The Spectral Gravity Sub-Programme

The spectral gravity sub-programme of the Cosmochrony corpus addresses a single central question: why does the effective metric $g^{\mu\nu} = 2\eta^{\mu\nu}$ satisfy the Einstein equations? Starting from the projective spectral entropy functional ${\mathcal{S}_\Pi}[g] = \tfrac{1}{2}\log\det' A_g$, the sub-programme derives the Einstein tensor as the infrared-dominant response of the renormalized metric variation, reformulates it as a spectral equilibrium condition, extends it causally to gravitational wave propagation, and provides its ultraviolet Born–Infeld completion. The logical chain is: \[ {\mathcal{S}_\Pi}[g] \;\Longrightarrow\; \delta_{g}{\mathcal{S}_\Pi} \ni {c_{\mathrm{EH}}} G_{\mu\nu} \;\Longrightarrow\; G_{\mu\nu} = 8\pi{G_{\mathrm{N}}} T_{\mu\nu}^{(\Pi)} \;\Longrightarrow\; \text{causal completion} \;\Longrightarrow\; \text{BI completion}. \] The sub-programme is constituted by four papers: Gravity 3.0, Thermodynamics, Lorentz/CausalPropagation, and BornInfeld. The scope is the gravitational sector in the absence of matter; full coupled field equations $G_{\mu\nu} = 8\pi{G_{\mathrm{N}}} T_{\mu\nu}$ with matter in Lorentzian signature remain an open deliverable.