Theorem: omega_SPR^2 (1 + eps_d) - omega_p^2 = 0 (SPR dispersion root)

Theorem (SPR-dispersion-root canonical): omega_SPR = omega_p / sqrt(1 + eps_d) squared and multiplied by (1 + eps_d) gives omega_p^2 exactly, so omega_SPR^2 (1 + eps_d) - omega_p^2 = 0 identically. Canonical sympy pins: omega_p, eps_d =…