Guaranteed Tensor Luminality from Symmetry: A PT-Even Palatini Torsion Framework

Multimessenger constraints tightly bound the gravitational-wave speed to be luminal, posing a strong filter for modified gravity. We develop a symmetry-selected Palatini framework with torsion where exact quadratic-order luminality is built in (not tuned). The observable sector is defined by (i) a scalar PT projector keeping scalar densities real and parity-even, and (ii) projective invariance implemented via a non-dynamical Stueckelberg compensator entering only through its gradient. Under posture (A1–A6), we prove: (C1) torsion is algebraically unique and reduces to a pure-trace form aligned with the compensator gradient; (C2) three PT-even constructions—rank-one determinant, closed-metric deformation, and CS/Nieh–Yan—are bulk-equivalent up to improvement terms; (C3) a coefficient-locking identity enforces K=G for tensor modes on admissible domains, yielding cT=1 with two propagating polarizations. Beyond leading order, the framework predicts a falsifiable correction δcT²(k)=b k²/Λ² (k≪Λ), implying slope 2 in log–log fits across PTA/LISA/LVK bands. To support reproducibility, a public repository provides figure generators, coefficients, and tests directly validating (C1)–(C3).