Gravitational Epistemology: A Framework for Cyclical Cosmology

This preprint proposes that time is not an independent background warped by gravity, but is locally defined by gravitational geometry, the structure produced by mass-energy distributions. From this foundation, it argues that our equations carry an intrinsic gravitational weight from Earth's well, potentially producing systematic bias in cosmic interpretations. Part of what appears to be accelerating expansion may be clock desynchronization along photon paths through inhomogeneous gravitational environments.A preliminary toy calculation, using observationally grounded structural parameters drawn from published large-scale structure surveys, numerical-relativity void simulations, and the Hamaus et al. (2014) universal void density profile, models this mechanism as a phenomenological coupling (eta) between local expansion-rate contrasts and accumulated path redshift. The dark-energy signal is defined precisely as the distance-modulus difference between Lambda-CDM and a matter-only baseline. The fraction of this signal attributable to the path effect, R(z), depends on eta: at perturbative coupling (eta ~ 0.01-0.05), R is 1-3%; at moderate backreaction (eta ~ 0.1-0.3), R is 5-15%; at strong coupling consistent with Wiltshire's timescape model (eta ~ 0.5-1.0), R reaches 15-40%. Analytic moments of the toy model are derived in closed form and verified by Monte Carlo simulation.This version introduces a precise, executable observational test protocol: correlating Type Ia supernova Hubble residuals from the Pantheon+ catalog with line-of-sight void fraction reconstructed from SDSS and DESI galaxy survey data. This test converts the coupling parameter eta from a free parameter into a measurable, falsifiable quantity. Detection thresholds are defined: eta becomes observable above approximately 0.2 with current data, and above approximately 0.05 with DESI DR3 and Rubin LSST.The framework predicts finite cycles without eternal expansion or permanent dark energy, reframing entropy, singularities, and cosmic fate within standard General Relativity. It proposes that the Hubble constant is not an arbitrary measured parameter but the gravitational memory of a prior cycle's collapse, and that collapse velocity and expansion velocity are the same equation read in opposite temporal directions.Testable predictions include correlations between supernova Hubble residuals and line-of-sight large-scale structure, sensitivity of measurements to observer gravitational environment, and environment-dependent variations in the locally measured Hubble constant. The framework predicts the correct direction of the observed Hubble Tension: locally measured H0 should exceed CMB-inferred H0 when the observer occupies a wall or filament environment.