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  "problem_id": "vibemathed:gabor-frames-totally-positive",
  "title": "Gabor Frames of Totally Positive Functions",
  "canonical_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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      "title": "arXiv",
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      "attempted_at": "2026-08-05T00:00:00.000Z",
      "human_collaborators": [
        "Jaume de Dios Pont",
        "Karlheinz Gröchenig",
        "Lukas Liehr",
        "Irina Shafkulovska",
        "Mitchell A. Taylor"
      ],
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      "outcome": "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.",
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