ExampleConstruction: AI-generatedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-26

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 support of Z/12Z is the pair of primes (2) and (3)

Example

As a $Z$ -module,

{Supp}_{Z} (Z / 12 Z) = {(2), (3)} .

Facts & Assumptions

Given: The $Z$ -module $Z / 12 Z$ .

[L1]

The support of $R / I$ is the set of prime ideals containing $I$ (The support of a cyclic quotient is its vanishing set).

[L2]

The support of a module is a set of prime ideals (Support of a module).

Verification

technique · direct

1.1

Apply [L1] with $R = Z$ and $I = (12)$ . A prime ideal of $Z$ contains $(12)$ exactly when its prime generator divides $12$ , so the only such prime ideals are $(2)$ and $(3)$ .

L1algebra

2.1

Therefore ${Supp}_{Z} (Z / 12 Z) = {(2), (3)}$ , as claimed.

step 1.1L2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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

A. Altman and S. Kleiman, A Term of Commutative Algebra, 13th ed., (13.27) (standard reference, not scraped)