{"id":"hexagon/2610.00681","pdf":"https://hexagonmath.org/pdf/2610.00681v1","url":"https://hexagonmath.org/abs/2610.00681v1","tags":["math.NT","msc:37P05","msc:11B75","msc:60F10","msc:37C30","Collatz conjecture，3x+1 problem，inverse tree，density propagation"],"score":0,"title":"Three Axes of Collatz Dynamics: 2-adic Measures, the Dimension Spectrum of Inverse Trees, and Critical Exponents of Density Propagation","domain":"math.DS","source":"hexagon","authors":["Zeng Chunping"],"reviews":0,"subject":"math.DS","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Magma"],"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}