Alphabeta MathHow 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.
Primitive Dirichlet characters and conductor
Definition
A character modulo is primitive if it is not induced from a proper divisor of . By Unique primitive ancestor of a Dirichlet character, every character has a unique primitive ancestor; its modulus is the conductor. The principal character modulo is primitive and has conductor .
Depends on
Used by
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
- Nickolas Andersen, Analytic Number Theory, section 16.1 (standard reference, not scraped)