Discovery of an Anomalous Posterior Geometry in the Hubble Constant: A Two-Basin Structure, its cold-dark-matter-mediated collapse, and Discrete Transition Inference (DTI)

Title: Discovery of an Anomalous Posterior Geometry in the Hubble Constant: A Two-Basin Structure, its cold-dark-matter-mediated collapse, and Discrete Transition Inference (DTI) Author: Junichi Fujiki (Independent Researcher, Osaka, Japan) Date: 2026-02-25 DOI: 10.5281/zenodo.18779376 Abstract The persistent Hubble tension motivates scrutiny not only of parameter values but of the geometry of the posterior itself. We report a decisive departure from the unimodal “single-basin” expectation: within a deep-likelihood subset of a converged Markov-chain ensemble (DL≤10), the one-dimensional posterior of the Hubble constant exhibits a statistically decisive two-basin structure. Hartigan’s dip test rejects unimodality (dip=0.00948, p≈0), and a 1D Gaussian-mixture comparison favors K=2 over K=1 with ΔBIC=1070.9. Conditioning the DL≤10 posterior on increasingly narrow Ωch2 slices collapses the H0 bimodality and reduces σ(H0) by up to 68.42%, demonstrating a cold-dark-matter–mediated compensation mechanism. We interpret the emergence of distinct basins as the macroscopic signature of a discrete early-time transition, formalized as Discrete Transition Inference (DTI) characterized by a transition parameter zc and rapid post-transition dissipation consistent with kination-like behavior. Description This deposit contains the complete, Overleaf-ready LaTeX source package for the manuscript: "Discovery of an Anomalous Posterior Geometry in the Hubble Constant: Two-Basin Structure, its Collapse via Cold Dark Matter, and Discrete Transition Inference (DTI)". This upload corresponds to version v3. Key Results Within the deep-likelihood subset (DL≤10), the 1D posterior of H0 exhibits a statistically decisive two-basin structure. Conditioning on narrow Ωch2 slices destabilizes and collapses this bimodality, providing empirical evidence for a cold-dark-matter-mediated compensation mechanism. Theoretical Outlook A natural microscopic completion to explore is an early scalar-sector transition triggered around z∼zc, followed by rapid post-transition relaxation (kination-like behavior). Contents of the Archive The attached ZIP file is a ready-to-compile LaTeX suite containing: main.tex: Main manuscript LaTeX source. references.bib: Bibliography file. tex_snippets/: Peer-review appendix snippets (sections and tables). figures/: Main manuscript figures (PDF format). drafts_and_misc/: Supplementary and draft figures/tables (PDF/TeX format). posterior_geometry_map_DL10/: Complete diagnostic collapse tables and related analytical artifacts. Reproducibility This package is structurally designed to compile out-of-the-box on Overleaf using the revtex4-2 document class. All figures are pre-compiled and provided as PDF files, allowing for immediate compilation without the need to execute external data-processing scripts. License Creative Commons Attribution 4.0 International (CC BY 4.0) Citation If you use this material or the associated datasets, please cite this record using the following Zenodo DOI: 10.5281/zenodo.18779376.