Resolution Cosmology and Quantum-Corrected Geodesics: A Correspondence with Koch et al. (2025)

This working paper establishes a formal correspondence between Resolution Cosmology (RC) and the quantum-corrected geodesic framework (“q-desics”) recently introduced by Koch, Riahinia, and Rincon (2025). Their approach demonstrates that classical geodesic motion does not follow from the expectation value of the metric alone; instead, motion depends on the expectation value of the Christoffel operator, leaving residual quantum corrections governed by a set of free integration constants ε. While mathematically robust, the q-desic framework lacks a physical interpretation of these parameters and therefore cannot yet make astrophysical predictions.

Resolution Cosmology provides that missing interpretation.
Within RC, spacetime is understood as an accumulated geometric record formed through irreversible “resolution events,” each carrying a thermodynamic cost proportional to the temperature at which the information was committed. This process stratifies spacetime into Deep, Middle, and Surface layers (“Strata”), where the oldest layers—resolved at the Planck epoch—carry the greatest gravitational weight. These structures manifest observationally as what is currently modeled as dark matter.

The correspondence proposed in this paper identifies:

• ε-parameters ←→ thermal resolution history of local spacetime (Deep Strata density)

• Koch et al.’s covariance measure (Cov) ←→ texture of the geometric record

• constant term in q-desic orbital velocities ←→ Planck-epoch mass-per-bit contribution (Deep Strata halo floor)

• inverse metric operator requirement ←→ structured compression of high-pressure geometry (superionic / lattice analog)

This mapping turns q-desics from a formal quantum-gravity construction into a physically interpretable—and predictive—framework. In return, q-desics provide RC with an operator-level mathematical formalism for motion through a quantum-textured spacetime.

The correspondence generates several falsifiable predictions accessible with existing surveys and instruments:

1. ε should correlate with black hole accretion history (“quasar–halo lag”), corresponding to RC’s prediction that black holes generate Deep Strata over time.

2. q-desic deviations should be larger in filament environments than in voids, distinguishing RC from particle-dark-matter models.

3. black hole horizon radii may show small but measurable ε-dependent shifts, potentially testable via gravitational-wave ringdown spectroscopy.

4. local fine-structure-constant variations (α) should correlate with Deep Strata density, linking precision spectroscopy to galactic dynamics.

In essence, this work proposes that quantum-corrected geodesics describe motion through the textured fossil geometry predicted by Resolution Cosmology. The two frameworks converge on a shared conceptual point: classical spacetime is not obtained by smoothing the metric alone, but by smoothing away the history of how the metric was written. Motion in regions where that history is non-trivial produces observable deviations—currently attributed to dark matter—that arise instead from the quantum-informational structure of spacetime itself.

This paper is part of the ongoing Resolution Cosmology series and is intended as a bridge between quantum-gravity formalism and cosmological phenomenology. The results are exploratory but fully testable with current observational datasets.