Effective Spectral Mass and the CRT Certification Barrier

his technical note develops an effective spectral-mass diagnostic for the modular obstruction in the accelerated odd-only Collatz cycle equation. For a valuation word D, a terminal cycle witness requires the carry sum C_L(D) to vanish modulo the moving denominator N_{L,S}=2^S-3^L. Using the Chinese remainder theorem, this condition is decomposed into prime-power congruences, leading to an effective mass M_{\rm eff} that measures how much of the moving modulus is controlled by spectral equidistribution.