Expansion, Gravity, and Growth: Do Late-Time Cosmological Sectors Close Consistently?

This work presents HERACLES (Horizon-Emergent Relaxation And Cosmological LERACExtended Suite), a pre-registered, model-independent program designed to audit cross-sector closure in late-time cosmology through a strict PASS/FAIL/INCONCLUSIVE governance. The suite targets three logically independent conditions: C1 (background relaxation), C2 (relativistic matter–light closure), and C3 (growth universality). For C1, the background expansion is reconstructed from Cosmic Chronometers 13, 14, Pantheon+ supernovae (full covariance), and DESI BAO (DR1), and the operational statistic is evaluated under ensemble reweighting. The baseline test yields P(Idyn ≤ 0) = 0.9667, satisfying the relaxative bound at the pre-registered threshold. For C2, the LERAC closure estimators applied to RSD growth data and Planck PR4 8, 12 CMB lensing indicate Stage µ and Stage Σ consistency, with slip η ≡ Σ/µ compatible with unity under robustness checks, and the matter–light sector passes the closure criterion. For C3, the B3 internal-growth audit finds no evidence of cumulative drift in ordered residuals (B3-soft pass) and the constant-amplitude null is preferred over simple drift alternatives; however, with the present low-redshift effective range the hard growth-universality exclusion remains power-limited, and the criterion is therefore classified as INCONCLUSIVE under HERACLES governance. Taken together, the results establish joint consistency between background relaxation and relativistic matter–light closure while transparently identifying the growth sector as the current limiting factor for hard universality claims. HERACLES provides a falsifiable, auditable framework for upgrading INCONCLUSIVE outcomes to PASS/FAIL as forthcoming survey-level tomographic products extend high-redshift leverage.