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.
The fundamental-group and minimum-modulus proofs of the fundamental theorem of algebra
The theorem Fundamental theorem of algebra by the fundamental-group obstruction and the published Fundamental theorem of algebra: every nonconstant complex polynomial has a complex root establish the same root-existence statement by genuinely different routes. The fundamental-group proof compares a root-free radial nullhomotopy with the nonzero degree forced by the leading term on a large circle. The minimum-modulus proof instead chooses a point where is least and shows that a positive minimum can be decreased. The first argument spends the calculation of ; the second spends compactness and the local expansion of a polynomial.
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Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 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
- Allen Hatcher, Algebraic Topology, Theorem 1.8 (standard reference, not scraped)
- J. Peter May, A Concise Course in Algebraic Topology, Chapter 1, §7 (standard reference, not scraped)
- J. Lebl, Basic Analysis I, The Fundamental Theorem of Algebra (standard reference, not scraped)