Abstract

We present a self-contained account of classical gravity organized as two logically independent layers, with an explicit statement of which claims are forced, which are interpretive, and which are imported. In the first layer we take a symmetric rank-2 field h_μν on a flat background and impose one requirement, linearized gauge invariance. This uniquely fixes the Fierz-Pauli Lagrangian, forces exactly two transverse-traceless (helicity ±2) modes, and, through coupling to the full stress-energy tensor, fixes the post-Newtonian structure reproducing the classical solar-system observables. Requiring the field to source itself produces, at second order, the gravitational stress-energy with an algebraically fixed coefficient; we compute this explicitly, recover the Isaacson energy density t₀₀ = (c⁴/32πG)⟨ḣ_ij ḣ^ij⟩, and verify the second-order Bianchi consistency symbolically. The all-orders closure to the Einstein-Hilbert action is the classic self-coupling theorem, cited rather than re-derived. In the second layer we record the sense in which these equilibrium field equations coincide with a thermodynamic equation of state δQ = T δS across local horizons. We then separate a testable interpretive hypothesis, that the graviton is emergent (phonon-like) rather than fundamental, from the forced results, and state that current experiments do not settle it. We close with a falsification ledger whose tensor and thermodynamic layers fail independently, distinguishing algebraically forced "survivals" (which are the content of general relativity) from realizable death conditions.