Alphabeta Math
PropositionStatement: AI-adaptedProof: AI-generatedPipeline-generatedverified 2026-09-26 (gpt-6-sol)
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.

Multiplier of a free group

Statement

Assume the Axiom of Dependent Choice and supplied projective-resolution data for group homology. Then M(F)=0 for every free group F.

Proof

Given: The stated choice and resolution data, and the free presentation F=F/1.

1.1given

Hopf’s numerator is 1∩[F,F]=1 and its denominator is [F,1]=1.

2.1step 1.1algebra∎

Thus the Hopf quotient, and hence M(F), is zero.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources