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: the Riemann surface of a multivalued function is automatically a subset of C squared
Statement
False claim. The Riemann surface of a multivalued function is, by definition and without further work, a subset of .
Facts & Assumptions
Given: The abstract germ-space definition and the logarithm-surface model.
A Riemann surface of a complete analytic function is defined abstractly as a germ space equipped with basis sets and a projection to the base domain (The germ space of a complete analytic function).
The logarithm surface admits a convenient helicoid model only after one chooses an additional realization (The logarithm surface admits the standard helicoid model).
Refutation
Fact [L1] shows that the definition itself produces an abstract space of germs, not an a priori subset of .
The geometric model in [L2] is an extra construction, not part of the definition. Therefore the claim that such a subset model is automatic 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
- Curtis T. McMullen, Riemann Surfaces, Theorem 4.3 (standard reference, not scraped)
- Lars V. Ahlfors, Complex Analysis, 3rd ed., Ch. 3 §4.3 (standard reference, not scraped)