The Temporal Accumulation Hypothesis III: Derivation from Baryon Self-Gravity, Verification Program, Re-Interpretation Protocol, and Environment Extension

We present the theoretical derivation, comprehensive verification program, and observational re-interpretation protocol for the Temporal Accumulation Hypothesis (TAH). Building on Papers I–II (20 tests, zero failures), we derive the metric correction parameter from first principles: the accumulated gravitational self-energy of baryonic matter produces a redshift-dependent correction η(z) = 1 − f_b² exp(−z/z_s), with f_b = 0.156 (Planck 2018) and z_s = 1.28. No parameters are fitted to the target datasets. Seven independent probes yield η = 0.979 ± 0.008 (2.7σ from ΛCDM). Fifteen creative tests are presented (C1–C15), including: gravitational-wave standard sirens (H0_GW consistent with Planck at 0.5σ), stellar chronometry, bulk flow surveys, TRGB–Cepheid per-galaxy σ correlation (Spearman r = 0.985, p < 0.001), Etherington relation redshift profile (χ²/N = 0.001 vs 0.40 for ΛCDM, 79× improvement), and S8 tension redshift evolution. External validation: Smawfield (2026) independently measures α = 0.58 ± 0.16 from 29 SH0ES Cepheid hosts, in exact agreement with the TAH-σ analytical prediction (0.00σ).