False statementConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passaudited 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: a local ODE solution extends across the whole time-domain of its vector field

Statement

False claim: Every local solution extends across the whole time-domain on which its vector field is defined.

Facts & Assumptions

Given: The false universal claim.

[L1]

$y^{'} = y^{2}$ , $y (0) = 1$ , has maximal solution $y (t) = (1 - t)^{- 1}$ on $(- \infty, 1)$ ( $y^{'} = y^{2}$ , $y (0) = 1$ , has maximal solution $y (t) = (1 - t)^{- 1}$ on $(- \infty, 1)$ ).

Refutation

technique · contradiction

1.1

Suppose the false claim were true; the vector field in [L1] is defined for all real times, but its solution has finite maximal endpoint $1$ .

assume-contraL1

2.1

The asserted extension would continue this maximal solution past $1$ , a contradiction.

step 1.1discharge-contradiction∎

Depends on

$y'=y^2$, $y(0)=1$, has maximal solution $y(t)=(1-t)^{-1}$ on $(-\infty,1)$

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

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)