"Unified Geometry of Spacetime: Lapse-Modulated Dark Matter, Black Hole Regularization, and CPT-Symmetric Temporal Topology in Extended Finsler-Timescape-Wisconsin Cosmology" - with complete theoretical derivations, auxiliary calculations, numerical verification tables, Python/Mathematica submitted to Classical and Quantum Gravity Extended Finsler Timescape-Lapse (EFT-Lapse) Theory is a working paper presenting a theoretical cosmology framework and its associated derivations and checks. Perplexity AI and Google Gemini were used to support literature discovery, drafting and refinement of the manuscript, formula/LaTeX development, and assistance with implementing/executing and cross-checking calculations; all outputs were reviewed, validated, and integrated by A. Backmund, who takes full responsibility for the scientific content and integrity of this work. This AI use is disclosed in the spirit of transparency and researcher responsibility as recommended by the European Commission’s “Living Guidelines on the Responsible Use of Generative AI in Research” (2025). ACKNOWLEDGMENTS AND AI DISCLOSURE The author thanks Perplexity AI and Google Gemini for research assistance in literature identification and manuscript refinement. Perplexity AI was used for systematic searches of scientific literature on Finsler geometry and cosmological models and mathematical derivations; Google Gemini assisted with mathematical verification and writing clarity. All theoretical content, ideas, scientific conclusions were developed and critically evaluated by A. Backmund LLM-EFT-Lapse Collaboration

This working paper introduces the Extended Finsler Timescape–Lapse (EFT‑Lapse) theory as a unified, field-theoretic framework that attributes the Hubble-tension discrepancy to inhomogeneous cosmology, spacetime lapse modulation, and time-symmetric (CPT-consistent) bidirectional causality, without introducing an additional exotic dark-energy component.The approach models spatially varying proper-time vs. coordinate-time relations via a lapse function N(r,t)N(r,t) controlled by an ultra-light scalar field, and formulates forward- and backward-causal contributions as distinct channels to avoid apparent double counting of backreaction and local-void effects.It further presents a decomposition into several orthogonal solution modes and outlines testable observational signatures and technical addenda supporting mathematical rigor.