The paper presents a novel framework for analyzing the Collatz Conjecture. Rather than attempting a traditional number-theoretic or combinatorial proof, the author translates the dynamical system into a functional-analytic/signal-processing domain. Specifically, the paper maps the sequence of multiplicative factors of a Collatz trajectory into a cumulative phase, which then generates an absolutely convergent "dyadic phase series". The core of the paper involves comparing the complex modulus of this series to a reference spectrum generated by the known attractor cycle using a Huber-weighted log-spectral distance (the "resonance scalar". The author posits that the Collatz conjecture is equivalent to bounding this asymptotic resonance below an empirically derived threshold. Crucially, the author does not claim to have solved the Collatz conjecture. Instead, the paper offers a meticulously categorized set of unconditional bounds, conditional theorems, and rigorous empirical observations, successfully reducing the conjecture to a single asymptotic spectral inequality.
Jason Mullings (Tue,) studied this question.