CorollaryStatement: Literature-sourcedProof: AI-adaptedjudge 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.

Squarefree power discriminant criterion

Statement

If integral $α$ generates $K$ and its power-basis discriminant is squarefree, then $O_{K} = Z [α]$ .

Facts & Assumptions

Given: The stated integral generator.

[F1]

The index-discriminant formula holds (Order-index discriminant formula).

Proof

technique · direct

1.1

The power order is an order, and [F1] says its discriminant is the square of its index times $d_{K}$ .

F1given

2.1

A square index dividing a squarefree integer is $1$ , so the two orders coincide.

step 1.1algebra∎

Depends on

Used by

A pure cubic power basis: why the squarefree-discriminant certificate does not apply Example

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

Milne, Corollary 2.10 (standard reference, not scraped)