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.本手稿针对Helix–Light–Vortex (HLV) 螺旋时间算子，构建了不可压缩纳维-斯托克斯（Navier–Stokes）方程的保守保结构扩展形式。该构造并非为求解克莱数学千禧年问题而提出，而是定义了一种有效非马尔可夫流体模型：其中相位/涡度通道由斜伴随保散度算子表征，记忆通道则由正型因果卷积核表征。在此假设下，相位通道具备能量中性特性，而记忆通道在积分能量意义下具有耗散性。对于指数衰减核，该模型可等价为局域内时内变量形式，使得记忆区段可兼容标准半群与数值时间步进方法。我们还提出了一种有限维矩阵离散化方案，其中勒雷（Leray）投影、图/斯托克斯算子与相位生成元满足守恒能量平衡的代数恒等式。可选的G格图拉普拉斯后端仅作为可复现的数值离散方案引入，而非额外的物理断言。最后，我们通过确定性Python基准测试，将基线衰减二维涡度动力学与记忆增强模型进行对比，并报告了能量、涡旋拟能、记忆失配以及流体版本的三重相位-记忆不稳定性得分等指标。本框架本质上可被视为一种可证伪的湍流记忆与流态诊断框架，而非对原始纳维-斯托克斯方程全局正则性的证明。