A Composite Right-Handed Majorana Mass in a Discrete Quaternionic Spacetime and a Seesaw Estimate of the Light-Neutrino Mass Scale

We derive the light-neutrino mass scale within a discrete-spacetime framework whose ontology is the Hurwitz quaternion lattice Γ_H (the F4 root lattice) acted on by a single non-trivial operation, the quaternionic inversion φ → φ⁻¹. The chain has four links, each closed by exact algebra or by lattice computations verified numerically to double-precision accuracy (residuals of order 10^-15–10^-17). (i) Protection: Weyl-group W(F4) character and translation theorems forbid any local bilinear Majorana mass, so the right-handed scale M_R, if it exists, must be a composite four-fermion condensate. (ii) Supply: integrating out the warp-field fluctuation δσ — whose coupling is fixed by the gravitational and cosmological sectors — yields an attractive scalar interaction, the unique channel able to source Δ_R = ⟨ν_R ν_R⟩. (iii) Selection: an ε-charge rule confines the gap to the right-handed neutrino, leaving the left-handed sector exactly massless. (iv) Scale: M_R is fixed as an inter-scale renormalization-group consistency condition whose single ultraviolet datum, g²(B-L)/g²(2R) = 3, follows from a support-matching rule established by a geometric trace-domain theorem and, independently, a parity-block reduction; a related basis-independent Dynkin-index statement passes an observational test on the SU(3)_c/SU(2)_R pair (predicted ratio 1; data 0.93). The result is M_R = 1.70×10^15 GeV and, with the structurally fixed Yukawa y_t = 1/√6, m_ν = (y_t v)²/M_R = 5.94 meV [band 2.0–17.9 meV], falsifiable through the absolute neutrino-mass scale (cosmological Σm_ν, KATRIN-class experiments, 0νββ). The chain is a conditional with a parameter-free consequent: whether the condensate forms depends on an unfixed right-handed Yukawa, but the value of m_ν, entering only through the existence condition, does not. M_R and m_ν are present-tense statements about the vacuum, independent of cosmological history (the framework's own cosmology forms no cosmic-string network). We state throughout which quantities are derived, which are external inputs (including the desert hypothesis), and where mean-field approximations enter. The general, model-independent form of this four-link mechanism — stated as a checklist any candidate ultraviolet completion can be tested against — is presented in a companion paper: K. Nakao, "A Symmetry-Protected Composite Seesaw: Proposal for a Mechanism Determining the Right-Handed Majorana Scale by Renormalization-Group Consistency," Zenodo (2026), doi:10.5281/zenodo.21435468.