A Pre-Registered Null-Model Benchmark for HLV-Constrained Memory Kernels in Finite-Dimensional Vorticity Dynamics Comparing Spiral-Time Kernels Against Generic Positive Convolution Baselines

A previous structure-preserving HLV–Navier–Stokes memory formulation showed that a skew-adjoint phase channel and a positive-type causal memory kernel can be inserted into an incompressible-flow setting without directly violating kinetic-energy balance. That result, however, does not establish that an HLV-constrained memory kernel produces predic- tive signatures that cannot also be produced by a generic positive convolution kernel. The present manuscript addresses this limitation by defining a pre-registered null-model bench- mark. We compare four finite-dimensional model classes: a no-memory damping baseline, a single-exponential positive memory kernel, an HLV-constrained positive two-mode kernel, and a generic positive two-exponential kernel. The comparison uses fixed train/test regime splits, held-out trajectory error, information criteria, bootstrap confidence intervals for rel- ative predictive advantage, and an explicit non-overclaim rule. In a controlled synthetic benchmark generated from the HLV-constrained family, the constrained kernel outperforms damping and single-exponential nulls. However, a sufficiently flexible generic positive two- exponential kernel becomes statistically indistinguishable from the HLV-constrained model. The result is deliberately conservative: it demonstrates a falsification-ready comparison protocol and shows that HLV-specific claims require predictive advantage against matched generic positive-kernel baselines, not only against simple damping or single-kernel nulls.