Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedjudge 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.

Gaussian and Eisenstein integral bases

Example

OQ(i)=Z[i], d=−4; and OQ(−3)=Z[(1+−3)/2], d=−3.

Facts & Assumptions

Given: The quadratic integer and discriminant formulas (Integers in a quadratic field, Discriminant of a quadratic field).

Verification

technique · direct
1.1

Insert d=−1 and d=−3 in the given integral-basis formula.

given
2.1

Insert the same residues modulo 4 in the given discriminant formula.

step 1.1given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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