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Theoretical analysis reveals nine solar and lunar astronomical observables derived from torus knot topology, indicating exact geometric foundations for celestial cycles.
Nine independent astronomical observables are derived from torus knot topology on S³ with zero free parameters: the tropical year (0.0002%), four lunar months (worst 0.013%), both angular diameters (0.02% after medium dressing), the solar circuit angle (0.048%), and the lunar orbital inclination (0.043%). The baseline refractive index of the transmission medium is identified as n₀ = 1 + Γ = 1 + 4/3549, resolving the systematic angular residual. Eclipse geometry is derived from finite-domain aperture overlap, and the totality condition is closed by the topological mass parameter M = dP/d = 8/3. The altitude law is shown to be mathematically identical to the standard astronomical prediction, with the circuit angle ε = arctan(13/30) replacing the measured obliquity as a derived quantity. Mean deviation across all nine observables: 0.018%. Maximum deviation: 0.048%. Free parameters fitted to astronomical data: zero.
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Coty Austin Trout (2026) studied this question.
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