We study the accelerated odd Collatz map F (m) = (3m+1) /2^v₂ (3m+1) through an exact binary decomposition into a carry-free quotient and a carry cocycle. The carry-free quotient over F₂x 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.
Roney Lima do Nascimento (Wed,) studied this question.