Scroll Gravity: Balance Theory and Observational Validation (Version 2)

The Balance Theory is a novel framework that unifies galactic dynamics with cosmic web alignment through an entropy-curvature coupling mechanism. It posits that galaxies are open systems dynamically linked to their cosmic environment, with their rotation curves and spin orientations governed by two key components: Scroll Potential: A geometric term, ϕ(r)=φ0(rλc)2e−r/λcϕ(r)=φ0(λcr)2e−r/λc, acting as an effective gravitational potential to explain flat rotation curves without invoking dark matter. Entropy-Curvature Coupling: A term (ΓΓ) encoding environmental entropy, which mediates angular momentum exchange between galaxies and cosmic filaments. The theory predicts a layered scroll geometry for galaxy halos, where concentric layers align with filaments, enabling torque-driven spin alignment. Validation includes: Spin-Filament Alignment: 3D kinematic analysis of MaNGA galaxies in SDSS filaments, showing late-type spirals align with filaments, while S0s exhibit perpendicular spins. Rotation Curve Fits: Successful modeling of SPARC galaxies (85% improved fits) with scroll parameters (λc∼5–10λc∼5–10 kpc, φ0φ0) correlating with HI asymmetry. Void Galaxy Tests: Residual alignment signals in low-density environments, suggesting primordial spin-filament coupling. Simulation Consistency: Matches IllustrisTNG’s mass-dependent spin-flip trends, reframing ΛΛCDM alignment as entropy-mediated effects. This work bridges galaxy-scale kinematics and cosmic-scale structure, offering an alternative to dark matter by attributing dynamics to the interplay of geometry and cosmic web entropy. Data and code are provided for reproducibility, including SPARC rotation curve fits, MaNGA alignment metrics, and simulation comparisons.