Exact Reduced OT/GKSL Equations and Controlled Recovery of Abelian and Newtonian Readout Sectors

Short summary: This work develops exact nonlinear OT/GKSL-based differential equations for a low-energy state--geometry interface and shows how standard static Abelian and Newtonian readout equations are recovered on a certified adiabatic weak-field window. In an Einstein-locked regime, state dependence is forced into source-side constitutive and holonomic channels rather than the gravitational kinetic term. A concrete chiral HS/NJL realization yields an explicit two-channel reduced dynamics and a symmetry-resolved lock-in law, making the framework calculable and experimentally targetable rather than merely programmatic. Summary: This manuscript develops a low-energy stable differential formulation of the OT/GKSL state--geometry interface in a gauge-enriched QED-type sector. The native level is an open-system dynamics on quantum state space, dρξ/dξ=L(ρξ)), not a primitive spacetime theory. Classical geometry appears only as a certified readout on an admissible window. Under Einstein lock, no state-dependent factor is allowed in front of the Einstein--Hilbert term, so readable state dependence is forced into source-side constitutive and response channels. From the OT variational formulation, the manuscript derives exact nonlinear reduced equations for admissible protocol curves, identifies a constitutive branch controlled by βeff(pκ)=−∂pκln⁡Λ(pκ), and a distinct holonomic branch controlled by the curvature of the induced readout connection. In a concrete chiral HS/NJL realization, Y(ρ)=σ(ρ)1+iγ5π(ρ)=r(ρ)exp ((iγ5φ(ρ)), the variables (r,φ)(r,\varphi)(r,φ) provide an explicit reduced two-channel dynamics. The manuscript then proves, on a certified adiabatic weak-field readout window, the controlled recovery of standard static low-energy equations, Δϕ=−ρ_el_can+O(ε_std), ∇^2Φ=4πG_0 ρeff+O(ε_std), together with their exterior solutions and a symmetry-resolved lock-in law given above in the document. The result is not merely programmatic: the manuscript establishes exact reduced OT/QED equations, a controlled recovery of standard Abelian and Newtonian readout sectors, and an explicit constitutive/holonomic channel split leading to experimentally addressable narrowband observables. Et voici une version encore plus courte, si vous voulez quelque chose de plus percutant pour la case de description :