The Figure-Eight and the Blood Moon: Analemma Derivation and Lunar Eclipse Radiance Map from Torus Knot Topology on S³
Year: 2026
Type: preprint
Abstract: Two macroscopic observational phenomena — the solar analemma and the lunar eclipse radiance spectrum — are derived from the same torus knot register set that generates particle masses, mixing angles, and the gravitational coupling. The analemma follows from three derived quantities: the circuit angle ε = arctan(13/30), the tropical year Y = 365 + 7/29, and the dressed circuit eccentricity e = 1/60 + Γ/Σ. The obliquity component of the equation of time is derived at 9.865 minutes (observed: 9.87, deviation 0.053%) and the eccentricity component at 7.659 minutes (observed: 7.66, deviation 0.009%), both after applying the Γ-order medium dressing. The dressing type is categorical: angular observations are local measurements that transit the GRIN field and receive multiplicative point-dressing (×n₀), while orbital eccentricity is a global circuit parameter perturbed by the gravitational coupling distributed across the spectral budget (additive per-channel dressing +Γ/Σ). The lunar eclipse radiance map is derived from the differential GRIN coupling δ = 1/45, yielding a spectral transmission that predicts blood-red lunar eclipses with a natural Danjon scale gradient. Mean deviation across all analemma observables: 0.024%. Zero free parameters throughout.
Author: Trout, Coty Austin
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204776205