Open Research Index

A proof of Conway's refinement conjecture

Dan Abramov

Palomar Registrypalomar/PALOMAR-2026-09-03-000002Sep 3, 2026math.LOscore 0

A Lean proof of Conway's 1976 refinement conjecture for omnific integers. For omnific integers a, b, c, d with ab = cd, it proves the existence of omnific integers e, f, g, h satisfying a = ef, b = gh, c = eg, and d = fh, including zero and degenerate cases. The proof proceeds through factorisation and refinement theory for generalised-power-series integer parts and connects the generalised-power-series and surreal-number formulations.

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-03-000002
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-03-000002/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-03-000002/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'