sin²(obliquity) as the Master Coupling Constant: A Unification via Constitutional Parity

sin²(obliquity) as the Master Coupling Constant: A Unification via Constitutional Parity
We propose a universal variance law for coupled oscillatory systems: σ² = k/(α−1)², where α is a frequency ratio and k is a dimensionless domain-specific coupling constant. Empirical k-values across five physical domains span three orders of magnitude: financial markets (k=0.45), seismic (k=0.02), ENSO (k=0.12), solar (k=0.125), and DNA supercoiling (k=0.04). The physical origin of these k-values has remained unaddressed. We derive from first principles that the master coupling constant for the Earth-Sun-Moon precession system is k_astro = sin²(obliquity) = sin²(23.44°) = 0.1582 — the squared projection of Earth's axial tilt onto the equatorial plane, and the standard frame-rotation coupling coefficient between the ecliptic and equatorial coordinate systems. This value is independently confirmed: the open-loop fraction at each 25,920-year Great Year boundary (0.4005 cycles) equals sin(obliquity) (0.3978) to within 0.68%. Solar and ENSO k-values are identified as downstream attenuations of this source constant; financial markets sit above it as a reflexive system with internal amplification. Four prospective tests are proposed, including a predicted 41,000-year Milankovitch oscillation in solar and ENSO k-values correlated with Earth's obliquity cycle. The Abhijit correction node of the Vimshottari nakshatra system (Research Note No. 1, doi:10.5281/zenodo.19008877) is identified as the oldest known implementation of this variance law, engineered to operate at the theoretical minimum variance the physical system permits.