RIZZ: Role-Indexed Zonal Encoding for Lattice-Faithful Trust in Language Models

Architectural defenses such as ASIDE and ISE give instructions and data distinct representations but only a few fixed roles. Information-flow control (IFC) systems such as FIDES and CaMeL track rich trust labels but never give them to the model. Closing this gap involves embedding the lattice of security labels into the model. We show the natural approach fails: composing ASIDE's rotation cycles back to the identity at tier~4, making the least-trusted tier equivalent to the root authority tier; label combination cannot be realized by composing transformations in any group; and a scalar signal cannot represent incomparable labels. We formally define lattice-faithfulness and propose two parameter-free lattice-faithful encoders (tag-block rotation and tag-subspace encoding) that use $|P|$ independent signals to embed $2^{|P|}$ labels. Experimental results confirm our theoretical results by showing that models trained with the non-lattice-faithful encoder succeed in all and only the tier pairs the algebra says are distinguishable ($\ge 0.997$ mean score) and fail in all and only the other tier pairs ($\approx 0.51$ mean score) regardless of scale ($3\times$) and seed.