https://github.com/daedalus/alphaproof-nexus
AlphaProof Nexus evolution on Erdős Problem #25 — does every congruence-avoiding set have a logarithmic density? Open problem, formalized in Lean 4.
https://github.com/daedalus/alphaproof-nexus
alphaproof-nexus erdos-problems formal-math lean lean4 open-problem theorem-proving
Last synced: 26 days ago
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AlphaProof Nexus evolution on Erdős Problem #25 — does every congruence-avoiding set have a logarithmic density? Open problem, formalized in Lean 4.
- Host: GitHub
- URL: https://github.com/daedalus/alphaproof-nexus
- Owner: daedalus
- Created: 2026-05-24T05:03:03.000Z (about 1 month ago)
- Default Branch: master
- Last Pushed: 2026-05-24T07:03:32.000Z (about 1 month ago)
- Last Synced: 2026-05-24T07:10:04.692Z (about 1 month ago)
- Topics: alphaproof-nexus, erdos-problems, formal-math, lean, lean4, open-problem, theorem-proving
- Language: Lean
- Size: 73.2 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Agents: AGENTS.md
Awesome Lists containing this project
README
# AlphaProof Nexus
Repository of Lean 4 formalizations for open Erdős problems, evolved via
AlphaProof Nexus (arXiv:2605.22763) evolutionary proof search.
## Problems
| # | Title | Status | Dir |
|---|-------|--------|-----|
| 1 | Sum-distinct sets | Proof complete (0 sorries) | `problems/1/` |
| 25 | Congruence-avoiding sets | 10 sorries (1 open) | `problems/25/` |
| 364 | Consecutive powerful numbers | 0 errors, 1 sorry | `problems/364/` |
| 634 | Triangle tilings | 0 errors, 3 sorries | `problems/634/` |
All 628 open Erdős problems have directories under `problems/N/`.
## Quick start
```bash
lean problems/25/Erdos25.lean
lean problems/25/population/member_04_gen1_head_truncation.lean
lean problems/634/population/member_07_gen7_geometric_obstruction.lean
lean problems/1/Erdos1.lean
lean problems/1/population/member_05_champion.lean
```
Requires Lean 4.29.1, `lean` on `PATH`.
See `AGENTS.md` for full workflow documentation.