Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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.

FALSE: A non-negative operator has a unique square root among all operators

Statement

A non-negative operator has a unique square root among all operators.

Facts & Assumptions

Given: The identity operator I on R2.

[L1]

A non-negative operator has a unique non-negative square root (A non-negative operator has a unique non-negative square root).

Refutation

technique · direct
1.1

The operator I is non-negative, and [L1] says its non-negative square root is uniquely I itself.

L1
2.1

Nevertheless (−I)2=I2=I and −I≠I. So I has at least two square roots, and uniqueness fails once the non-negative condition on the square root is dropped.

step 1.1algebra∎

Depends on

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