The Collatz conjecture (3n+1 problem) remains an open question in number theory, defying traditional proof methods despite extensive numerical verification. This paper introduces an exploratory mathematical framework that reinterprets the Collatz process as a non-Markovian dissipative dynamical system. We construct a heuristic pseudo-energy functional (n) that incorporates four components: a logarithmic baseline, a 2-adic entropy sink, a nonlocal memory term based on historical trajectory gradients, and an adaptive parity-response operator. The functional is designed to mimic a discrete Lyapunov-like stability measure. Numerical experiments up to n 10^12 demonstrate empirical monotonic decrease of (n) along all tested trajectories, with a stability coefficient exceeding 0. 9999999994. While this does not constitute a rigorous proof of the Collatz conjecture, the framework provides a novel heuristic invariant for analyzing recursive integer dynamics. Potential applications include recursive stability scoring, anomaly detection in discrete systems, and adaptive damping in algorithmic control.
ANDRII ARTSYBASHEV (Tue,) studied this question.