Research Directions
1. The Fine-Structure Constant α
Central Question: Can the fine-structure constant α ≈ 1/137.036 admit an elegant and exact mathematical expression?
Key Result: α Λ_φ + τ = 1, where Λ_φ = 360/φ² − ln φ and τ = 4k_B T_CMB / E_R, predicting α⁻¹ = 137.036014 with 0.11 ppm accuracy.
The three-layer decomposition reveals:
- Geometric layer: 360/φ² (golden angle, circle optimization)
- Arithmetic layer: −ln φ (Dirichlet regulator of ℚ(√5))
- Thermodynamic layer: τ (CMB thermal energy)
2. The Riemann Hypothesis
Approach: Bost-Connes system over ℚ(√5) with golden unitarity.
Key Results:
- Strong log-concavity bound: (log Φ)″(u) ≤ −67.65 for all u ≥ 0
- Quantitative Turán inequalities
- Weil positivity evidence across 168 primes (tail bounds < 10⁻¹¹⁰)
- Research program with explicit gap identification
3. Room-Temperature Superconductivity
Approach: Beyond BCS theory, connecting Bost-Connes arithmetic to Cooper pairing mechanisms.
Key Insights:
- Quantum metric as universal Tc diagnostic
- Non-equilibrium light-induced pathways
- McMillan ceiling analysis for conventional phonon-mediated superconductors
4. Spherical Membrane Model of Particles
Idea: Electrons and photons as spherical membranes S²(r), with a unified fiber bundle classification:
- Spin 0 → Scalar membrane (Higgs)
- Spin 1/2 → Spinor membrane (electrons)
- Spin 1 → Vector membrane (photons)
- Spin 2 → Tensor membrane (gravitons)
The Arithmetic Axioms
- α⁻¹ = 360/φ² = 137.508 is the birth value of the universe
- The evolution from 137.508 to 137.036 encodes the age of the universe
- Physical constants are necessary consequences of number-theoretic optimization
- The Riemann zeta function is the partition function of the universe
- The golden ratio φ is a fundamental constant of nature