Double Determination of Linearized Gravity: An Adjudicated Instance of Transversal Rigidity

We report the execution and adjudication of T0-A, the first theorem-objective of the RCD 3.0 compatibility program. The question, frozen under cryptographic hash before any literature search, asks whether the form of linearized gravitational dynamics is rigid under two inferentially independent families of routes — one informational (entanglement equilibrium), one classical-mechanical (massless spin-2 self-consistency). The adjudication proceeded through four instruments produced and audited by a five-model adversarial panel under a declared standard of proof: a typing lemma establishing a unique comparison object (the gauge-invariant condition Θ_μν = 0 with free coupling α); genealogical graphs establishing that the shared trunk of the two routes is pure kinematics and does not bear the conclusion (with Nordström gravity as the material separator); a bilateral hypothesis map with four labels per hypothesis, exhibiting four coincidence-forcing rows — two per route — and zero shared dynamical rows; and an archival verification matrix closed against primary sources with a human-in-the-loop custody step. The adjudicated outcome is T0-RIGIDITY-OF-FORM: in d = 4, at first order, on a local arena whose matter sector is governed by a conformal UV fixed point, at fixed renormalization scheme and with a single source and operator, the form of the linearized dynamics is doubly and transversally determined — while the scale (Newton's constant) remains free in both routes and enters, in every informational route located, through a single identified bridge. We state exactly what is and is not claimed, and the five conditions under which the adjudication is modified or revoked.