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Precise statement
Heil, Ramanathan and Topiwala conjectured in 1996 that any finite set of time-frequency shifts of a nonzero square-integrable function is linearly independent. This refutes it: there is a Schwartz function admitting 12 linearly dependent time-frequency shifts.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Pro
ChatGPT (GPT-5.6 Pro) developed the counterexample and its proof strategy in dialogue with the authors. They initiated the search, told it to enlarge the phase-space configuration when it stalled, steered it from abstract methods toward elementary ones, and had it turn an existential construction into a fixed finite one. The authors then replaced several of the model's arguments with elementary proofs and closed gaps they call occasionally substantial: the whole of Section 6.2 and Appendix A was originally two sentences.
A preprint one day old with no external confirmation. The authors certify their numerical estimates with interval arithmetic, but that is their own rigor rather than third-party review.
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.