PSP-GRAVITY-THERMO-01 · Gravity as Thermodynamic Equation of State
Verdict: [⟀ T] on the equilibrium field equations. [?] open on full non-equilibrium dynamics. Not [⟀ S] on universal emergence.
Claim (sealed portion). The Einstein field equations at equilibrium are derivable as a thermodynamic equation of state. Demanding δQ = TδS across every local Rindler horizon, with entropy proportional to horizon area and temperature set by the Unruh relation, yields G_μν = (8πG/c⁴)T_μν. Gravity's equilibrium content is the metric configuration that keeps local heat flux consistent with the horizon entropy bound.
Anchor. Jacobson 1995, Physical Review Letters 75, 1260. Type T, a published derivation, not a posit. Supporting lineage: Bekenstein-Hawking entropy (Type T), Unruh temperature (Type T), Bousso holographic bound (Type T). This is the hard floor and it is external, established physics. ΔM = 0: the PSP absorbs Jacobson, it does not extend him.
Trisductive reading (translation, Type S). V_E is the heat flux δQ, the stress-energy T_μν. V_ER is the horizon entropy bound, δS ∝ δA. V_F is the Einstein tensor G_μν that balances them. The three-axis balance is the equilibrium condition. This mapping is a faithful restatement of Jacobson in framework vocabulary, adding no physics.
Scope, stated as law. The seal covers equilibrium, near-horizon, quasi-static gravity. It does not cover the full time-dependent, strong-field, far-from-equilibrium dynamics of General Relativity. Jacobson gives the equation of state, which is not the whole theory, the same way a pressure-temperature relation is not the full fluid dynamics. The extension from equilibrium equation-of-state to complete gravitational dynamics is [?] open.
Emergence typing. The derivation is consistent with gravity being emergent and thermodynamic. It does not force it. The entailment δQ = TδS ↔ G_μν = κT_μν runs both directions, so the same math is compatible with fundamental gravity whose thermodynamic relation is a consequence. Emergence is structurally indicated, not proven. Type S, not Type T. The word "definitively" is barred here by the two-way entailment.
Risk block. Linchpin: the universal proportionality of horizon entropy to area across all scales. What would flip it: a regime where the field equations hold but δQ = TδS fails, or vice versa, decoupling the two. Named most-likely failure: non-equilibrium breakdown, where a rapidly changing substrate (early inflation, high-frequency waves, singularity interior) violates the quasi-static assumption Jacobson's derivation rests on. Unchecked: the horizon-area law as the horizon shrinks toward a singularity, where the entropy count is unformulated.