ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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.

A quadratic-field codifferent

Example

For $K = Q (i)$ , $O_{K}^{\lor} = (2 i)^{- 1} Z [i], D_{K} = (2 i) = (2), N D_{K} = 4 = ∣ d_{K} ∣ .$

Verification

Given: $O_{K} = Z [i]$ and $f = X^{2} + 1$ .

1.1

The monogenic formula gives $D_{K} = (f^{'} (i)) = (2 i) = (2)$ . Taking the fractional-ideal inverse gives $O_{K}^{\lor} = (2 i)^{- 1} Z [i]$ .

givenalgebra

2.1

Its norm is $4$ , agreeing with the discriminant $d_{K} = - 4$ and the norm-of-the-different theorem.

step 1.1algebra∎

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

Keith Conrad, The Different Ideal, Examples 3.6 and 4.4 (standard reference, not scraped)