BAO Global Ruler

The Baryon Acoustic Oscillation scale is calibrated against the sound horizon at photon-baryon decoupling — a ruler whose physical length ΛCDM assumes to be strictly universal and fixed at roughly 147 Mpc. However, SCT's dynamical cosmological term Λ_eff(x,t) varies with the local ratio of parent-frame mesh dissipation to local gravitational binding strength, meaning that the effective expansion history differs between dense cluster environments and underdense voids. When the BAO ruler is measured in different large-scale environments — the KBC Supervoid versus dense filament nodes — the inferred sound horizon length shifts slightly because the locally enhanced Λ_eff in the void region accelerates post-recombination expansion differently than ΛCDM's constant Λ predicts. This produces a systematic scatter in the BAO peak position that ΛCDM has no mechanism to accommodate.

Within the SCT framework, the BAO ruler itself remains physically well-defined — the sound horizon at decoupling is determined by the pre-collision plasma state, which thermalizes identically to ΛCDM. The discrepancy arises in the mapping from the physical ruler to observed angular scales and redshifts. Because the hereditary time transmission chain propagates the weakening tensor mesh down through nested comoving frames, observers in different large-scale environments effectively inhabit slightly different proper-time regimes. The angular diameter distance integral is consequently modified by the position-dependent Λ_eff profile, stretching or compressing the projected BAO scale on the sky by a few tenths of a percent — enough to explain the coherent BAO offset seen between DESI and Planck without invoking early dark energy or modified gravity.