DefinitionDefinition: Literature-sourcedProof: Not applicablejudge 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.

Equivalent nontrivial absolute values

Definition

Let $∣ \cdot ∣_{1}$ and $∣ \cdot ∣_{2}$ be nontrivial absolute values on a field $F$ . They are equivalent when there is a real number $c > 0$ such that

$∣ x ∣_{2} = ∣ x ∣_{1}^{c}$

for every $x \in F$ .

Depends on

Absolute values on a field

Used by

Dependency tree · one level

1 result within one dependency step 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 5 (standard reference, not scraped)
Keith Conrad, Ostrowski's Theorem for Q (standard reference, not scraped)