The Gauge–Gravity Stratification Sub-Programme

The gauge–gravity stratification sub-programme of the Cosmochrony corpus addresses a single central question: why does the same admissible spectral functional produce Einstein gravity and Yang–Mills gauge dynamics at different spectral orders? The answer replaces the classical question "what symmetry unifies gravity and gauge?" with "at what Seeley–DeWitt order does the admissible projection respond?". Starting from the joint spectral entropy functional S_Π[g,A] = 1/2log' Ag,A, the sub-programme establishes two things. Q12 gives the Yang–Mills equations D_μ Faμν = 0 from the a₄ vertical variation at fixed base metric, the gauge component Ωᵍᵃᵘᵍᵉμν = Fμν being isolated from the total bundle curvature. Q13 gives a conditional Einstein–Yang–Mills system from the joint variation of a single matched renormalized local action: the metric variation of the same tr_ρ(F²) term supplies the Yang–Mills energy–momentum tensor, and since tr_ρ(F²) = I_ρ FᵃμνFa\,μν, canonical matching fixes cEH = 1/(16πGN) and cFI_ρ = 1/(4gYM²), so that 8πGN = 1/(2cEH) depends on the Einstein coefficient alone. No coupling is predicted: GN, gYM and the cosmological coefficient are independent renormalized matching data, and no numerical value for GNgYM² follows. The a₆ sector is given only as a representative spanning list of invariants, modulo integrations by parts and Bianchi identities, with matching coefficients. Statements about Λ⁴, Λ² and logΛ behaviour belong specifically to a proper-time cutoff and are not scheme-independent; the derivations are Euclidean. Interpretive status. The stratification a₂ → gravity, a₄ → gauge is offered as an organising reading, not a theorem.