The Navigable Earth: Surface Scale, Cosmic Microwave Temperature, and Tidal Period from Triadic Mode Selection on the Clifford Torus Cavity

The navigable scale of the earth's surface is derived from the Helmholtz spectrum on the Clifford torus cavity bounded by the 273 km firmament. On a flat torus with aspect ratio p:q = 3:8 (set by T(3,8)), the eigenvalue of the (1,1) mode — the lowest mode engaging both torus directions simultaneously — is q² + p² = 73. The triadic invariant R = P × I × Pr ≠ 0 selects this mode: all lower modes have one direction at zero. The navigable circumference is C = (d−1) × R_f × E = 2 × 273 × 73 = 39,858 km (observed: 40,075 km, deviation 0.54%), where (d−1) = 2 is the photon polarization count. Six observables closed: circumference, pole-to-equator distance, effective curvature scale, CMB temperature (1638/601 = 2.72546 K, 8.2 ppm from FIRAS), tidal period, and horizon formula. Zero free parameters.