RIG-RoPE: Relation-Stratified Multimodal Attention with Instance-Local Rotary Geometry and Representation-Aware Traversal Coordinates

Multimodal rotary positional encodings apply temporal, height, and width phases to interleaved text, image, and video tokens. This creates two ambiguities: cross-instance spatial displacement depends on preprocessing chart choices unless registration is declared, and scalar advance across visual blocks is often inherited from coordinate extrema rather than defined at the representation level. We introduce RIG-RoPE, combining instance-local rotary geometry, relation-stratified attention, and representation-aware traversal coordinates. RIG-RoPE normalizes relation-homogeneous scores separately, allocates mass with a common H/W-neutral LogSumExp statistic, and uses traversal extent that is additive over ordered slices and sublinear over parallel spatial scale. Text advances by unit increments, image patches are simultaneous, and video accumulates over tokenizer temporal tokens. In a matched, inference-only Qwen2-VL-2B checkpoint experiment, native and RIG text-only paths were exactly equal. RIG was exactly invariant to a whole-chart single-image translation and to translating only the second instance of an unregistered image pair. Native attention remained sensitive to the latter, while an H/W-collapse control confirmed that RIG retained same-instance spatial effects; visual embeddings and all parameters were unchanged. Across three seeds of a frozen tiny task, RIG also had zero clean-to-Gauge logit change, whereas the raw-H/W baseline changed in every seed. Gauge-accuracy differences were +2/72, 0, and 0, failing the preregistered stability gate. These results support the specified activation and Gauge mechanisms, not stable task improvement, universality, or empirical superiority.