Auditing Neural-Torus Preservation in Quantum Reservoirs: Geometry, Topology, and Input Accessibility

Apparent preservation of a neural manifold can mean at least four distinct things: reproducing its native geometry, making the source geometry linearly decodable, retaining its topology, or preserving temporal correspondence. We introduce an audit that separates these notions using grid-cell population activity, whose two-dimensional torus provides an experimentally validated reference. We re-establish this torus in nine session–modules from three rats using pure grid cells, joint $H_1+H_2$ persistent homology, and 199 cell-wise circular-shift nulls; every session exceeds both null thresholds (empirical $p=.005$). We then evaluate a dual-branch collision quantum reservoir computer (QRC) that exposes 210 one- and two-body Pauli features. Its held-out decoded RDM similarity is $.9977$, but a six-PC delay embedding reaches $.9964$ despite having substantially poorer native geometry ($.1293$ versus $.4567$). Near-perfect decoded correspondence can therefore largely reflect source recoverability rather than adoption of the source metric. Model-specific tests detect a torus in five of six QRC modules and six of six matched echo-state-network modules; temporal-correspondence controls pass for both. The dual QRC exceeds the ESN in decoded RDM for all six modules ($.9977$ versus $.9469$), but with $n=6$ the retained exact two-sided test cannot attain significance across the four-test Holm family ($p_{\mathrm{raw}}=.0313$, $p_{\mathrm{Holm}}=.125$). No adjusted primary or exploratory contrast is significant. The central result is a decomposition, not a leaderboard: native geometry, decodability, topology, and temporal correspondence are complementary and non-substitutable notions of preservation.