Optical number representations (NRs) beyond the common binary radix-2 concept and based on multiple-valued logic (MVL) and redundant NRs (RNRs) are presently restricted to optical free-space techniques. The present paper is an attempt to apply these concepts to lightwave circuits (LWCs). Starting with planar waveguide (WG) devices, capable to provide logic, their extension to 3D and large coupler size is assumed. The attempt to RNR by Wgs is based on two tuning parameters (i) the geometry N >= 3 of the optical architectures and (ii) the degree of repetitive triangularization where (ii) determine the increase of the parallelism dependent on (i). This parallelism is applied for RNR and (i) and (ii) determine (1) the number of couplers (2) the number of additional interconnections and (3) the distribution of the additional interconnections at the couplers. The proposed concept includes the common binary radix-2 logic and the higher radix WG logic is by the organization of the cores of the couplers. The reason for establishing RNR by LWCs is its necessary for minor depth optical WG logic. The large sized couplers, arising y repetitive triangularization, are aimed to be implemented by fibers and the logic circuits by active fiber bundles but the goal of the ongoing work is the photonic integration of the architectures.