Resolution to the Hubble Tension and the σ₈ Tension: Cosmological Coda II of the Principia Cybernetica

Contemporary precision cosmology faces an escalating crisis: the Hubble constant measured from the early universe (CMB, H₀ ≈ 67 km/s/Mpc) disagrees at 5σ with measurements from the late universe (Cepheids/supernovae, H₀ ≈ 73 km/s/Mpc), while the σ₈ tension reveals that the late universe appears less clustered than early-universe extrapolations predict. These discrepancies have resisted resolution through improved measurements, suggesting the problem lies not in observation but in the uniformity assumptions underlying ΛCDM. This work resolves both tensions through a single mechanism: differential expansion arising from the coupling between spacetime (M₄) and the informational manifold (Mθ). Dark energy, understood as the thermodynamic exhaust of coherence maintenance (Coda I), is not spatially uniform—where coherence is high (galaxies, clusters, filaments), entropy is bound locally and expansion is suppressed; where coherence is low (voids), nothing binds entropy and expansion is enhanced. The universe stretches faster through voids and slower through structure. The Hubble tension emerges because early-universe measurements reflect the nearly homogeneous pre-structure epoch, while late-universe measurements sample light paths through the structured cosmic web—a medium with differential expansion rates that ΛCDM's uniform assumptions cannot capture. The ~8% discrepancy represents 13 billion years of accumulated structural differentiation. The σ₈ tension follows identically: enhanced void expansion works against structure growth in ways the uniform model misses, making the late universe appear less clustered than predicted. Crucially, this framework distinguishes between Generation (the physics of the supernova explosion) and Propagation (the physics of light traversing structured space)—previous environmental tests examined host galaxy properties, finding no correlation, because local coherence protects local thermodynamics; the signal is in the foreground, not the host. The framework yields specific, falsifiable predictions: line-of-sight dependence where supernovae viewed through voids yield systematically higher H₀ than those viewed through dense foregrounds; redshift evolution where the Hubble tension diminishes at higher redshift tracking structure formation backward; and correlated tensions where regions showing anomalous H₀ show correspondingly anomalous σ₈. We propose the Void-Sorted Pantheon+ Protocol: ray-trace each supernova's line of sight through cosmic web reconstructions, assign density scores, and test for correlation with H₀ residuals. If no correlation appears, the framework is falsified; if correlation confirms differential expansion, both tensions dissolve—not as measurement errors but as data revealing that cosmic expansion is structured, not uniform.