Theorem: r_H^3 * 3 M_star - a^3 m_p = 0 (Hill-sphere cube-root identity)

Theorem (Hill-sphere-cube canonical): r_H = a (m_p / (3 M_star))^(1/3) cubed gives r_H^3 = a^3 m_p / (3 M_star), so r_H^3 * 3 M_star - a^3 m_p = 0 identically. Canonical sympy pins: r_H, M_star, m_p, a_h = sp.symbols('r_H M_star m_p a_h',…