Implement `opt_einsum` generator for full cc about termfactory HOT 3 OPEN

for order in range(1, max_order+1):

for omega_term in master_omega.operator_list:
    specifier_string = f"m{omega_term.m}_n{omega_term.n}"

connected_opt_path_list = compute_m3_n0_fully_connected_optimized_paths(A, N, ansatz, truncation)
linked_opt_path_list = compute_m3_n0_linked_disconnected_optimized_paths(A, N, ansatz, truncation)
unlinked_opt_path_list = compute_m3_n0_unlinked_disconnected_optimized_paths(A, N, ansatz, truncation)

return_dict = {
    (3, 0): [connected_opt_path_list, linked_opt_path_list, unlinked_opt_path_list]
}

def compute_m0_n0_fully_connected_optimized_paths(A, N, ansatz, truncation):
    """Calculate optimized einsum paths for the fully_connected terms."""

    fully_connected_opt_path_list = []

    if ansatz.ground_state:

        if truncation.at_least_linear:
            if truncation.singles:
                fully_connected_opt_path_list.append(oe.contract_expression((A, A, N), (A, A, N)))

        if truncation.at_least_quadratic:
            if truncation.singles:
                fully_connected_opt_path_list.extend([
                    oe.contract_expression((A, A, N, N), (A, A, N), (A, A, N)),
                    oe.contract_expression((A, A, N, N), (A, A, N), (A, A, N))
                ])
            if truncation.doubles:
                fully_connected_opt_path_list.append(oe.contract_expression((A, A, N, N), (A, A, N, N)))

        if truncation.at_least_cubic:
            if truncation.singles:
                fully_connected_opt_path_list.extend([
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N), (A, A, N)),
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N), (A, A, N)),
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N), (A, A, N)),
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N), (A, A, N)),
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N), (A, A, N)),
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N), (A, A, N))
                ])
            if truncation.doubles:
                fully_connected_opt_path_list.extend([
                    oe.contract_expression((A, A, N, N, N), (A, A, N), (A, A, N, N)),
                    oe.contract_expression((A, A, N, N, N), (A, A, N, N), (A, A, N))
                ])
            if truncation.triples:
                fully_connected_opt_path_list.append(oe.contract_expression((A, A, N, N, N), (A, A, N, N, N)))
    else:
        raise Exception('Hot Band amplitudes not implemented properly and have not been theoretically verified!')

    return fully_connected_opt_path_list