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: continuation along two paths with the same endpoints always agrees
Statement
False claim. Analytic continuation along two paths with the same endpoints always gives the same terminal germ.
Facts & Assumptions
Given: The logarithm loop example.
Starting from the principal logarithm germ at , one loop once around the origin ends at the germ of rather than at the initial germ (Continuing the logarithm once around the unit circle adds 2 pi i).
Refutation
Compare the constant path at with the once-around loop based at . These two paths have the same endpoints, but [L1] gives different terminal germs.
Therefore the universal claim is false.
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
- Lars V. Ahlfors, Complex Analysis, 3rd ed., Ch. 8 §1.4 (standard reference, not scraped)