Emergent Dark Energy from Dual-Sector Energy Exchange: Multi-Probe Observational Analysis and Interpretation

Version 1. 2 — 21 March 2026 (closes the background-level programme of v1. 0 and v1. 1) This version extends the single-probe H (z) fit of v1. 1 to a full three-probe analysis combining 29 cosmic chronometer H (z) measurements, 13 BAO distance measurements (6dFGS, SDSS MGS, BOSS DR11/12, eBOSS DR14), and 1588 Type Ia supernovae from the Pantheon+ data release with full 1588×1588 statistical and systematic covariance matrix. Central result: the three-probe combination converges to lambdaₑff = 0, with a 1-sigma profile-likelihood upper bound of lambdaₑff < 0. 05. The best-fit H₀ = 68. 77 km/s/Mpc is stable across all probe combinations and anchored by the BAO data. At the best-fit solution, the dual-sector model is background-level indistinguishable from ΛCDM. This result is interpreted as an internally consistent outcome of the model's structure: the one-directional coupling Q = lambda * Hₓ * rhoᵧ depletes the hidden-sector density monotonically, and ΛCDM appears as the late-time limit within the present background formulation. The three-probe data confirm the system is at or near this limit. The framework retains distinguishable predictions at the perturbation level (growth rate, matter power spectrum), which are identified as the next research step. A modified coupling structure Q = 3 xi Hₓ (rhoᵧ - alpha rhode) is noted as a theoretical outlook for a separate follow-up paper. All results are at the homogeneous background level only. No perturbation analysis is included. The Pantheon+ absolute magnitude MB is marginalised analytically using the full inverse covariance matrix at each parameter evaluation (Cholesky factorisation).