Theorem: omega^2 - N^2 sin^2(theta) at theta = pi/2 equals 0 (internal-wave isentropic limit)

Theorem (internal-wave-pi/2 canonical): at theta = pi/2 (horizontal wavenumber, vertical particle motion), sin(pi/2) = 1, so omega² = N²·1 = N², residual omega² - N²·sin²(pi/2) = N² - N² = 0 identically. Canonical sympy pins: N_w, theta =…