Brane Induced Curvature Mass: Geometric Halos and Galactic Rotation Curves

Brane Induced Curvature Mass (BICM) framework provides a geometric alternative to dark matter by modeling galaxies as deformations h(u,v) on a tensionful two dimensional brane. Curvature energy ρcurv ∝ |∇ h|^2 is interpreted as an effective mass component that produces realistic galactic rotation curves, lensing profiles and an effective cosmological constant. This dataset includes the full LaTeX source of the paper, figures, numerical results and the implementation of the BICM Laboratory, a Python and Streamlit based tool that performs: • axisymmetric brane simulations and curvature mass maps • rotation curve generation from geometric profiles • Helmholtz baryon coupling to generate induced geometric halos • full comparison against 175 SPARC galaxies for BICM, MOND and NFW • lensing predictions (κ, γₜ, α) • a simple cosmological tension module for Λeff The material provides a complete, reproducible exploration of BICM as a phenomenological framework that unifies galactic dynamics, baryon driven halo formation, weak lensing and an effective cosmological constant within a single geometric model.