Two Fitted Constants: Van der Waals' a and b, the Critical Ratios They Return for Free, and the 3/8 No Gas Obeys

Census row CC-93 priced as a packet: van der Waals' 1873 equation (p + a/v^2)(v - b) = RT carries two substance-specific constants determined empirically for each gas. From measured critical inputs the notebook inverts a and b for three gases (CO2: a = 0.365671 Pa m^6/mol^2, b = 42.85 cm^3/mol; N2 and H2O likewise), shows the round trip T_c = 8a/(27Rb), p_c = a/(27b^2), V_c = 3b returning the inputs identically (at the critical point the cubic is (v-3b)^3 -- the fits read back), and verifies the reduced form p_r = 8T_r/(3v_r - 1) - 3/v_r^2, the law of corresponding states, as the equation's real derived content. Its one genuinely free prediction, the universal Z_c = 3/8 = 0.375, is priced against the measured Z_c of CO2 (0.274), N2 (0.290) and H2O (0.229) and fails every gas by 23-39%. Statistical mechanics' later estimates of a and b for model potentials are closure-by-replacement for those models, not a derivation of any real gas's constants. EXTENSION. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.