A RecursiveEntropic Architecture for Cosmological Structure with Dimensional Invariance(REACS-DI): From Bohr Radius to Galaxy Filament — A Dimensionless Recursion of Space, Time, and Energy

This paper introduces the Recursive Entropic Architecture for Cosmological Structure with Dimensional Invariance (REACS-DI), a scale-invariant framework investigating whether atomic-scale geometry, when transformed through a single dimensionless scaling constant, can reproduce structural features of the filamentary cosmic web. Rather than relying on scale-specific assumptions or fitted cosmological parameters, REACS-DI explores whether proportional correspondence across space, time, and energy can emerge from unit-invariant, empirically grounded relations. A fixed recursive scaling constant S \sim 10^{34\text{–}35} is derived from ratios of characteristic atomic and cosmological reference quantities. Applied spatially, this factor maps the Bohr radius to filamentary length scales consistent with observations from large-scale structure surveys. Applied temporally, it extends atomic oscillation timescales into cosmological epochs, while energetic scaling yields an inverse correspondence between atomic binding energy and macroscopic gravitational regimes. These transformations preserve the functional form of fundamental physical laws, supporting dimensional invariance under recursion. To test the hypothesis, lattice-based simulations seeded from scaled hydrogenic density distributions are constructed and evolved under entropy gradients. The resulting structures exhibit interconnected filaments, nodal clustering, and void distributions consistent with known cosmic web morphology. Two-point correlation analysis confirms non-random spatial organisation aligned with observational statistics. Entropic evolution further demonstrates structural persistence and controlled degradation under thermodynamic pressure. REACS-DI does not seek to replace existing cosmological models, but to offer a falsifiable, simulation-driven framework suggesting that large-scale cosmic structure may arise as a recursive, informational extension of atomic-scale geometry rather than as a scale-dependent phenomenon.