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: every continuous function is differentiable almost everywhere
Statement
Every continuous real function on a compact interval is differentiable almost everywhere.
Facts & Assumptions
Given: The statement above.
We refute it by a published counterexample.
Refutation
The published theorem The Takagi series converges uniformly to a continuous nowhere differentiable function gives a continuous function on whose finite derivative exists at no point.
In particular that function is not differentiable almost everywhere, so the statement 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
- Pieter C. Allaart and Kawshik Kawamura, The Takagi Function: A Survey (standard reference, not scraped)