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 rather than as a collection of independently existing objects. 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 it is the panel that crosses Gate VI (dynamical coupling). The whole paper is held to one self-imposed discipline: 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 argument and his 2016 entanglement-equilibrium argument 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 (conditions 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 — so the recovered law is an equation of state of records; and (ii) type its lawhood not as external legislation but as declaration-relative nomological invariance (Paper 17), world-side-holding yet warrant-graded. R-B (the identification): conditionally on A1–A4 (illustrated by a stretched-horizon proxy; a genuine dressed diffeomorphism-invariant gravitational instance is left open, as in Paper 35), the geometry–matter law is an equation of state of records; the claim is the typed conditional, not the existence of the genuine instance. It sits consistently above Paper 33's bound-type localized-source layer (M_loc), discharging the standing of the law, not the magnitude of the source. R-C (which-entropy / circularity, 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), reproducing the Sakharov / Susskind–Uglum induced-gravity scaling (pure-induced limit; in general the divergence renormalizes 1/G by a counterterm), so the identification does not predict G. R-D (lawhood): a nomological-standing profile NomStandProf = (NomInvStatus, μ_cov, μ_prov, μ_arrow, LawNSUStatus) keeps world-side invariance and warrant-side provenance independent; circular support (cutoff/measure fixed by the very law under test) returns LawNSUStatus = undetermined. R-A (flagship witness, same-regularity / different-warrant): across a sample of local causal horizons, two record-provenances realize the same world-side equation-of-state regularity (the common entropy density under transport) yet differ in warranted lawhood standing, because one calibrates the entropy density independently per horizon and the other funnels it through a common bottleneck (residual covariance diagonal versus rank-one). 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 resolution of the which-entropy/species problem, no construction of a genuine dressed gravitational local algebra, no discharge of Paper 33's backreaction-magnitude deferral, no completion of quantum gravity, no new physics. Gate VII (a distinctive empirical signature) is flagged, not claimed; the adopted, declaration-relative, self-uncertifiable history amplitude is handed to Paper 37. Presents no new physics; results are interpretive (L2) on imported physics (L1) and the framework's domain-general discipline (L2-G).