When Growth Does Not Break but Geometry Still Holds: HERACLES Constraints on Vacuum-Like Dark-Sector Exchange

Recent cosmological analyses have motivated the question of where late-time new physics can reside without disrupting sectors that already appear observationally closed. This work applies the HERACLES framework—a pre-registered suite of independent consistency criteria spanning background expansion (C1), relativistic matter–light closure (C2), and growth universality (C3)—to isolate the logically admissible window for late-time modifications. The background consistency test C1confirms a relaxative kinematic bound for the late-time expansion history, and the relativistic closure test C2finds no statistically significant departure from matter–light consistency within current sensitivity. This study further applies C3using internal B3 audits on DESI DR1 ShapeFit tomographic bins (BGS, LRG z0–z2, ELG, QSO), [1, 2] constructing a redshift-ordered growth-amplitude proxy and testing for cumulative drift and explicit drift alternatives. [1, 2] No evidence is found for ordered residual drift (B3-soft PASS), and simple drift alternatives are not preferred over the universal-amplitude null within the statistical power of the present binning (hard-lite regime). The resulting C3verdict is therefore PASS (hard-lite), i.e., consistent with universal growth under cumulative-drift audits. Taken together, C1–C3closure disfavors scenarios in which dark-sector energy exchange acts as a persistent source or sink for structure growth over the observed redshift range. Instead, the combined results favor a background-dominant, vacuum-like class of late-time dynamics, in which acceleration emerges from effective geometric relaxation while the clustering sector remains approximately universal. Cosmic growth remains a decisive falsification channel [3, 4] for future high-redshift tomography, where the hard-lite regime is expected to transition to fully decisive B3-hard tests.