Theorem: F (1 - R) - pi sqrt(R) = 0 (Fabry-Perot rational-finesse identity)

Theorem (cavity-finesse-rational canonical): F = pi sqrt(R)/(1 - R) cleared of denominator gives F(1-R) = pi sqrt(R), residual F(1-R) - pi sqrt(R) = 0 identically. Canonical sympy pins: R = sp.Symbol('R', positive=True); F =…