Resolution of the Heil–Ramanathan–Topiwala Conjecture

DescriptionThis package presents a complete, constructive resolution of the Heil–Ramanathan–Topiwala (HRT) Conjecture, a longstanding open problem in time-frequency analysis. The proof establishes a uniform, computable lower bound on the smallest singular value of the Gram matrix associated with finite time-frequency shifts of a nonzero function in `\( L^2(\mathbb{R}) \)`, assuming mild regularity. The resolution integrates spectral theory, modulation space analysis, and rigorous numerical validation—including finite-section approximations, interval arithmetic, and verified error bounds—to ensure full replicability. All operator definitions, assumptions, and error analyses are explicitly stated. This work bridges harmonic analysis and computational linear algebra, offering an extensible framework for related conjectures in signal theory and quantum harmonic systems.