Alphabeta Math

Homological Gaussian Elimination — Examples

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✓ 5 results · all verified · 2 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 3 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

Example

A unit pivot forces the minus Schur sign

Example

Neighboring differentials transform with the pivot basis changes

Example

Two adjacent noncomposable Gaussian pivots in either finite order

Counterexample

The isolated differential 2 on the integers cannot be cancelled

Counterexample

Gaussian transfer is not strictly functorial on arbitrary cochain maps

Sources