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: any positive zero of sine characterizes pi

Statement

If p>0 and sin⁡p=0, then p=π.

Facts & Assumptions

Given: The proposed implication for positive sine zeros.

[L1]

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

[L2]

The least positive zero of sine is π (Pi is equivalently the first sine zero, twice the first cosine zero, and half the least common period).

[L3]

For every real x, sin⁡x=0 if and only if x=mπ for some integer m (The zero sets of sine and cosine and the least positive common period 2 pi).

Refutation

technique · direct
1.1

Put p=2π. By [L1], p>0, and by [L3], sin⁡p=0.

L1L3algebra
1.2

Yet 2π≠π because π>0.

L1algebra
2.1

Thus a positive zero need not equal π. The correct characterization in [L2] requires the least positive zero.

step 1.1step 1.2L2∎

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: 38 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