The Spectral Gravity Sub-Programme

The spectral gravity sub-programme of the Cosmochrony corpus addresses a single central question: under which conditions does the projective spectral entropy functional S_Π[g] = 1/2log' Ag support an infrared Einstein sector for the effective metric? The sub-programme separates the physical proper-time cutoff (power-sensitive terms a₀Λ⁴, a₂Λ²) from zeta regularization (finite and logarithmic terms governed by a₄), decomposes the renormalized metric variation into Einstein, cosmological, higher-derivative, and non-local sectors, and states the exact conditions under which the Einstein term dominates. The renormalized couplings — including the sign and value of Newton's constant — are matching data, not predictions. Conditionally on supplied coefficients, stationarity of the difference functional Γ_Π = S_Πʳᵉⁿ - W_Π yields the Einstein–matter coupling Gμν + Λᵣₑₙ gμν = 8πGN Tμν. On the posited local four-derivative Lorentzian truncation, the massless graviton branch is exactly luminal, and the ultraviolet completion of determinantal Born–Infeld type is an admissible member of an explicitly parametrised family, not a uniquely selected one. The sub-programme is constituted by four papers: Gravity, Thermodynamics, Lorentz/CausalPropagation, and BornInfeld. Interpretive status. The sub-programme establishes which local structures spectral geometry allows and where every remaining gap lies — the matching principle for the couplings, the integrability bridge to any thermodynamic reading, the in-in construction of a Lorentzian spectral action, and the selection principle for the ultraviolet completion. Gravity emerging as a spectral response remains a structural possibility, not an established result.