ExampleConstruction: Literature-sourcedVerification: 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.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Binary icosahedral cover of A5

Example

$SL (2, 5) \to PSL (2, 5) ≅ A_{5}$ is the sourced binary-icosahedral universal-cover example.

Facts & Assumptions

Given: Use Weibel, §6.9, Example 6.9.1, cited above.

[L1]

Weibel's Example 6.9.1 identifies $SL (2, 5) \to PSL (2, 5)$ as a universal central extension with kernel ${\pm I}$ .

Verification

technique · direct

1.1

The central quotient map $SL (2, 5) \to PSL (2, 5)$ has kernel ${\pm I} ≅ C_{2}$ , and the cited example identifies it as the universal central extension.

L1given

2.1

With the standard isomorphism $PSL (2, 5) ≅ A_{5}$ , this is the binary-icosahedral universal cover asserted in the statement.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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

Charles A. Weibel, An Introduction to Homological Algebra, Chapter 6, Example 6.9.1 (standard reference, not scraped)