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.
Once the cited Riemann mapping theorem is granted, the new bridge implications in the grand equivalence are choice-free
The only place where the grand theorem imports a choice-bearing result is the existing Riemann mapping supplier used in clause 9. Everything else newly proved on this page is independent of that step: homotopy invariance of line integrals, the null-homotopy version of Cauchy's theorem, the complement-connectedness criterion, the harmonic-conjugate bridge, the contractibility bridge, and the winding-number/degree dictionary.
So, relative to the already-cited choice strength of the Riemann mapping page recorded in Choice strength used in the extremal proof of the Riemann mapping theorem, the new bridge implications here are choice-free.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
18 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
- Matthias Weber, Complex Analysis, Theorem 5.2.6 (standard reference, not scraped)