Open Research Index

H2 obstruction to lifting discrete matrix representations

AItoBit

Palomar Registrypalomar/PALOMAR-2026-10-15-000010Oct 15, 2026math.GRscore 0

A Lean proof that a discrete matrix representation lifts across a surjective homomorphism of commutative rings with square-zero kernel exactly when its explicitly constructed second-cohomology obstruction vanishes. The proof constructs the conjugation action and defect cocycle for an abelian group extension, proves the lifting criterion, and applies it to reduction of invertible matrices. The underlying additive kernel is identified with matrices over the coefficient-ring kernel. This is classical obstruction theory motivated by DARPA Challenge 18, not a solution of its homotopy/Langlands…

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-2026-10-15-000010
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-15-000010/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-15-000010/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'