A Structure-Preserving Spiral-Time Memory Extension of Incompressible Navier–Stokes Dynamics Effective HLV Couplings, Energy Balance, Matrix Discretization, and Reproducible Falsification Tests

This manuscript formulates a conservative, structure-preserving extension of the incompressible Navier–Stokes equations motivated by the Helix–Light–Vortex (HLV) spiral-time operator. The construction is not proposed as a solution of the Clay Millennium problem. Instead, it defines an effective non-Markovian fluid model in which a phase/vorticity channel is represented by a skew-adjoint divergence-preserving operator and a memory channel is represented by a positive-type causal convolution kernel. Under these hypotheses, the phase channel is energy-neutral, while the memory channel is dissipative in an integrated energy sense. For exponentially decaying kernels, the model admits an equivalent local-in-time internal-variable formulation, making the memory sector compatible with standard semigroup and numerical time-stepping methods. We also provide a finite-dimensional matrix discretization in which the Leray projection, graph/Stokes operator, and phase generator satisfy algebraic identities that preserve the energy balance. An optional G-lattice graphLaplacian backend is introduced only as a reproducible numerical discretization, not as an additional physical claim. Finally, a deterministic Python benchmark compares baseline decaying two-dimensional vorticity dynamics against the memory-augmented model and reports energy, enstrophy, memory mismatch, and a fluid version of the triadic phase-memory instability score. The resulting framework is best interpreted as a falsifiable turbulencememory and regime-diagnostic scaffold, not as a proof of global regularity for the original Navier–Stokes equations.