The Photon as a Colliding Particle, Priced: Compton's Momentum Postulate and the Shift It Returns

Census pricing (row CC-102) of the photon-collision postulate of Compton's 'A Quantum Theory of the Scattering of X-rays by Light Elements,' Phys. Rev. 21, 483-502 (1923), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step -- Einstein's light quantum (CC-101) promoted to a particle carrying momentum p = h nu/c into a single elastic collision with an electron treated as free and at rest -- is postulated, not derived; classical wave theory returns no shift at all. Verified in the notebook (17 checks, exit 0) from the postulate plus named CODATA constants (inputs, never spent as derived): Compton wavelength h/(m_e c) = 2.426310 pm; shifts 0.7106 pm (45 deg), 2.4263 pm (90 deg), 4.1420 pm (135 deg) at the paper's reported angles; at the named Mo K-alpha input (0.07093 nm, 17479.8 eV) recoil electrons of 173.4 eV (45 deg) and 578.2 eV (90 deg), with two-body conservation verified from the momentum side at 90 deg (KE 578.2 eV both ways; recoil angle 44.04 deg). Remainders at full size: the free-electron ride is priced -- the 45 deg recoil of 173.4 eV falls below the named carbon 1s binding scale of 284.2 eV, so that shell cannot be treated as free at that angle -- and the unshifted line stands outside the step (whole-atom Compton wavelength 0.000111 pm, electron/atom ratio 21874.7). Scout grade throughout: no verbatim primary reading claimed. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.