Published June 6, 2026
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Physical Ontology of the Macroscopic Vacuum: Holographic Entropy, Spectral Resonance, and Topological MOND in the IT³ - PHAM Framework
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Description
This work establishes the strict physical ontology of the macroscopic vacuum within the unified IT³–PHAM framework, eliminating all phenomenological parameter fitting by grounding every geometric invariant in pure algebraic geometry and spectral action. We prove that: (1) the macroscopic D2-brane boundary obeys an exact area quantization S_out/S_in = 3, mandated by the Euclidean metric signature of the cubic lattice; (2) cosmological redshift is not kinematic expansion but discrete topological dissipation governed by the dynamic writhe ||Wr||_dyn ≈ 1.0904, with macroscopic Dark Energy emerging strictly from the Casimir tension of the IR lattice; (3) the 123.39-year Gleissberg solar cycle emerges as the inertial resonance between baryonic and leptonic vacuum modes, scaling precisely via μ_geom = m_p/m_e ≈ 1836.15; (4) the cosmological acceleration scale a_0 ≈ 1.21×10⁻¹⁰ m/s² (the MOND threshold) is analytically derived as the transverse projection of de Sitter surface gravity via the Cabibbo angle sin θ_C = Λ_3/(2Λ_1); (5) the outer Solar System is governed by a hexadecapole (l=4) topological lattice with 12 phase-locked libration islands, replacing the Planet Nine hypothesis; and (6) the Cosmological PHAM (C-PHAM) operator functions as a Diophantine attractor on the constructible field K = Q(√2,√3,√5). The Big Bang singularity is strictly forbidden by Gromov's Non-Squeezing Theorem, capping maximum energy density at the top quark threshold Λ_top ≈ 173.595 GeV.
This package includes the complete LaTeX manuscript, Python visualization scripts for generating breakthrough figures demonstrating topological MOND, spectral resonance, Diophantine attractors, and Hopf fibrations, and computational verification tools.
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IT3_PHAM_Grand_Figure.png
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