Function split_solid_by_face_surface_json 

pub fn split_solid_by_face_surface_json(
    request_json: &str,
) -> Result<String, JsValue>

Cut a solid by the analytic carrier of a selected face’s surface (Golovanov §6.4). The face may be a plane, cylinder, cone, or sphere; the kernel recognizes its analytic type and extends it to span the body. Returns { "pieces": [<below/inside>, <above/outside>] }. Errors on non-analytic faces or when the carrier does not cleanly divide the body.