Three Axes of Collatz Dynamics: 2-adic Measures, the Dimension Spectrum of Inverse Trees, and Critical Exponents of Density Propagation
Source: hexagonmath.org/abs/2610.00681v1
This work presents a systematic measurement and critical diagnosis of three research axes on the Collatz (3n+1) problem, with the aim of determining which tools can advance the problem and which are structurally incapable of doing so. The three axes are: the 2-adic statistics of individual orbits, the combinatorial structure of the inverse tree, and the critical exponent of density propagation (the Terras-Krasikov-Lagarias line). On the first axis we establish a strict identity and a divergence criterion. For the odd-step map m -> m' = (3m+1)/2^a with a = v_2(3m+1), one has log m_{K+1} - log…
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