Admissibility and Physical State Classification in the q-desic Framework of Quantum Gravity

The q-desic framework introduced by Koch, Riahinia, and Rincón provides a novel link between quantum-gravitational structure and test-particle motion by defining trajectories in terms of expectation values of an affine connection operator. While formally correct and conceptually promising, the framework leaves open a key question: which quantum spacetime states and resulting trajectory corrections should be regarded as physically admissible and observationally meaningful?

This work provides a conservative admissibility completion of the q-desic framework. Accepting the q-desic equations of motion and their derivation exactly as given, it introduces no new dynamics, no modified force laws, and no competing theory of quantum gravity. Instead, it develops a structured classification of quantum spacetime states and q-desic corrections based on framework-internal consistency, trajectory-level record relevance, covariance structure, uncertainty compatibility, and stated operator-control regimes.

The analysis partitions the q-desic state space into admissible, inadmissible, and marginal or suppressed sectors, and distinguishes structural or universal statements from genuinely state-dependent quantum deviations. It further clarifies the conditions under which q-desic motion reduces to classical geodesic motion and identifies when purported quantum corrections should be excluded from admissibility or treated conservatively due to truncation or underdetermination.

The resulting framework addresses known interpretational gaps in the q-desic program without fixing quantum-gravity microphysics or introducing phenomenological assumptions. It provides a prerequisite layer for future quantitative or observational studies of q-desic motion, while remaining fully agnostic about the underlying theory of quantum gravity.