Visionary Abstract:
We propose a radically new paradigm for decoding the hidden metrics of Calabi–Yau manifolds—treating harmonic forms not as passive mathematical artifacts but as dynamic resonant sources that seed the geometry itself. Drawing inspiration from cymatics and wave propagation, we hypothesize that harmonic representatives of cohomology classes encode deep geometric structure through their potential to initiate and guide vibrational modes across the manifold. By modeling these forms as dynamic signal sources—acoustic or quantum-like—we investigate whether their propagation behaviors can reconstruct the Ricci-flat metric algorithmically or numerically.
Where previous generations of mathematicians were constrained by the static limitations of pen and paper, this endeavor belongs to the machine age. Only modern computing—capable of high-dimensional simulation, continuous state tracking, and dynamic memory allocation—can perform the recursive, living bookkeeping that such a resonant framework demands. This is not metaphor. It is a concrete geometrical approach that unites harmonic analysis, metric emergence, and string compactification under one vibrational language. If realized, this method could finally unveil the shape of compactified space—not by static deduction, but by listening to the manifold’s own harmonic song.