DEPRECATED RECORD Exploratory Phenomenology of Finite Closure Geometry (FGC): Structural Residues and Cosmological Signatures

This companion paper presents an exploratory phenomenological investigation of the Finite Closure Geometry (FCG) framework, focusing on possible cosmological signatures arising from structural residues induced by finite closure. All results are explicitly conditional, model-dependent, and provisional. The purpose of this work is not to establish new fundamental principles, but to examine whether the structural consequences of global non-closure are compatible with current cosmological observations. Assuming the structural results developed in the foundational FCG companions—namely, the impossibility of global perfect closure under finite resolution and the existence of non-vanishing structural residues—the paper explores how such residues could enter effective cosmological dynamics under mild and physically motivated assumptions (homogeneity, isotropy, and slowly varying closure scale). Within this exploratory setting, structural residues are shown to be compatible with an effective cosmological constant–like contribution, potentially accompanied by extremely small redshift dependence, mild suppression of structure growth, and long-wavelength correlations affecting CMB observables. Dimensional estimates suggest that the associated scales can coincide with observed cosmological magnitudes without invoking new dynamical fields, modified gravity, or vacuum energy summations. The framework remains explicitly falsifiable. Precise measurements of the equation of state, large-scale structure growth, and CMB–LSS correlations provide clear criteria under which this phenomenological interpretation would be disfavored. This paper is intended as a phenomenological probe, not a derivation. It demonstrates that Finite Closure Geometry admits observationally consistent realizations while leaving open the selection of closure schemes, the detailed form of residual contributions, and their relation to other approaches such as holography or entanglement-based models. A global conceptual map, epistemological positioning, and guided reading of the foundational FCG papers is provided in the foundational Paper 0: https://zenodo.org/records/18001440