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 : Advisory. This manuscript is part of a testable certified-domain OT/GKSL architecture organized in distinct layers: native dynamics, certified readout, Einstein-locked nonlinear closure, and controlled recoveries. The Einstein kinetic sector remains locked, Bianchi-compatible closure is enforced, and readable state dependence is confined to the source/response sector. It should be read as one structured component of a closed operational framework, not as a standalone modified-gravity model. 1. Foundations of the Architecture Foundations | Establishes the core Einstein-locked OT/GKSL architecture for certified geometric readout and coherence-dependent gravitational sourcing. 2. Emergence and Recovery of Classical Physics Exact Reduced OT/GKSL Equations | Demonstrates the controlled recovery of classical Newtonian and gravitational sectors as exact non-linear reductions of the native OT/GKSL state dynamics. Certified Einstein Non-Linear Readout | Develops the full non-linear Einstein-locked readout closure for the metric sector. Non-Linear Dynamics and Readout | Explores the exact reduced non-linear evolution on collective state manifolds. The Seeley–DeWitt Bridge | Formalizes the operational connection between native state dynamics and the effective classical readout. The SDW Bridge: Composite Brout–Englert–Higgs Dynamics, Spectral Separation, and the Emergent Graviton | Formalizes the emergence of the Brout-Englert-Higgs composite scalar and the spin-2 graviton via the Seeley-DeWitt expansion, strictly preserving the Einstein-Lock. Bridge between QCD and OT/GKSL Readout | Connects the Optimal Transport / GKSL framework to Quantum Chromodynamics, exploring the constitutive bridge and effective low-energy dynamics. 3. The Certified Boundary and Structural Limits Certified Spacetime Readout on Finite Support: A Unified Temporal and Geometric Boundary | Unifies the temporal and geometric branches of classical readout into a single certified spacetime problem. Introduces the unified spacetime readout burden and derives the central unified certified-budget inequality, proving that temporal precision, geometric coframe nondegeneracy, and bridge compatibility draw from the same finite entropic and informational resources and cannot be made simultaneously ideal. Certified Causality, Locality, Nonlocality, and Relativity in the Einstein-Locked OT/GKSL Framework | Determines the exact status of causality, locality, nonlocality, and the principle of relativity within the Einstein-locked OT/GKSL architecture. Shows that causal-local spacetime semantics is a certified readout property rather than a primitive native axiom; proves a patchwise gluing theorem for certified local causal structure; and derives a unified finite-budget inequality showing that temporal precision, geometric certification, bridge admissibility, and overlap compatibility all compete for a single residual causal-local headroom on finite effective support. Entropic Tick Cost and Certified Temporal Readout in the Einstein-Locked OT/GKSL Framework | Demonstrates that classical ticks are finite-resource readout objects extracted from native entropic ordering, rather than primitive background parameters. Decomposes the entropic tick cost into native, extraction, and certification branches, and derives a theorem-level certified temporal budget inequality connecting temporal resolution, finite effective support, and certification margins. Entropic Tick Cost & Spectral Budget | Establishes a theorem-strength certified boundary for classical spacetime by proving a fundamental trade-off between entropic tick resolution, coframe stability, and finite informational budget. Optimal-Transport Gravity Trilemma | Identifies the certified operational boundary of geometric readout by proving the fundamental trade-off between temporal resolution, coframe stability, and bridge fidelity. Toy Certified Pipeline from Optimal Transport QCD | Provides a protocol-level implementation and scaling model for certified bridge margins. 4. Cosmological Dynamics & Global Readout Constraints Vacuum-like Residual Energy from Constitutive-Holonomic Balance in a Minimal Reduced OT-C3 Sector | Demonstrates analytically that the macroscopic cosmological constant emerges as a non-zero vacuum-like residual energy resulting from the exact balance between scalar constitutive dissipation (source sector) and the non-commutative holonomic barrier of the Optimal Transport geometry. Homogeneous Closed Readout Dynamics under Finite Spacetime Budget | Constructs a homogeneous and isotropic model (G-FLRW) demonstrating how the spacetime budget acts as a branch-selection mechanism, effectively identifying the vacuum-like sector (Λ) as the maintenance cost of certified spacetime solvability. 5. Experimental Protocols and Testability Testing Source-Side State Dependence in Gravity with Lock-In Atom Interferometry | Proposes a concrete experimental protocol to falsify source-only emergent gravity at low energy. A Lock-in Atom-Interferometric Test (Clock) | Detailed operational implementation of the low-energy readout test for the Einstein-locked framework.