Alphabeta Math

Homological Gaussian Elimination

About this page
Pipeline-generated
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

✓ 7 results · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 7 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Category Theory
Homological Algebra
Set Theory
2 · Logical flowchart

3 · Items

Definition

Complexes, homotopies and contractibility in an additive category

Definition

An invertible cochain differential block and its candidate reduction

Lemma

Triangular basis changes diagonalize an invertible differential block

Theorem

Gaussian elimination splits a contractible two-term complex

Proposition

Explicit strong deformation retract from Gaussian cancellation

Corollary

Gaussian cancellation preserves homotopy type and abelian-category homology

Theorem

Finite iteration of current invertible-block cancellations

Proposition

Additive functors preserve chosen Gaussian cancellations

Proposition

Transferred maps are functorial up to homotopy, with strict naturality limits

Sources