TheoremStatement: Literature-sourcedProof: AI-adaptedprecheck 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.

The stalk of the affine structure sheaf at a prime is A_p

For $p \in Spec A$ , there is a canonical isomorphism $O_{Spec A, p} ≅ A_{p}$ .

Given: A prime $p$ and the affine structure sheaf.

technique · direct

1.1given

The opens $D (f)$ with $f \notin p$ are cofinal neighborhoods of $p$ , and their sections are $A_{f}$ .

2.1step 1.1

Hence the stalk is ${\underset{\to}{l i m}}_{f \notin p} A_{f}$ .

3.1step 2.1∎

This colimit is $A_{p}$ by the universal property of localization.

Depends on