TheoremStatement: Literature-sourcedProof: Literature-sourcedjudge 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.

Power-basis and polynomial discriminants

Statement

Let $K = Q (α)$ . If $f$ is the degree- $n$ monic minimal polynomial of $α$ , then $disc (1, α, \dots, α^{n - 1}) = (- 1)^{n (n - 1) / 2} N_{K / Q} (f^{'} (α)) = disc (f) .$

Facts & Assumptions

Given: $K = Q (α)$ and $\deg f = n$ .

[F1]

The basis discriminant is the square of its embedding determinant (Embedding determinant formula).

Proof

technique · direct

1.1

Fact [F1] makes the determinant the Vandermonde product of the conjugates of $α$ .

F1given

2.1

Squaring it and regrouping the root differences is the polynomial discriminant, equivalently the displayed derivative norm.

step 1.1algebra∎

Depends on

Used by

Dependency tree · two levels

8 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, Remark 2.28 (standard reference, not scraped)