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 wild different exponent

Example

At the unique prime over $2$ in $Q (\sqrt{2})$ , $e = 2$ and the different exponent is at least $2$ .

Verification

Given: $X^{2} - 2$ is Eisenstein at $2$ .

1.1

Eisenstein gives a unique prime above $2$ with ramification index $2$ .

givenalgebra

2.1

Because $2 ∣ e$ , the extension is wild, so the valid conclusion is the wild lower bound $v_{P} (D_{K}) \geq 2$ ; no equality $e - 1$ is inferred.

step 1.1algebra∎

Depends on

Different exponents in tame and wild ramification

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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, Theorem 4.13 (standard reference, not scraped)