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.