A One-Parameter, Four-Channel Consistency Test for EFC Background Coupling (β·T(a))

We present a one-parameter, four-channel consistency test of late-time background coupling in Energy-Flow Cosmology (EFC), implemented as a modification to the Friedmann equation H²(a) = H₀²[Ωₘa⁻³ + ΩΛ(1 + β·T(a))], where β is a dimensionless coupling amplitude and T(a) is a fixed transition function that vanishes as Ωₘ → 1.The construction is deliberately minimal: the Poisson equation is unmodified (μ = 1), and all cosmological effects arise solely through changes in the expansion rate, altering Hubble friction in the growth equation. This design creates a direction-sensitive empirical test: Poisson-sector modifications enhance growth and are disfavoured by BOSS DR12 redshift-space distortions, while background coupling (β > 0) suppresses growth and aligns with observations.A single value β ≈ 0.08 is tested against four independent late-time cosmological probes: BAO distances (BOSS DR12), growth rates fσ₈ (BOSS DR12), CMB lensing (ACT+SPT+Planck 2025), and Type Ia supernova distances (Pantheon+). The model shows a mild joint preference in BAO+RSD (Δχ² ≈ −3.9 for one additional parameter), while remaining consistent with CMB lensing and supernova constraints within 1σ. The coupling naturally vanishes at high redshift, producing a null effect in Lyα forest measurements and automatic recovery of standard gravity at recombination.The result is not a detection of new physics but a consistency and direction test demonstrating that EFC’s coupling must enter through the background expansion rather than the Poisson equation. Four independent channels, one parameter, zero internal contradictions.