Variable Speed of Light in the Chute Framework: The Speed of Light as a Local Material Property of Pressurized Spacetime

The Chute Cosmology framework (Barkley, 2026) proposes that our universe occupies the seventh shell in a ten-shell chain of nested black hole interiors. This companion paper develops a specific and consequential prediction of that framework: the speed of light is not a universal constant but a local material property of spacetime—the propagation speed of vortex disturbances in a pressurized medium that varies systematically based on three factors. First, c varies with shell depth, decreasing exponentially from Shell 1 through Shell 10 according to c_n = c_1 · e^(−α(n−1)), where α encodes brane pressure scaling. Second, c decreases over cosmic time within any given shell as brane stress accumulates from structure formation and gravitational collapse. Third, c is further modified by the cumulative deep-shell creation of daughter universes, whose formation represents local brane punctures that alter the medium's propagation characteristics. We demonstrate that this three-factor model provides a unified physical mechanism for several otherwise disconnected anomalies in modern cosmology. The Hubble tension—the persistent ~5σ discrepancy between early-universe measurements of H₀ (~67.4 km/s/Mpc from Planck) and local measurements (~73.0 km/s/Mpc from SH0ES)—is naturally resolved as a calibration artifact arising from different propagation speeds at different cosmic epochs. Tentative observations of fine structure constant variation at high redshift (Webb et al., 2001) find a specific physical mechanism in the depth- and time-dependence of c. The onset of cosmic acceleration approximately five billion years ago is reinterpreted as a manifestation of cumulative brane degradation from deep-shell universe creation. We present eight testable predictions and discuss the framework's relationship to prior variable-c cosmologies, analogue gravity models, and the preservation of local Lorentz invariance.