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.
Wiener lemma is developed on the Fourier analysis track
Statement
The Wiener inverse theorem — that a nowhere-vanishing function on the circle with absolutely convergent Fourier series has an inverse with absolutely convergent Fourier series — belongs to the Fourier-analysis track, which owns its statement and proof. This page proves only the character computation and the resulting Gelfand transform; it neither states nor proves the Wiener theorem, and it creates no load-bearing forward reference to the Fourier track.
Remarks
- Orientation only. The remark records the ownership boundary so that the character computation is not mistaken for the Wiener theorem.
- Not a supplier. Nothing on this page depends on this remark, and the Fourier track may cite this page's example as an orientation pointer only.
Used by
Nothing in the library uses this result yet.
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Vahid Shirbisheh, Lectures on C-star Algebras, v2 — §2.6 and §3.1, printed pp. 44–67 (standard reference, not scraped)