Theorem: v_p^2 - 2 k T/m = 0 (Maxwell-Boltzmann most-probable-speed identity)

Theorem (Maxwell-Boltzmann v_p canonical): v_p = sqrt(2 k T/m) squared yields v_p² = 2 k T/m; residual v_p² - 2 k T/m = 0 identically. Canonical sympy pin: k, T, m = sp.symbols('k T m', positive=True); v_p = sp.sqrt(2*k*T/m); residual =…