Open Research Index

Pascal Cofactors

John Fairfax-Ball

Palomar Registrypalomar/PALOMAR-2026-10-02-000014Oct 2, 2026math.NTscore 0

A Lean 4 formalisation of p-adic valuation laws for alternating cofactors C_d(p^a) = (p^(ad)+1)/(p^a+1) with odd d. It proves finite-window coefficient scaling and an exact pre-extremal restricted-binomial-gcd formula, identifies the sparse endpoint, proves the least extremal row T_p(C_d(p^a)) = p^(ad)+1 for odd d >= 5, and gives the full cubic classification for p^(2a)-p^a+1. The Palomar Challenge records coefficient scaling, the exact bounded gcd formula, the odd-degree least-row theorem, and the cubic classification.

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-2026-10-02-000014
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-02-000014/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-02-000014/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'