Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-21
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: continuity of the right-hand side guarantees unique ODE solutions

Statement

False claim: Every continuous right-hand side gives a unique local solution through each initial value.

Facts & Assumptions

Given: The false universal claim.

[L1]

y′=2∣y∣ has distinct delayed-start solutions through the origin (y′=2∣y∣ has a continuum of delayed-start solutions through the origin).

Refutation

technique · contradiction
1.1

Suppose the false claim were true; [L1] gives a continuous right-hand side with distinct solutions through the same initial value.

assume-contraL1
2.1

This contradicts the asserted uniqueness, so the claim is false.

step 1.1discharge-contradiction∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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