Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedaudited 2026-09-06
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.

This page defines H1 by crossed homomorphisms

Statement

This page defines H1(G;M) as crossed homomorphisms modulo principal ones.

Refutation

Given: The page's definition of group cohomology.

1.1

Here H1(G;M) is defined as the first right derived invariant functor.

given
2.1

The crossed-homomorphism description is a later low-degree interpretation, not this definition; it is intentionally reserved for the group-theory track.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources