Function channel_direction 

fn channel_direction<const N: usize>(
    entry: Jet<N>,
    position: [f64; 3],
    k: Complex,
    q: &[f64],
    measure: f64,
) -> Complex

Both families use the same input shapes and slot layout, except that cylinders have only the kx transverse slot. Contract each small local jet directly; no global Jacobian or output-sized cotangent seeds are needed.