A Palatini PT-Even Torsion Framework:Conditional Uniqueness, Bulk Rank-One Equivalences, and Tensor Luminality via Coefficient Locking

We present a symmetry-based framework for torsionful gravity in the Palatini formulation that ensures luminal gravitational waves (cT = 1) without parameter tuning and without extra propagating modes. The organizing principle is a scalar PT projector on observable scalar densities, paired with projective symmetry implemented by a Stueckelberg compensator epsilon (x) that enters only through the invariant trace Tₘu − partialₘu epsilon. Within a two-derivative, parity-even posture (A1–A5) we establish three conditional results: (C1) pure-trace alignment, fixing torsion by partialₘu epsilon while axial and traceless irreps vanish; (C2) three-route bulk equivalence, showing that determinant/rank-one, closed-metric, and PT-even CS+ constructions share the same quadratic bulk up to improvement currents; and (C3) coefficient locking, which removes TT–non-TT mixing and enforces K = G, hence cT = 1 exactly at quadratic order with only two tensor degrees of freedom. The leading parity-even NLO correction is unique and predicts delta cT² (k) = b k² / Lambda² for k Lambda. We propose falsifiable diagnostics: a quadratic-slope test for delta cT² across frequency bands, and a route-equality/flux-ratio null (Delta A_* - 0) in the strict spurion limit. A projectively invariant Stueckelberg completion with mT - infinity (or a Lagrange current enforcing Tₘu − partialₘu epsilon) explains the gradient-only appearance of epsilon and justifies treating it as nondynamical at low energies; residual dynamics would yield controlled, testable deviations. All figures and reductions are reproducible from a public code release. The framework delineates a symmetry-selected, data-facing sector of torsionful modified gravity consistent with multimessenger bounds.