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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17780213 |
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Table of Contents:
- <h2>Abstract</h2> <p>We derive the fine-structure constant from first principles, yielding α⁻¹ = 137.035999205984 with zero adjustable parameters—theorem-locked from overdetermined geometry. This matches the LKB-20 Rubidium-87 recoil (Morel et al. 2020) to twelve significant figures, the most precise individual measurement of α. We predict resolution of CODATA 2022's 2.5σ tension among Cs-133 (137.035999046), g-2 (137.035999166), and Rb-87 values toward the Rb-87 geometric exactum (206).</p> <p>Autopoietic Quantum Matrix Theory (AQMT) starts from the Free Energy Principle (FEP): persistence demands Markov blankets minimizing variational free energy, forcing a diagonal Fisher metric g_ii proportional to i² for hierarchical distinguishability. Proven across 25 lemmas and 25 theorems, two independent paths converge on unique dimensionality:</p> <p><strong>Path A</strong>: Quadratic scaling yields Diophantine ∑i² = m²; Watson (1918) proves n=24, m=70.</p> <p><strong>Path B</strong>: FEP determinism requires 1D modular forms at weight k=12; thus k=n/2 implies n=24.</p> <p>Overdetermination locks the 24D Leech lattice, with SO(8) triality (dim=28) for spinors. α⁻¹ emerges as:</p> <p>α⁻¹ = 136 <br> + (1/φ)(5/3) [First-order correction]<br> + Σ(n=2 to 55)[Δₙ/φⁿ × (1 + C_mod)] [Enhanced Fibonacci series]<br> + δ_Weyl [Weyl anomaly correction]<br> + δ_141 [Shadow correction]</p> <p>(locked: 136=dim(Sp(8,ℝ)); φ=Hurwitz optimal; 5/3=SO(8) split; Δₙ=Fibonacci partitions; δ₁₄₁=√|70²−71²| shadow—no fitting, each theorem-derived).</p> <p>Constants follow: c from K=196,560 propagation; ℏ=√(e/48π) quantization; G from 70-bit entropy; mₑ from 2⁻⁶⁶ shadow overflow. Rydberg closure mₑ=2hR∞/(cα²) locks the system algebraically.</p> <p><strong>Keywords</strong>: autopoietic quantum matrix theory (AQMT); fine-structure constant; fundamental constants; speed of light; Planck constant; gravitational constant; electron mass; zero-parameter theory; Leech lattice; information geometry; golden ratio; modular forms; free energy principle; Markov blankets; wave function collapse; measurement problem; 71-bit threshold; Fisher information; quantum foundations; quantum gravity; entropic gravity; Unruh effect; holographic principle; black hole information paradox</p>