Alphabeta Math
CounterexampleConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06
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The underlying bar contraction is not equivariant

Statement refuted

The identity-insertion contraction of homogeneous bars is G-equivariant for every group G.

Counterexample

Given: A group G with h≠1 and the bar generator (1).

1.1

The contraction has s(1)=(1,1), so hs(1)=(h,h).

given
2.1

But s(h⋅(1))=s(h)=(1,h), which differs from (h,h). Thus equivariance fails.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources