Registered Prediction: Two-Peak Frequency Ratio of the Quantum-Genesis Stochastic Gravitational-Wave Background - f2/f1 = (2-sqrt(2))/(2-sqrt(3)) = 2.186184748

Abstract

Pre-registration of an exact, parameter-free prediction of the Quantum Genesis program: the stochastic gravitational-wave background carries a two-peak spectral structure with frequency ratio f2/f1 = W(2)/W(3) = (2-sqrt(2))/(2-sqrt(3)) = 2.186184748..., a degree-4 algebraic number (minimal polynomial x^4-16x^3+44x^2-32x+4). The attached document carries the premise-labeled derivation (per-write entropy ln 2 via the exact channel-sum identity z*K_z = ln 2, one substrate scale K0, threshold atom W(q) = 2-sqrt(q)), a pre-committed falsification ledger (including the ~0.45 percent ratio precision needed to discriminate the nearby 13/6, the Pi_c-reading alternative ratios 0.924/1.082, and the third-peak cap falsifier), a deterministic sympy verification script regenerating every number, and raw-byte SHA-256 pins of the full reproducible derivation chain. Registered BEFORE any pulsar-timing-array analysis by this program; the deposit timestamp constitutes the registration.

DOI: 10.5281/zenodo.21172955

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