0023412 & 0.500 & 0.500 \\\\ \\bottomrule \\e"
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      "preview": "\\begin{itemize} \\item Pearson $r(R,\\;P(C\\ge1))$: -0.165 (all), -0.969 (excluding $\\mathrm{dst}=\\mathrm{target}$). \\item Spearman $\\rho(R,\\;P(C\\ge1))$: -0.843 (all), -0.965 (excluding $\\mathrm{dst}=\\mathrm{target}$)."
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      "preview": "\\begin{itemize} \\item Parameter set: $N=100,\\;K=6,\\;n_0=1,\\;\\mathrm{target}=50,\\;\\mathrm{src}=6$. \\item Number of $\\mathrm{dst}$ values satisfying the bimodality criterion (Fig.~3 rule): 15, spanning 43--57."
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/inputs/caseA/selected_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $\\Delta$ & $R$ & $A(t_1)$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 43 & 37 & 120 & 4 & 1.146 & 0.0020160646 & 0.00231041 & 0.446 & 0.554"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/inputs/caseB/analysis_summary.tex",
      "preview": "\\begin{itemize} \\item Pearson $r(R,\\;P(C\\ge1))$: -0.439 (all), -0.406 (excluding $\\mathrm{dst}=\\mathrm{target}$). \\item Spearman $\\rho(R,\\;P(C\\ge1))$: -0.472 (all), -0.471 (excluding $\\mathrm{dst}=\\mathrm{target}$)."
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      "preview": "\\begin{itemize} \\item Parameter set: $N=100,\\;K=6,\\;n_0=1,\\;\\mathrm{target}=50,\\;\\mathrm{src}=1$. \\item Number of $\\mathrm{dst}$ values satisfying the bimodality criterion (Fig.~3 rule): 18, spanning 36--64."
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/inputs/caseB/selected_table.tex",
      "preview": "\\begin{tabular}{r r r r r r r r r} \\toprule $\\mathrm{dst}$ & $t_1$ & $t_2$ & $\\Delta$ & $R$ & $A(t_1)$ & $A(t_2)$ & $P(C=0)$ & $P(C\\ge1)$ \\\\ \\midrule 36 & 34 & 108 & 3 & 1.043 & 0.0020860594 & 0.00217576 & 0.367 & 0.633"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/inputs/flux_validation_cn.tex",
      "preview": "% Deterministic bimodality validation via flux/master equation (no randomness). % Outputs live under figures/data/bimodality_flux_scan/ /latest/."
    },
    {
      "path": "research/reports/ring_valley_dst/manuscript/inputs/flux_validation_en.tex",
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/inputs/flux_validation_en.tex",
      "preview": "% Deterministic bimodality validation via flux/master equation (no randomness). % Outputs live under figures/data/bimodality_flux_scan/ /latest/."
    },
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/ring_valley_dst_cn.tex",
      "preview": "\\documentclass[11pt,fontset=fandol]{ctexart} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amsfonts} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{enumitem} \\usepackage{placeins} \\usepackage[hid"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/research/reports/ring_valley_dst/manuscript/ring_valley_dst_en.tex",
      "preview": "\\documentclass[11pt]{article} \\usepackage[a4paper,margin=1in]{geometry} \\usepackage{amsmath,amssymb,amsfonts} \\usepackage{graphicx} \\usepackage{booktabs} \\usepackage{enumitem} \\usepackage{placeins} \\usepackage[hidelinks]"
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      "github_url": "https://github.com/zhouyi-xiaoxiao/valley-k-small/blob/main/scripts/README.md",
      "preview": "# Scripts 公开脚本表面只保留 3 个入口： - `scripts/reportctl.py`: 唯一 Python CLI - `scripts/ka`: keepalive / recurring Codex shell 入口 - `scripts/README.md`: 本说明 ## `reportctl` 全部子命令（29 个） 报告操作: - `list` - `resolve` - `run` - `build` -"
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