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May 5, 2026Open Access

A Resonance--Spectral Approach to the Collatz Problem: Empirical Universality and Analytic Constraints.

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Key Points

The aim is to establish a novel analysis framework for the Collatz conjecture through resonance and spectral methods.
Translates Collatz trajectories into a functional-analytic context
Maps multiplicative factors to a cumulative phase leading to a dyadic phase series
Compares the modulus of the series to a reference spectrum using a Huber-weighted log-spectral distance
Establishes unconditional bounds and conditional theorems related to the Collatz conjecture
Reduces the conjecture to a single asymptotic spectral inequality
Empirically derives a threshold for bounding the asymptotic resonance

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Implication

Novel framework analyzes the Collatz conjecture, revealing empirical inequalities and constraints.

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Cite This Study

Jason Mullings (2026) studied this question.

synapsesocial.com/papers/69fc2c1f8b49bacb8b347cc9 https://doi.org/10.5281/zenodo.20042346

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