What are the odds someone who can prove whatever those things are can also talk about harmonic resonance equations and the practical matters of designing instrument-compatible chording arrangements, two topics entrenched heavily in mathematics (and physics, and materials science, and human usability concerns) but with a completely different specific focus?

The odds are near zero. Everyone learns their own domain. Quoting random properties of a specific subdomain of a branch of all possible learning demonstrates your knowledge, not disproves theirs.

You mean she might have had to memorize a simple formula? Such "rock solid" mathematical chops.