CorollaryStatement: Literature-sourcedProof: AI-generatedPipeline-generatedaudited 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.

Discriminant valuations from different exponents

Statement

For a rational prime $p$ , $v_{p} (d_{K}) = \sum_{P ∣ p} f (P / p) v_{P} (D_{K}) .$

Proof

Given: the prime-ideal factorisation of the different.

1.1

Factor $D_{K}$ into its finite prime powers and apply norm multiplicativity, using $N P = p^{f (P / p)}$ over $p$ .

givenalgebra

2.1

The norm-of-the-different identity makes the $p$ -adic valuation of that product $v_{p} (d_{K})$ , which is the displayed sum.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

12 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, Corollary 4.16 (standard reference, not scraped)