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 acted on by a single non-trivial operation, quaternion inversion φ → φ-1. The chain closes by exact algebra or lattice computations verified numerically to double-precision accuracy: (i) Protection — Weyl-group W(F4) and Grassmann statistics forbid any elementary bilinear right-handed Majorana mass. (ii) Supply — integrating out the warp-field fluctuation δσ couples fermions by gravity and cosmological sector, must be a composite four-fermion condensate. (iii) Selection — an exact-trace ratio confines the gap to the right-handed neutrino sector, leaving ΔR uniquely exactly massless. (iv) Scale — MR is fixed as an ultraviolet renormalization-group consistency condition that establishes, by a parity-symmetric Dynkin-index statement, that the SU(3)c×SU(2)2L/SU(2)2R gauge kinetic ratio predicts g2L2/g2R2 = 3, giving MR = 1.70×1015 GeV, and with a structurally fixed Yukawa yν = 1/√6, mν = (yνv)2/MR = 5.94 meV [band 2.0–17.9 meV], falsifiable through the absolute neutrino-mass scale (cosmological Σmν, KATRIN-class experiments, 0νββ). This version corrects a significant error and retracts a claim made in v11. Version v11 argued, on the strength of a maximum temperature Tmax = √(MPT0) ≈ 1.7 TeV, that the framework's own lattice-subdivision cosmology never restores B−L and therefore forms no cosmic-string network. That bound compared a physical-frame temperature with a comoving-frame cutoff; the frame-consistent bound is instead Tmax = MP, higher by a factor √(MP/T0) ≈ 7×1015. Corrected, the framework predicts a stable string network of tension Gμ ∈ (0.6–5.4)×10-8, a derived (not scanned) quantity that exceeds central pulsar-timing-array bounds by roughly two orders of magnitude unless loop energy is released predominantly into particles rather than gravitational waves. We state the corrected position, the falsification condition, and the retraction explicitly in the text. The seesaw chain and the central prediction mν = 5.94 meV are unaffected either way. Further changes in this version: the numerical value quoted for the infrared-scale cross-check has been corrected and its status downgraded from "independent consistency" to "unexplained numerical proximity"; the dimensionful input of the framework is now stated as the self-dual length rc, with R★ identified as a derived bookkeeping quantity rather than a primary scale; the falsification threshold on Σmν is sharpened to 61 meV, with the prior-dependence of current cosmological bounds stated explicitly; and the stated scope of the protection theorems, and the dependence of one renormalization-group argument on work not yet published, are now flagged explicitly. No numerical result of the main chain (protection, supply, selection, scale) has been revised. Full details, including the frame analysis underlying the retraction, are given in the "Changes in this version" note directly after the abstract and in the closing "Honest accounting" section of the paper. Companion / related preprints from the same project: gravitational and gauge-sector derivations from the same discrete structure (see project references cited in the bibliography).