CorollaryStatement: Literature-sourcedProof: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 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.

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Kernel of the universal central extension

Statement

For perfect G, the universal-central-extension kernel is M(G).

Proof

Given: Use the free-presentation universal extension of a perfect group $G = F / R$ .

1.1

Its kernel is $(R \cap [F, F]) / [F, R]$ .

given

2.1

Hopf’s formula identifies this kernel with $M (G)$ .

step 1.1algebra∎

Depends on

Used by

Binary icosahedral cover of A5 Example
Universal central extension groups are superperfect Proposition

Dependency tree · two levels

9 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

Clara Löh, Group Cohomology (standard reference, not scraped)