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

This manuscript develops a low-energy, operational framework in which classical spacetime is not fundamental, but emerges as a certified readout of a deeper dynamics on quantum states. The native level combines GKSL/Lindblad open-system evolution, quantum optimal transport (OTq) geometry, and a fermionic/gauge sector treated through Hubbard–Stratonovich/NJL and Seeley–DeWitt bookkeeping. The Einstein–Hilbert kinetic sector remains strictly fixed (“Einstein lock”): G0 is universal, no state-dependent factor multiplies R, and any preparation dependence is confined to a source-only constitutive factor μ(pκ) plus a covariant response sector.

The paper’s main structural result is a conditional OT–C3 trilemma / no-go theorem. Under three assumptions — non-flat admissible OT geometry, a nondegenerate local OT-to-readout holonomy bridge, and Einstein-lock source-only infrared structure — the effective susceptibility βeff cannot vanish identically on the certified window. In physical terms, complete gravitational blindness to internal coherence is possible only through readout shutdown, bridge failure, or a nongeneric compensation mechanism. A second major result is a windowed exponential rigidity theorem: under stacking/composability of independently audited source modules, the constitutive law is forced into an exponential form in the canonical quadratic state coordinate.

A major extension of the manuscript is the inclusion of realistic gauge sectors. In the QED/U(1) case, the reduced readout splits into three branches: a constitutive source-only channel, a local QED renormalization channel, and an independent holonomic channel proportional to gauge curvature. Thus, even if the constitutive slope vanishes, the holonomic branch may remain observable. In the QCD/SU(3)c case, non-Abelian color geometry further strengthens the trilemma: the strong null becomes even less generic once realistic internal gauge curvature is admitted. Overall, the manuscript does not propose a variable-G0 theory, but a falsifiable source-side framework in which constitutive and holonomic channels provide distinct, symmetry-resolved laboratory observables.