BECU–OLON: Α----->Ω EDITION, Beyond the Dark Sector

BECU–OLON: Α → Ω EDITION investigates a unified non-local fractional cosmology framework exploring geometric structure amplification, anisotropic spacetime response, Weyl-curvature lensing couplings, stochastic heteroscedastic dynamics, and non-local memory evolution beyond the conventional dark-sector paradigm. Built upon a continuous fractional spacetime architecture (d = 2.67), the framework investigates an alternative geometric interpretation of galactic dynamics, weak lensing, low-ℓ CMB anisotropies, and large-scale structural evolution without explicitly invoking independent collisionless dark matter components. The Ω Edition consolidates the complete theoretical architecture developed across the BECU–OLON program, including: • fractional geometric propagation,• structural order parameter dynamics,• conformal Weyl coupling formalism,• non-local screened Helmholtz memory kernels,• triaxial anisotropic tensor geometry,• stochastic heteroscedastic uncertainty evolution,• BipoSH anisotropy diagnostics,• and explicit observational falsifiability conditions. This release is presented as an exploratory but fully testable cosmological research framework intended for open scientific evaluation, independent reproduction, mathematical criticism, and future observational stress testing. License: Creative Commons Attribution 4.0 International (CC BY 4.0)