I am an independent researcher exploring discrete graph representations of the Hydrogen atom. I've encountered a numerical result that seems too precise to be a coincidence, and I’m looking for feedback from the computational physics community.
The Model: I constructed a discrete lattice representing the electron state space (a paraboloid dual to the SO(4,2) algebra). I coupled this to a photon phase fiber (U(1)). I defined the "Geometric Impedance" κ as the ratio of the Matter Phase Space Capacity (S) to the Gauge Action (P).
The Anomaly: At principal quantum number n=5 (the first shell where g-orbitals appear), this ratio converges to: κ=P5S5≈137.036
This matches the inverse Fine Structure Constant (1/α) with 0.15% error.
The match requires modeling the photon phase path as a helix (Spin 1) rather than a scalar circle, with a pitch δ that emerges as the geometric mean of the lattice scales (δ=π⟨L⟩).
The Code: I have archived the Python code and the derivation on Zenodo/GitHub. DOI: https://zenodo.org/records/18512634 GitHub: https://github.com/jloutey-hash/geometric-hydrogen-lattice
Has anyone encountered this specific geometric resonance at n=5 before? I am trying to determine if this is a known topological property of the conformal group or a novel finding.
