Struct HolonomyComputer 

pub struct HolonomyComputer {
    pub christoffel: [[[f64; 2]; 2]; 2],
}

Approximate holonomy by integrating parallel transport around a small loop.

Uses the formula: Hol(γ) ≈ exp(-∫∫D R^{1}{2 12} du dv) for a 2D manifold with Gaussian curvature K.

Fields

christoffel: [[[f64; 2]; 2]; 2]

Christoffel symbols Γ[k][i][j] at the base point

Implementations

impl HolonomyComputer

pub fn new(christoffel: [[[f64; 2]; 2]; 2]) -> Self

pub fn parallel_transport_step(&self, v: &[f64; 2], dx: &[f64; 2]) -> [f64; 2]

Parallel transport a 2D vector v along the direction (du, dv) for a small step.

dv^k = -Γ^k_{ij} v^i dx^j

pub fn holonomy_angle_square_loop(&self, eps: f64) -> f64

Approximate holonomy angle around a small square loop of size ε.

Returns the rotation angle φ such that Hol ≈ R(φ). Uses: φ ≈ R^{1}_{2 12} · ε² (area law).