Gravitational Dynamics Without a Global Dynamician: The Geometry–Matter Equation of Motion as a Declaration-Relative Equation of State of Records, Not a Legislated Law

This paper is the thirty-sixth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates. It is the centre panel (second of three) of the tenth grouping — the dynamical quantum-mechanics–gravity interface, or emergent-spacetime, trilogy (35 Emergent Spacetime → 36 Gravitational Dynamics → 37 Cosmological Boundaries) — and the panel that crosses Gate VI (dynamical coupling), under one discipline it never violates: description, not derivation. When geometry is a quantum degree of freedom (Paper 32) reconstructed only from records (Paper 35), a tacit Global Dynamician stands behind the interface: an external, global, unique legislator that imposes the geometry–matter equation of motion. The thesis is that there is no Global Dynamician relative to the framework's declared architecture. Jacobson's 1995 local-Clausius and 2016 entanglement-equilibrium arguments already show, under strong semiclassical assumptions, that Einstein dynamics can be recovered as an equation-of-state result; that result is imported and re-described, never re-derived. The framework's entire own contribution is exactly two moves: (i) under a declared, admissibility-gated identification (A1–A4), read the Clausius/entanglement entropy as the framework's record-bearing entropy — a coarse-graining state entropy of a declared support, distinct from Paper 6's process-cost profile (S_hor ≠ S_ent ≠ S_public-record) — so the recovered law is an equation of state of records; and (ii) type its lawhood as declaration-relative nomological invariance (Paper 17), world-side-holding yet warrant-graded. R-B: conditionally on A1–A4 (illustrated by a stretched-horizon proxy; the genuine dressed gravitational instance is left open as in Paper 35), the geometry–matter law is an equation of state of records — the claim being the typed conditional, not the existence of the instance; it sits consistently above Paper 33's localized-source layer, discharging the standing of the law, not the magnitude of the source. R-C: the which-entropy / species / circularity problem is imported as a live defect — a computed toy makes the effective Newton constant cutoff- and species-dependent (G_eff = a^2 / 4 ħ ζ_eff N_eff; pure-induced limit, with a counterterm renormalizing 1/G in general), so the identification does not predict G. R-D: lawhood is adjudicated through a nomological-standing profile whose world-side (NomInvStatus, coverage) and warrant-side (provenance, non-self-undermining) axes are independent; circular support returns "undetermined." R-A (flagship): across a sample of local causal horizons, two record-provenances realize the same world-side equation-of-state regularity yet differ in warranted lawhood standing, because one calibrates the entropy density independently per horizon and the other through a common bottleneck (residual covariance diagonal versus rank-one) — the world/warrant split applied to the lawhood of a dynamical law itself. R-E: no thermodynamic re-derivation self-certifies that gravity is entropy or that any constant is predicted. The Global Dynamician is retired relative to the framework's declared architecture (external-legislator clause displaced by the imported recovery; predictive clause undercut by the circularity; unique-global-law and brute-governing-law realism declined, not refuted). The paper crosses Gate VI but not U3: no derivation of the Einstein equation, no prediction of G or the cosmological constant Λ, no species-problem resolution, no genuine dressed gravitational local algebra, no discharge of Paper 33's backreaction-magnitude deferral, no quantum-gravity completion, no new physics; Gate VII (a distinctive empirical signature) is flagged, not claimed. Results are interpretive (L2) on imported physics (L1).