Alphabeta MathHow 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: local Lipschitz continuity is necessary for uniqueness of an ODE solution
Statement
False claim: A first-order ODE can have a unique solution through a point only if its vector field is locally Lipschitz there.
Facts & Assumptions
Given: The false necessity claim.
An almost-Lipschitz vector field has a unique solution through zero but is not locally Lipschitz there (An almost-Lipschitz vector field has a unique solution through zero but is not locally Lipschitz there).
Refutation
Suppose the false claim were true; [L1] gives uniqueness at zero while its vector field has no local Lipschitz constant there.
This contradicts the asserted necessity, so the claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
5 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
- Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, Ch. 2 (standard reference, not scraped)
- Jiri Lebl, Basic Analysis I, Section 6.3 (standard reference, not scraped)