Spike Structures and 2-adic Transition Laws in the Accelerated Collatz Map

We study the accelerated Collatz map through its 2-adic exponent structure. The positive odd integers split into families B = {8n+1}, D = {4n+3}, and C = {8n+5} with division exponents 2, 1, and at least 3. A modulo-24 refinement of C reveals cyclic lifting among three linear forms; half-rotation, rotation, and tower lemmas describe these spike structures. We prove the complete one-step transition law and, more strongly, that every finite positive exponent word (a_0, ..., a_{L-1}) is realized by exactly one odd residue class modulo 2^{1+sum a_i}. Thus the local transition theory encodes all finite words rather than forbidding any of them. We also record the classical cycle-equation bound log_2 3 < R < log_2(10/3) < 2, which makes the formerly studied balanced case R = 2 vacuous, and explain why finite residue graphs cannot exclude cycles. Any further obstruction must therefore enter through the global Diophantine condition required for an exponent word to close as a positive integer cycle.