ExampleConstruction: Literature-sourcedVerification: 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.

PSL(2,7) and a low-rank family entry

Example

$PSL (2, 7)$ is a sourced Lie-type entry under the table's low-rank convention.

Facts & Assumptions

Given: Use Smith's Lie-type family table and its rank-one notation cited above.

[L1]

Smith's table lists type $A_{n}$ as the linear family $L_{n + 1} (q)$ , and its rank-one discussion explicitly names $L_{2} (q)$ as Lie type. In standard notation $L_{2} (q) = PSL (2, q)$ .

Verification

technique · direct

1.1L1given

Specializing [L1] to $n = 1$ and $q = 7$ places $L_{2} (7) = PSL (2, 7)$ in the linear Lie-type family.

2.1step 1.1∎

This is precisely the claimed table-level Lie-type example; no structural construction is being inferred.

Used by

Nothing in the library uses this result yet.

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Stephen D. Smith, CFSG—A User’s Manual, lecture 1, pp. 17 and 43 n. 6 (standard reference, not scraped)