Brane Induced Curvature Mass Model: Sheet Tension, Curvature Energy and Galactic Rotation Curves

Brane Induced Curvature Mass Model is a geometric gravity framework that replaces dark matter and dark energy with curvature energy on a tensioned two dimensional brane. The model treats the observable spatial slice as a deformable sheet with tension σ, described by a height field h(u, v). Gradients of this sheet store curvature energy ρcurv ∝ σ|∇h|², which acts as an effective mass density. The repository contains the full mathematical construction, numerical implementation and Streamlit based interactive tools for: • generating axisymmetric brane profiles h(r) and their curvature mass Σcurv(R) • producing toy galactic rotation curves v₍c₎(R) from curvature mass • solving the baryon coupled Helmholtz equation ∇²h − m²h = λΣ_b to create baryon driven geometric halos • fitting SPARC galaxy rotation curves using a minimal set of geometric parameters • deriving weak lensing observables [κ(R), γ_t(R), α(R)] from Σcurv(R) • exploring the cosmological sector in which uniform brane tension behaves as an effective Λ This project provides a complete sandbox for testing the hypothesis that galactic dynamics, baryon–halo correlations, gravitational lensing and cosmological acceleration can emerge from a single geometric mechanism. It includes the full paper, figures and a numerical pipeline for reproduction and further development.