Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-13
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: circumference divided by radius equals pi

Statement

For every circle of radius r>0, its circumference C(r) satisfies C(r)/r=π.

Facts & Assumptions

Given: A radius r>0.

[L1]

A circle of radius r>0 satisfies C(r)=2πr, has diameter d(r)=2r, and obeys C(r)/d(r)=π (Every circle has circumference 2 pi r and circumference-to-diameter ratio pi).

[L2]

The number π is positive (Pi as twice the smallest positive zero of cosine).

Refutation

technique · direct
1.1

Since r>0, division in [L1] gives C(r)/r=2π.

givenL1algebra
1.2

By [L2], 2π≠π, so the asserted ratio is false.

L2algebra
2.1

The valid normalization is circumference divided by diameter: [L1] gives C(r)/(2r)=π. The false statement omits this factor of 2.

step 1.1step 1.2L1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 58 results over 16 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources