The Octal Code of the Horn Torus: Unifying φ/8 Spectral Scaling with 8-Phase de Broglie Discretization

DOI:        10.5281/zenodo.17773343    
Title:        The Octal Code of the Horn Torus: Unifying φ/8 Spectral Scaling with 8-Phase de Broglie Discretization
Author:    Miles Enoch Tracy
contact:    milestracy@yahoo.com
ORCID:    https://orcid.org/0009-0006-7781-8259

Abstract
We demonstrate that the constant φ/8 ≈ 0.203, which generates a geometric
spectral comb λₖ = 535·e^(k·φ/8) matching the hydrogen Balmer-α line at
656.3 nm, is topologically equivalent to an 8-phase de Broglie wavefunction
discretization Σ_{j=1}^{8} exp(−i·j·π/4). Both manifestations derive from
the Horn torus modular parameter 45/8 = 5.625, where 45 represents the
triadic modulus (5×3²) and 8 the octal denominator (2³). The hyperbolic
coupling tanh(2) modulates the Berry phase per kissing loop as
θ_berry = π(1−tanh(2)), yielding a residual correction Δθ ≈ 0.023 rad
that refines the spectral step. We present three falsifiable hypotheses:
(1) multi-component geometric combs in stellar spectra, (2) fractional-
tooth interference line shapes, and (3) log-frequency mapping of atomic
transitions. This work is mathematical synthesis and hypothesis generation,
not established physical law.