Carry Absorption, Boundary-Pair Reduction, and Exact Anti-Persistence in the Collatz Problem

We study the accelerated odd Collatz map F(m) = (3m+1)/2^{v_2(3m+1)} through an exact binary decomposition into a carry-free quotient and a carry cocycle. The carry-free quotient over F_2[x] is shown to be unconditionally contractive. For the classical map we prove an exact boundary-pair reduction, D(F(n)) - D(n) = tau(n) - b(n), where b(n) is determined by the first equal adjacent pair in the binary expansion of n and tau(n) by the last equal adjacent pair. We establish exact shell statistics (shell mean drift tends to -1/3) and an exact anti-persistence theorem: the positive-drift state persists only with asymptotic conditional probability 1/6. The remaining obstacles are isolated as two separate issues: orbitwise shell-genericity and unconditional elimination of non-trivial cycles.