BECU--OLON V15: Foundations and Explanations of Fractional Infrared Cosmology

BECU--OLON V15 develops the theoretical foundations of an exploratory emergent infrared geometric framework aimed at investigating whether several large-scale cosmological phenomena traditionally attributed to independent dark-sector components may instead arise from non-local geometric propagation, fractional infrared scaling, and memory-driven structural amplification. The framework introduces an effective infrared scaling regime,d_eff ≈ 8/3 ≈ 2.67,interpreted as a coarse-grained transport geometry emerging dynamically through spectral diffusion, non-local propagation, and infrared renormalization flow. Within this architecture, galactic rotation flattening, weak-lensing consistency, stochastic heteroscedastic structure growth, and large-scale cosmological anisotropies are treated as interconnected manifestations of a unified non-local geometric sector. BECU--OLON V15 establishes the foundational mathematical structure of the framework through:• localized dynamical scaling,• spectral diffusion interpretation,• infrared renormalization flow,• fractional propagation operators,• Weyl-coupled geometric response,• and explicit observational falsifiability conditions. This work is presented as an exploratory but mathematically structured cosmological research program intended for independent verification, observational stress testing, and future theoretical development.