ExampleConstruction: AI-generatedVerification: 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.

An Eisenstein total-ramification calculation

Example

In $Q (\sqrt[3]{2})$ , the prime $2$ is totally ramified: $2 O_{K} = P^{3}$ .

Verification

Given: $α^{3} = 2$ .

1.1

$X^{3} - 2$ is Eisenstein at $2$ , and its reduction is $X^{3}$ .

givenalgebra

2.1

The Eisenstein ramification corollary gives the unique prime $P = (2, α)$ with exponent $3$ .

step 1.1algebra∎

Depends on

An Eisenstein prime is totally ramified

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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

J. S. Milne, Algebraic Number Theory, Proposition 3.53 (standard reference, not scraped)