ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-04

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.

The two-adic square test separates 17 and 5

Example

In $Q_{2}$ , the number $17$ is a square but $5$ is not.

Facts & Assumptions

Given: The $2$ -adic square criterion.

[L1]

An element $2^{n} u$ with odd $u$ is a square in $Q_{2}$ exactly when $n$ is even and $u \equiv 1 (m o d 8)$ (Square criterion in Q_2).

Verification

technique · direct

1.1

One has $17 = 2^{0} \cdot 17$ with $17 \equiv 1 (m o d 8)$ , so [L1] shows that $17$ is a square in $Q_{2}$ .

L1givenalgebra

2.1

One has $5 = 2^{0} \cdot 5$ with $5 \equiv 5 (m o d 8) \neq 1$ , so [L1] shows that $5$ is not a square in $Q_{2}$ .

L1givenalgebra∎

Depends on

Square criterion in Q_2

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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

Keith Conrad, Hensel's Lemma, Theorem 4.5 (standard reference, not scraped)