Optimal-Transport Gravity Trilemma: Holonomy, GKSL Dynamics, and Source-Side Coherence

This manuscript develops a constrained and low-energy testable theory of the state–geometry interface in which classical spacetime geometry is not fundamental, but appears only as a certified readout on a controlled infrared window Wacc. The native layer is formulated on the manifold of full-rank quantum states D∘, with GKSL/open-system dynamics

dρξ/dξ=L(ρξ),

and, in the detailed-balance subclass, an entropic clock defined by

dEntπ(ρξ)/dξ=−σ(ρξ)≤0.

At readout level, the two-derivative gravitational sector is kept strictly Einstein,

Gμν=8πG_0/c4 Tμν_tot, with no term of the form μ(ρ) R,

The manuscript derives a local bridge between state-space holonomy and readout holonomy, together with a conditional trilemma excluding βeff≡0 on the certified window when OT non-flatness, bridge fidelity, and Einstein lock are simultaneously maintained. It also formulates reduced operational equations in which the low-energy response separates into a constitutive branch governed by

βeff(pκ):=−∂_pκ (ln⁡Λ(pκ)),

and an independent holonomic branch controlled by projected curvature. The result is a certified and falsifiable low-energy framework for testing whether preparation-dependent quantum-state structure can induce readable gravitational signatures.

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.

• Master Reading Guide to the Low-Energy-Testable Optimal-Transport Gravity–GKSL Certified-Domain Architecture | This record presents the master architectural entry point to the low-energy-testable Optimal-Transport Gravity--GKSL certified-domain architecture.

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.

• Bekenstein–Hawking Entropy as Certified Horizon Readout in the Einstein-Locked OT/GKSL Framework part1 | Établit les fondations théoriques démontrant comment l'entropie d'un trou noir n'est pas une mesure d'états cachés, mais la limite de certification opérationnelle (Readout) de la géométrie à l'horizon des événements.

  Toward a Full Native Derivation of the Bekenstein–Hawking Formula in the Einstein-Locked OT/GKSL Framework Part2 | Complète la dérivation mathématique rigoureuse de la formule de l'aire (A/4) exclusivement à partir de la dynamique dissipative quantique (GKSL) et du Transport Optimal, sans postuler de gravité quantique microscopique.

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.

• Experimental Separation of Readout and Causal-Local Correlation Layers in the Einstein-Locked OT/GKSL Framework Proposes a falsifiable experimental protocol (CLCP) to test the layered structure of correlation observables by separating certified readout and causal-local licensing thresholds on a controllable quantum platform .

6. Mass Generation:

• Mass Generation and Vacuum-Like Residual Sourcing Theorem in the Einstein-Locked Optimal-Transport/GKSL Framework | This paper establishes a theorem-oriented source-side mechanism for mass generation and vacuum-like residual sourcing within the Einstein-locked OT/GKSL framework for open quantum sources
• A Theorem on a CDM-Like Intermediate Branch in the Einstein-Locked OT/GKSL Framework | This paper establishes a theorem-level result within the Einstein-locked OT/GKSL framework: cold-dark-matter-like behavior can arise internally as a stable intermediate branch of the reduced constitutive--holonomic source-side sector, without introducing a new primitive dark particle and without modifying the Einstein--Hilbert kinetic block.

7. Dirac Electron Dynamics: Optimal-transport + GKSL:

• Certified Recovery of Dirac Electron Dynamics in Central Abelian Potentials from the Einstein-Locked Optimal-Transport-GKSL Framework | This paper establishes a certified recovery of standard relativistic electron dynamics from the fermionic gauge-enriched sector of the Einstein-locked Optimal Transport OT/GKSL framework. The paper identifies and constructs a certified fermionic readout regime in which the Einstein-locked OT/GKSL framework recovers standard Abelian Dirac dynamics in mathematically controlled form.