A conditional parameter-free prediction of the neutrino mass-squared ratio from a two-clock cosmological framework: Δm²₃₁/Δm²₂₁ = 4π² cos²(π/8)

We present a conditional parameter-free prediction for the active Majorana-neutrino mass-squared ratio, R ≡ Δm²₃₁ / Δm²₂₁ = 4π² cos²(π/8) = 33.69694… Assumptions. Active neutrinos are Majorana. The underlying two-clock cosmological framework supplies two structural inputs: (i) a canonical refoliation angle θ_can = π/4 between an absolute background tick T and the laboratory clock τ, and (ii) minimal-holonomy mass-spectrum rules R1–R3 including all-order protection of m₁ = 0. Conditional on these inputs, two derivations in the present article fix the ratio: the metaplectic half-angle laboratory readout of θ_can gives I_clk = cos(π/8), and the minimal-holonomy proposition gives the Takagi singular values (0, m₀/ρ, m₀) with ρ ≡ 2π I_clk. The capacity-scale normalization m₀ cancels from R. No continuous coupling, mixing angle, or normalization enters. Comparison with data. Using the last fully published NuFIT 6.0 global fit and uncorrelated-error propagation, R_data = 33.55 ± 0.92, giving a 0.16σ residual; the data are consistent with the prediction but do not yet strongly confirm it. Limitations and falsifier. The spectrum is intrinsically normal-ordered. The ratio is invariant under any flavour-universal multiplicative matching factor between E* and the laboratory scale; non-universal Weinberg-operator running is not treated. The strict ratio ρ² requires all-order protection of m₁ = 0. A Δχ²_R ≥ 9 post-JUNO/DUNE profile-likelihood departure of R from 33.6969 would falsify the prediction.