A Detailed Multi-Step Descent Analysis of the Accelerated Collatz Map

This work studies the accelerated Collatz map acting on odd integers viaT*(n) = (3n + 1) / 2^{ν2(3n + 1)}. Using explicit 2-adic valuation analysis, we prove deterministic finite-stepdescent results. In particular, every odd integer decreases within at mostthree accelerated steps. One-step, two-step, and three-step descent arecharacterized by residue classes modulo powers of two. The results are elementary, fully rigorous, and independent of probabilisticassumptions. Exhaustive numerical verification up to 10^7 confirms thetheoretical predictions. The paper establishes a structural, valuation-drivenframework for understanding descent in Collatz dynamics.