We formulate Curvature-Entropy Coupling (CEC) as a minimal late-time cosmological extension in which cosmic acceleration is not attributed to a rigid cosmological constant, but to a scalar degree of freedom whose background value is operationally tied to the integrated history of structure growth. In its most economical form, the model is written as a non-minimally coupled scalar-tensor theory with a macroscopic closure phi (a) = phiᵢ + kappa G (a), where G (a) is a measurable functional of f sigma₈ (z). This construction gives CEC its distinctive content: expansion and growth are no longer independent sectors fitted separately, but are constrained by a common state variable. We develop the minimal action, state the kill-switch conditions under which the model collapses back to General Relativity plus Lambda, and incorporate the local-gravity viability layer required by any serious referee: the GR limit, Cassini/MICROSCOPE compatibility, and a screening interpretation that confines non-trivial effects to cosmological or strong-field regimes. Finally, we attach a preliminary robustness note based on a 30-seed large-scale-structure exercise, which does not yet constitute a global cosmological fit but does show that the extracted summary parameters remain within narrow bands across seeds. The resulting manuscript is best positioned as a falsifiable bridge-paper within the broader FCL program.
César Daniel Reyna Ugarriza (Mon,) studied this question.