Terras’ Coefficient Stopping Time (CST) conjecture

Prove that for every integer n ≥ 2, the stopping time t(n) (the least j with T^j(n) < n) equals the coefficient stopping time τ(n) (the least j with C_j(n) = 3^{q_j(n)}/2^j < 1) for the Collatz map T.

Background

The authors define the stopping time t(n) as the least j with T^j(n) < n and the coefficient stopping time τ(n) as the least j with C_j(n) = 3^{q}/2^{j} < 1. It is immediate that t(n) ≥ τ(n).

Terras conjectured equality for all n ≥ 2. This CST conjecture is significant because it would imply the nonexistence of nontrivial cycles. The paper’s paper of paradoxical sequences provides computational support to CST up to very large bounds.