ExampleConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-05

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 Hilbert-symbol computation at an odd prime

Example

In $Q_{3}$ , one has

(3, 2)_{3} = - 1.

Facts & Assumptions

Given: The odd-prime Hilbert-symbol formula (The odd-prime Hilbert symbol formula).

Verification

technique · direct

1.1

Write $3 = 3^{1} \cdot 1$ and $2 = 3^{0} \cdot 2$ . The formula from The odd-prime Hilbert symbol formula gives $(3, 2)_{3} = (- 1)^{0} {(\frac{1}{3})}^{0} {(\frac{2}{3})}^{1} = (2 / 3)$ .

givenalgebra

2.1

The nonzero square class modulo $3$ is only $1$ , so $2$ is a nonsquare and $(2 / 3) = - 1$ . Hence $(3, 2)_{3} = - 1$ .

step 1.1givenalgebra∎

Depends on

The odd-prime Hilbert symbol formula

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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

Andrew V. Sutherland, 18.782 Lecture 10, Theorem 10.7 (standard reference, not scraped)