{"id":51309551,"url":"https://github.com/iotexproject/rs-proximity-gaps","last_synced_at":"2026-07-01T02:32:36.971Z","repository":{"id":356594494,"uuid":"1221056794","full_name":"iotexproject/rs-proximity-gaps","owner":"iotexproject","description":"Lean 4 formalization, Python verification, and manuscripts for two ePrint papers on FRI proximity gaps above the Johnson radius (Chai \u0026 Fan, IoTeX, 2026) — ePrint 2026/861 + 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Reed--Solomon Proximity Gaps — Companion Repository\n\nManuscripts, Lean 4 formalization, and Python verification scripts for two\npapers by Raullen Chai and Xinxin Fan (IoTeX Network):\n\n\u003e **Paper 1 — FRI Soundness Above the Johnson Bound via Threshold Halving.**\n\u003e Cryptology ePrint Archive, Paper [2026/861](https://eprint.iacr.org/2026/861.pdf), 2026.\n\u003e Self-contained materials in [`paper1/`](paper1/).\n\u003e\n\u003e **Paper 2 — Action-Orbit FRI Soundness above Johnson:\n\u003e Universal $K$-Bounds at Ethereum-Deployed Reed--Solomon Parameters.**\n\u003e Cryptology ePrint Archive, Paper [2026/858](https://eprint.iacr.org/2026/858.pdf), 2026.\n\u003e Self-contained materials in [`paper2/`](paper2/).\n\nThe papers attack the open intermediate zone (Johnson radius $\u003c \\delta \u003c $\nlist-decoding capacity) of the Reed--Solomon proximity-gap problem — the\ndeployment regime of every FRI-based STARK on Ethereum's roadmap.\n\n[![CI](https://github.com/iotexproject/rs-proximity-gaps/actions/workflows/ci.yml/badge.svg)](https://github.com/iotexproject/rs-proximity-gaps/actions/workflows/ci.yml)\n\n---\n\n## Repository Layout\n\nThe repository is organized **per paper**: each paper directory is\nself-contained.\n\n```\nrs-proximity-gaps/\n  paper1/\n    paper.pdf                  Paper 1 manuscript\n    PROOF_CHAIN.md             Step-by-step trace of Paper 1's main theorem\n    lean/                      Lean 4 + Mathlib formalization\n      STATUS.md                Per-theorem status board (paper label ↔ Lean identifier)\n      FRISoundness/            Named theorems (zero `sorry`, zero project-level axioms)\n      lakefile.toml, lean-toolchain\n    scripts/                   Python verification scripts (stdlib only)\n      CAVEATS.md               Methodology caveats from a public-facing audit\n      deployment_params.py     Deployment parameter table generator\n      proximity_gap_diagram.py Proximity-gap figure\n      ca-bound/                Half- and equal-threshold CA\n      fri-coupling/            FRI even/odd coupling and proximity gap\n      op1-barrier/             Equal-threshold CA equals C(n,w)/|F|\n      op2-obstruction/         M_max \u003e= 2 at FRI parameters\n      list-size/               Moments and pairwise / k-wise independence\n      char2-circle/            Characteristic-2 / circle-FRI extensions\n      cs-construction/         Crites--Stewart construction sweep\n      archive/                 Earlier exploratory scripts\n    outputs/                   Saved script outputs (mirrors scripts/)\n\n  paper2/\n    paper.pdf                  Paper 2 manuscript\n    scripts/\n      CAVEATS.md               Caveats for the deployment-scale spot checks\n      deployment-l3/           Paper 2 L3 / boundary-lift / GS m=2 list-decode\n\n  LICENSE                      Apache 2.0\n```\n\n---\n\n## Quick start\n\n**Build the Lean formalization** (Paper 1):\n\n```bash\ncd paper1/lean\nlake exe cache get   # download Mathlib cache (~5 min)\nlake build           # builds FRISoundness (zero `sorry`)\n```\n\n**Run a verification script**:\n\n```bash\npython3 paper1/scripts/op1-barrier/op1_scaling.py\npython3 paper2/scripts/deployment-l3/issue419_action_orbit_check.py\n```\n\n**Regenerate Paper 1's deployment-parameter table or proximity-gap figure**:\n\n```bash\npython3 paper1/scripts/deployment_params.py [--latex] [--per-round-max]\npython3 paper1/scripts/proximity_gap_diagram.py\n```\n\nPer-script docstrings document what each script computes; methodology\ncaveats live in each paper's `scripts/CAVEATS.md`. Saved outputs (where\npre-computed) mirror the scripts layout under `paper1/outputs/`; redirect\nstdout to refresh, e.g.\n`python3 .../op1_scaling.py \u003e paper1/outputs/op1-barrier/op1_scaling.output.txt`.\n\nThe CI workflow (`.github/workflows/ci.yml`) runs `lake build` and a sample\nof Python scripts on every push.\n\n---\n\n## Citation\n\n```bibtex\n@misc{ChaiFan2026FRI,\n  author = {Chai, Raullen and Fan, Xinxin},\n  title  = {{FRI} Soundness Above the {J}ohnson Bound via Threshold Halving},\n  year   = {2026},\n  howpublished = {Cryptology ePrint Archive, Paper 2026/861},\n  url    = {https://eprint.iacr.org/2026/861},\n  note   = {Companion repository: \\url{https://github.com/iotexproject/rs-proximity-gaps}}\n}\n\n@misc{ChaiFan2026ActionOrbit,\n  author = {Chai, Raullen and Fan, Xinxin},\n  title  = {Action-Orbit {FRI} Soundness above {J}ohnson:\n            Universal $K$-Bounds at Ethereum-Deployed {R}eed--{S}olomon Parameters},\n  year   = {2026},\n  howpublished = {Cryptology ePrint Archive, Paper 2026/858},\n  url    = {https://eprint.iacr.org/2026/858},\n  note   = {Companion repository: \\url{https://github.com/iotexproject/rs-proximity-gaps}}\n}\n```\n\n---\n\n## License\n\n[Apache License 2.0](LICENSE).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fiotexproject%2Frs-proximity-gaps","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fiotexproject%2Frs-proximity-gaps","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fiotexproject%2Frs-proximity-gaps/lists"}