A Parameter-Free Prediction of the Tensor-to-Scalar Ratio

Abstract

Extract from Cosmology from a Three-Bit Seed (10.5281/zenodo.22586235). This note states the framework's sharpest near-term prediction in the form a B-mode analysis will meet, ahead of the next BICEP/Keck, Simons Observatory and LiteBIRD releases. The tensor-to-scalar ratio is derived with no adjustable parameters: it vanishes exactly at leading order by the T_d symmetry of the regular tetrahedron, and its first non-vanishing correction is a closed-form function of the one derived constant, p = ln 2/(2π²), times a computed correspondence factor. At the pivot k = 0.05 Mpc⁻¹ the physical ratio is r = 0.0279 ± 0.0005 with tensor tilt n_t = −0.02833 fixed by a zero-parameter consistency relation; a flat-template analysis, the BICEP/Keck convention, will report r_0.05 = 0.0292 ± 0.0005, about 9% under the current combined limit and neutral against BK18. The falsification gate is stated in advance: any B-mode measurement whose 95% interval excludes the band rules the prediction out, and the monograph's robustness ranges will not be invoked against a discrepant result. The companion zero-parameter tilt n_s(k*) = 0.97268 is stated alongside.