Marco Gericke, Information Physics Institute, Hamburg
This paper presents a comprehensive validation of the Universal Model Framework (UMF) through its integration with Jan Boeyens’ chemical cosmology, number theory, and the periodicity of mat ter. The UMF establishes prime numbers as fundamental operators governing physical reality across scales, from nuclear structure to cosmological organization. We demonstrate that Boeyens’ observa tions of prime-based periodicity in chemical elements emerge naturally from the UMF’s distinction logic operating on a p-adic fractal substrate with Hausdorff dimension DH ≈ 1.59. Rigorous testing confirms: (1) accurate prediction of 264 stable nuclides through dual conver gence bands at the golden ratio τ = 0.618 and Lucas constant 0.5802, with automatic exclusion of Technetium (Z = 43) and Promethium (Z = 61); (2) derivation of the fine-structure constant α = 1/137.035999 from prime gap harmonics; (3) scale-invariant fractal dimension across atomic and galactic structures; (4) information-entropy correlation in nuclear binding energies (r = 0.96); (5) Möbius topology projection of the periodic table separating matter/antimatter sectors; (6) Fi bonacci phyllotaxis nuclear packing with characteristic 137.5◦ divergence angles; (7) biological cod ing respecting the same 8:24 periodicity ratio found in elemental organization; and (8) cosmological Möbius symmetry with α-condensates mediating nucleosynthesis. These results establish the UMF as a mathematically complete framework unifying quantum phenomena with cosmological structure through prime-number theoretic principles, fractional dynamics, and projective geometry.
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