A Symmetry-Protected Composite Seesaw: Proposal for a Mechanism Determining the Right-Handed Majorana Scale by Renormalization-Group Consistency

We propose a mechanism for the origin and value of the right-handed Majorana scale M_R of the type-I seesaw. The mechanism consists of four links, each stated as a general condition on an ultraviolet completion rather than as a property of any particular model. Protection: an exact symmetry of the short-distance theory (in the class considered here, the point symmetry of a discrete spacetime acting on the fermion representation, combined with Fermi statistics) forbids every local bilinear Majorana mass, so that M_R, if it exists, is necessarily a composite four-fermion condensate. Supply: the exchange of a scalar mode already present in the theory for independent reasons — a dilaton-like field coupled multiplicatively to the fermion mass form — generates an attractive four-fermion interaction in exactly the scalar channel, with a sign fixed by the positivity of the exchange kernel rather than chosen. Selection: a conserved charge grading of the interaction vertices confines the resulting gap to the right-handed neutrino, leaving the left-handed sector exactly massless and making the chiral asymmetry of the outcome a consequence rather than an input. Scale: the value of M_R is fixed neither by the condensate dynamics nor by an external input, but as the unique matching scale at which the renormalization-group flow of the left-right symmetric theory above M_R is consistent with the measured low-energy electroweak data below it. The single ultraviolet boundary datum this inverse problem requires — the coupling ratio g²(B-L)/g²(2R) at the cutoff — is computable in the ultraviolet completion as a charge trace over the module on which both generators act. The logical structure is a conditional with a parameter-free consequent: if the condensate forms, its scale and the resulting light-neutrino mass are determined. We state the four links abstractly and give a checklist of properties a candidate ultraviolet completion must have for the mechanism to operate. We then present one worked realization, on a discrete quaternionic spacetime (the Hurwitz quaternion lattice), in which every structural condition of the mechanism is verified by exact algebra or by lattice computations with double-precision residuals (10^-14–10^-17). In that realization the boundary ratio evaluates to 3, and the chain outputs M_R = 1.70×10^15 GeV and m_ν = 5.94 meV [band 2.0–17.9 meV]. The mechanism is offered as a proposal: its interest is that it converts the three questions ordinary seesaw model building leaves open — why M_R exists, what fixes its value, and why the left-handed sector is protected — into properties an ultraviolet completion either has or does not have, and can be checked for. The detailed worked realization, including the full renormalization-group systematics, error budget, and an independent reproducibility audit, is developed in a companion paper: K. Nakao, "A Composite Right-Handed Majorana Mass in a Discrete Quaternionic Spacetime and a Seesaw Estimate of the Light-Neutrino Mass Scale," Zenodo (2026), doi:10.5281/zenodo.21437973.