CounterexampleConstruction: Literature-sourcedVerification: AI-adaptedPipeline-generatedjudge 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.

A modulus need not be a conductor

Statement refuted

“Every character modulo $q$ has conductor $q$ .”

Facts & Assumptions

Given: Induction (Induced Dirichlet characters) and unique primitive ancestors (Unique primitive ancestor of a Dirichlet character).

Counterexample

technique · direct

1.1

Induce $χ_{4}$ to modulus $12$ ; on units it agrees with reduction modulo $4$ and it vanishes at every nonunit modulo $12$ .

given

2.1

Its primitive ancestor is $χ_{4}$ , so uniqueness in the given theorem makes its conductor $4$ , not $12$ .

step 1.1given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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

Andersen, Theorem 16.2 (standard reference, not scraped)