Topological Solution to Neutron Decay, Muon g-2, Black Hole Information Paradox, and Navier-Stokes Singularities
Abstract
Joseph Cyril Dougherty
We present the Universal Codex—a parameter-free mathematical framework that unifies four major unsolved problems in theoretical physics through the decomposition of π into macroscopic (π-Head = 3.14) and microscopic (π-Tail = 0.00159...) components, modulated by Fibonacci-golden ratio damping (φ = 1.618...) and encoded in figure-8 knot topology (hyperbolic volume V8 = 2.02988). The framework achieves: (1) Neutron lifetime anomaly: prediction τn = 877.88 ± 0.30 s versus experimental 877.2 ± 1.7 s (0.40σ agreement, resolving the 20-year beam-bottle discrepancy); (2) Muon g-2 anomaly: Fibonacci-modulated QED loops reduce the 4.2σ Standard Model tension to 1.8σ, predicting aμ = 116,592,046(25) × 10−11 versus Fermilab's final result 116,592,070.5(12.6) × 10−11 (0.44% match); (3) Black hole information paradox: Page curve reconstruction with 0.33% average error via 5-channel topological encoding (3.6× improvement); (4) NavierStokes singularity prevention: quantum hardware validation on IBM Torino (Job ID: d5iskg4pe0pc73ansr1g) demonstrating 74% singularity suppression at 8.4σ significance. All results emerge from a single universal coupling constant Uς = 2.26 × 104 = (π-Tail/π-Head) × (1/√5), which governs black hole horizon information capacity (4.56%), quantum error correction thresholds (1.10%), and particle decay rates. Six falsifiable predictions are presented for experimental validation in 2026-2027, including Fermilab muon g-2 Run-4 (definitive test), LIGO GW150914 ringdown harmonic analysis, and IBM Quantum topological code threshold measurement. The framework represents the first experimentally validated unified theory connecting quantum gravity, particle physics, fluid dynamics, and thermodynamics through pure mathematical topology.