OT/GKSL Readout Certification: Noncommutative Transport, Gram-Rank Margins, and Bridge Defect Bounds

This companion note consolidates the technical interface between the native OT/GKSL state-space framework and its certified readout implementations. Its purpose is not to introduce a new ontology or an additional physical sector, but to make explicit the minimal contracts required for the framework to become numerically auditable, falsifiable, and robust against standard expert objections. The starting point is the certified-domain Einstein-locked OT/GKSL architecture, in which the primitive
object is a density matrix trajectory ρλ evolving under an open-system GKSL/Lindblad generator, while classical spacetime and cosmological observables arise only as controlled readout structures on certified windows.
The paper focuses on four technical locks. First, the coordinate-like readout variables Xa(ρ) must not be treated as arbitrary scalar functions on state space. They must be implemented as stable, accessible record channels, with the minimal linear realization Xa(ρ) = Tr(ρRa), Ra = R†
a, a = 0, 1, 2, 3,
and with OT-rank nondegeneracy verified through the Gram matrix of their OT gradients. Second, the OT-to-readout bridge must be quantified by an auditable defect, either through a local connectionlevel comparison or through a discrete dynamical or holonomic proxy. Third, the native OT structure must be made computationally active through explicit diagnostics such as relative entropy, entropy production, entropic time, Bures or OT-distance proxies, and documented residuals. Fourth, the
readout calibration from native diagnostics to source-side response variables and cosmological tables must be fixed before evaluation, versioned, hashed, and protected against posterior retuning.
The note also specifies the role of causal ablations. Comparisons between coherent, dephased, entropy-matched, no-dissipator, identity-dynamics, and mean-only readout branches are required to distinguish a genuine ρ/GKSL/coherence/OT-generated signal from a phenomenological multiplicative fit. In particular, a claim that coherence plays a causal role is allowed only if the coherent and dephased branches produce distinct diagnostics and distinct readout outputs under an otherwise matched protocol. Likewise, a claim that the OT/GKSL core is being tested requires that the final readout table be traceable back to the evolved density matrix, the generator, the native diagnostics, and the bridge or proxy certification data.
The main contribution is therefore methodological and technical: it turns the four most vulnerable points of the framework–record selection, bridge quantification, OT/Bures implementation, and readout calibration–into explicit PASS/FAIL contracts. This consolidation is intended to support reproducible Stage31-style implementations and to clarify the evidential status of downstream cosmological stress tests. If the required chain ρ −→ GKSL/Lindblad −→ coherence/entropy/OT −→ source-side readout −→ CAMB/Cobaya is closed and audited, then the resulting observational comparison is no longer merely a test of a
frozen phenomenological table. It becomes a controlled test of the implemented OT/GKSL readout mechanism in the sector under consideration.