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.
Complex-analytic and Banach-space open mapping theorems
The complex-analytic open mapping theorem, Open mapping theorem for holomorphic functions, concerns a nonconstant holomorphic function on a complex domain. Its conclusion comes from the local power form of a one-variable holomorphic map.
The Banach-space result documented in the references has different hypotheses and a different proof: it concerns a surjective bounded linear map between complete normed spaces. It is not used here, and neither theorem is a specialization of the other despite the shared name.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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
- J. Lebl, Guide to Cultivating Complex Analysis, Theorem 5.5.1 (standard reference, not scraped)
- MIT 18.102, Introduction to Functional Analysis, Theorem 2.32 (standard reference, not scraped)