The 4.D Clockwork Universe — v7: What Is Time? Entropy on S³ and the Geometric Origin of Cosmological Constants

Version 7 adds a new introduction addressing a foundational question: what is time, and what breaks when cosmology forces it to be absolute? From first principles, absolute time is unmeasurable by construction — every clock is a comparison between physical processes subject to geometry and energy. We acknowledge this daily (GPS: +38. 4 μs/day correction) yet retain absolute time in our cosmological models. Entropy — the most fundamental clock — is dynamical by definition. Constraining it to three dimensions may be the source of the residuals we attribute to new fields and parameters. Retained: 11 parameter-free Monuments, pⱼoint 0). TESTABLE FALSIFICATION PATHS The framework makes specific, zero-parameter predictions for upcoming observations: redshift drift dot-z (z) measurable by ELT/ANDES, evolving w (z) from DESI DR3+, sub-solar-mass black hole mergers at LVK O4/O5, G (z*) /G₀ from a 4DCU-consistent Boltzmann pipeline (distinguishing 1. 150 from 1. 162 at 1% precision), and the K-ladder fractal universality across cosmic epochs. RELATION TO ESTABLISHED FRAMEWORKS 4DCU sits within the scalar-tensor (Brans-Dicke / Horndeski) family of modified gravity theories, with the scalar field Ti = 1/gamma identified from Special Relativity and additional discrete algebraic structure from H₄. The speed of light emerges as a theorem rather than a postulate; Lorentz invariance is derived as the tangent-space linearization of SO (4) rotations on S³. STATUS AND SCOPE Skeleton 42 is the final framework iteration. Further work proceeds as topical papers extracted from this document, each targeting a specific result (Monument 14, K-ladder, Occam ledger, SPARC rotation curves) for specialist review. Three working frontiers (WF3. 1, 3. 2, 3. 3) remain open, ranked by maturity; their closure would convert additional Planck-measured parameters into parameter-free structural predictions. Feedback from specialists in cosmology, modified gravity, Coxeter group representation theory, and mathematical physics is actively sought. Author: Miroslav Ivanov YosifovIndependent Researcher, Plovdiv, BulgariaORCID: 0009-0007-1842-656XContact: YosifovSpace@gmail. com