HCC+: Hyperbolic Guarding for Certified Attention Retrieval

We study the Lipschitz stability of attention retrieval in hyperbolic spaces. Existing methods lack deterministic guarantees on attention-weight preservation under finite-precision representations. We introduce HCC+, a theoretical framework exploiting three properties of the Poincar'e ball: exponential volume growth enabling query-independent boundary truncation; logarithmic covering radius of hyperbolic 1-centers enabling dimension-independent critical-key identification; and a packing bound with constants independent of the embedding dimension. We prove two deterministic guarantees: for exact retrieval, the per-layer attention deviation is bounded by 10% of its ideal value; for soft attention, the total variation distance decays as O(1/√n), the rate of finite-sample variance. As a consequence of the guarding mechanism, the framework achieves a storage reduction factor of 6.1× relative to FP16. We provide the first deterministic, query-independent retrieval certificate in non-Euclidean geometry.