https://github.com/iotexproject/rs-proximity-gaps
Lean 4 formalization, Python verification, and manuscripts for two ePrint papers on FRI proximity gaps above the Johnson radius (Chai & Fan, IoTeX, 2026) — ePrint 2026/861 + 2026/858.
https://github.com/iotexproject/rs-proximity-gaps
action-orbit correlated-agreement cryptography ethereum formal-verification fri interactive-oracle-proof johnson-bound lean4 mathlib proximity-gap reed-solomon stark succinct-proofs zero-knowledge-proofs zk-stark
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Lean 4 formalization, Python verification, and manuscripts for two ePrint papers on FRI proximity gaps above the Johnson radius (Chai & Fan, IoTeX, 2026) — ePrint 2026/861 + 2026/858.
- Host: GitHub
- URL: https://github.com/iotexproject/rs-proximity-gaps
- Owner: iotexproject
- License: apache-2.0
- Created: 2026-04-25T17:39:00.000Z (2 months ago)
- Default Branch: main
- Last Pushed: 2026-05-20T04:48:25.000Z (about 1 month ago)
- Last Synced: 2026-05-20T08:15:28.724Z (about 1 month ago)
- Topics: action-orbit, correlated-agreement, cryptography, ethereum, formal-verification, fri, interactive-oracle-proof, johnson-bound, lean4, mathlib, proximity-gap, reed-solomon, stark, succinct-proofs, zero-knowledge-proofs, zk-stark
- Language: Python
- Homepage: https://proximityprize.org
- Size: 24.2 MB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Reed--Solomon Proximity Gaps — Companion Repository
Manuscripts, Lean 4 formalization, and Python verification scripts for two
papers by Raullen Chai and Xinxin Fan (IoTeX Network):
> **Paper 1 — FRI Soundness Above the Johnson Bound via Threshold Halving.**
> Cryptology ePrint Archive, Paper [2026/861](https://eprint.iacr.org/2026/861.pdf), 2026.
> Self-contained materials in [`paper1/`](paper1/).
>
> **Paper 2 — Action-Orbit FRI Soundness above Johnson:
> Universal $K$-Bounds at Ethereum-Deployed Reed--Solomon Parameters.**
> Cryptology ePrint Archive, Paper [2026/858](https://eprint.iacr.org/2026/858.pdf), 2026.
> Self-contained materials in [`paper2/`](paper2/).
The papers attack the open intermediate zone (Johnson radius $< \delta < $
list-decoding capacity) of the Reed--Solomon proximity-gap problem — the
deployment regime of every FRI-based STARK on Ethereum's roadmap.
[](https://github.com/iotexproject/rs-proximity-gaps/actions/workflows/ci.yml)
---
## Repository Layout
The repository is organized **per paper**: each paper directory is
self-contained.
```
rs-proximity-gaps/
paper1/
paper.pdf Paper 1 manuscript
PROOF_CHAIN.md Step-by-step trace of Paper 1's main theorem
lean/ Lean 4 + Mathlib formalization
STATUS.md Per-theorem status board (paper label ↔ Lean identifier)
FRISoundness/ Named theorems (zero `sorry`, zero project-level axioms)
lakefile.toml, lean-toolchain
scripts/ Python verification scripts (stdlib only)
CAVEATS.md Methodology caveats from a public-facing audit
deployment_params.py Deployment parameter table generator
proximity_gap_diagram.py Proximity-gap figure
ca-bound/ Half- and equal-threshold CA
fri-coupling/ FRI even/odd coupling and proximity gap
op1-barrier/ Equal-threshold CA equals C(n,w)/|F|
op2-obstruction/ M_max >= 2 at FRI parameters
list-size/ Moments and pairwise / k-wise independence
char2-circle/ Characteristic-2 / circle-FRI extensions
cs-construction/ Crites--Stewart construction sweep
archive/ Earlier exploratory scripts
outputs/ Saved script outputs (mirrors scripts/)
paper2/
paper.pdf Paper 2 manuscript
scripts/
CAVEATS.md Caveats for the deployment-scale spot checks
deployment-l3/ Paper 2 L3 / boundary-lift / GS m=2 list-decode
LICENSE Apache 2.0
```
---
## Quick start
**Build the Lean formalization** (Paper 1):
```bash
cd paper1/lean
lake exe cache get # download Mathlib cache (~5 min)
lake build # builds FRISoundness (zero `sorry`)
```
**Run a verification script**:
```bash
python3 paper1/scripts/op1-barrier/op1_scaling.py
python3 paper2/scripts/deployment-l3/issue419_action_orbit_check.py
```
**Regenerate Paper 1's deployment-parameter table or proximity-gap figure**:
```bash
python3 paper1/scripts/deployment_params.py [--latex] [--per-round-max]
python3 paper1/scripts/proximity_gap_diagram.py
```
Per-script docstrings document what each script computes; methodology
caveats live in each paper's `scripts/CAVEATS.md`. Saved outputs (where
pre-computed) mirror the scripts layout under `paper1/outputs/`; redirect
stdout to refresh, e.g.
`python3 .../op1_scaling.py > paper1/outputs/op1-barrier/op1_scaling.output.txt`.
The CI workflow (`.github/workflows/ci.yml`) runs `lake build` and a sample
of Python scripts on every push.
---
## Citation
```bibtex
@misc{ChaiFan2026FRI,
author = {Chai, Raullen and Fan, Xinxin},
title = {{FRI} Soundness Above the {J}ohnson Bound via Threshold Halving},
year = {2026},
howpublished = {Cryptology ePrint Archive, Paper 2026/861},
url = {https://eprint.iacr.org/2026/861},
note = {Companion repository: \url{https://github.com/iotexproject/rs-proximity-gaps}}
}
@misc{ChaiFan2026ActionOrbit,
author = {Chai, Raullen and Fan, Xinxin},
title = {Action-Orbit {FRI} Soundness above {J}ohnson:
Universal $K$-Bounds at Ethereum-Deployed {R}eed--{S}olomon Parameters},
year = {2026},
howpublished = {Cryptology ePrint Archive, Paper 2026/858},
url = {https://eprint.iacr.org/2026/858},
note = {Companion repository: \url{https://github.com/iotexproject/rs-proximity-gaps}}
}
```
---
## License
[Apache License 2.0](LICENSE).