Basis covariance and fluctuation diagnostics for measurements in closed quantum gravity

Proposals for observations in closed quantum gravity must specify how unresolved microscopic alternatives become measurement outcomes. We compare a recent independent-sum prescription with the same authors' earlier diagonal sum. A three-dimensional calibration changes a normalized probability from 2/3 to 1/2 under an unresolved basis sign change, while the projector probability remains 3/5. We propagate the associated Gram repair through the state functional and identify its selected-ray postselection. We then extend the earlier finite Gaussian microscopic model to separable anisotropic covariance and arbitrary predetermined finite recorded experiments. Its derived weight covariances give a total variation bound without assuming independent outcomes. Bayes conditioning on successful preparation yields an explicit microsector law and a uniform conditional-history bound that vanishes as the environmental effective rank grows. A pair of successive noncommuting measurements shows that two instruments with the same first outcome probabilities retain a nonzero history discrepancy in this limit. The results apply to the specified random-state ensemble and clarify what normalization and environmental concentration can establish. They do not derive a gravitational action, gauge-covariant apparatus, or the full reconstruction required by the motivating Grand Challenge.

This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, authorized its preparation and publication and is responsible for it.