Gabor Frames of Totally Positive Functions
Statement
For which lattice parameters does a totally positive window function generate a Gabor frame? Gröchenig and Stöckler initiated the program in 2013; this paper gives the complete characterization, together with a Kadets-type theorem for shift-invariant spaces.
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No person has examined this. Everything below was judged by machines. say whether it holds →
proof attempt · #1
Jaume de Dios Pont, Karlheinz Gröchenig, Lukas Liehr, Irina Shafkulovska and Mitchell A. Taylor, using GPT-5.4That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
GPT-5.4 surveyed the limit-operator literature and suggested the connection that led the authors to Seidel's work, from which the proof of Theorem 3.3 was adapted; it also suggested simplifications including a simpler perturbation sequence in Lemma 4.4. Codex 5.5 and Claude Opus 4.7 assisted with the Lean formalization. Gröchenig, who posed the program, is among the authors.
Machine-checked by Lean on #1 · not a person
lean: partially checkedLeanscope Lean formalization of the core argument; statement correspondence not independently audited
The paper carries a Lean formalization written with Codex 5.5 and Claude Opus 4.7 assistance; all arguments and formalizations were independently checked by the authors. No external review yet. Tier: the Lean formalization was written with model assistance and checked by the authors themselves; author checking is not independent review.
Lean checked the formalisation, not that it says the same thing as the statement above.
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