Piano Tuner and Broglie's Law - Phase and group velocities in quantized waves

The product of particle mass with phase velocity opposes de Broglie's hypothesis. The product of mass with group velocity establishes the hypothesis as a Law in physics, like Bragg's law that does indeed depend on phase velocity. The product of the two velocities is equal to c^^2, where the phase velocity vp is greater than c. Many examples are referenced, including room temperature superconductors with chiral symmetry; multi-dual quasicrystal quanta; physical intrinsic spin; etc