IndisputableMonolith.ClassicalBridge.Fluids.LNALSemantics
This module defines the LNAL spatial semantics for the 2D fluids bridge, centering on one-voxel execution of a single LNAL step applied to (Reg6 × Aux5) states together with supporting encoding and independence functions. Researchers assembling the discrete Navier-Stokes pipeline cite it as the M2 interface layer imported by Simulation2D and Regularity2D. The module consists entirely of definitions with no theorems or proofs.
claimvoxelStep : (Reg_6 × Aux_5) → (Reg_6 × Aux_5) implements one LNAL step on a voxel; independent : array of voxels → array of voxels applies the step uniformly across the spatial field.
background
The module sits inside the ClassicalBridge.Fluids layer and imports the single-voxel LNAL VM together with the finite-dimensional Galerkin2D model of 2D incompressible Navier-Stokes on the torus. LNAL supplies the core (Reg6 × Aux5) voxel type; Galerkin2D supplies the truncated Fourier-mode state space. The supplied LNAL doc states that the file defines a minimal bridge-local interface whose spatial state is an array of (Reg6 × Aux5) voxels.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the LNAL semantics required by Simulation2D (M3), which packages the one-step simulation hypothesis, and by Regularity2D (M6), which states the top-level composition theorem for the full 2D pipeline: Galerkin2D (M1) + LNAL encoding/semantics (M2) + one-step simulation (M3) + CPM instantiation (M4) + continuum limit packaging (M5).
scope and limits
- Does not prove correctness of the encoded simulation against the continuum equations.
- Does not contain the continuum-limit argument.
- Does not introduce viscosity, forcing, or boundary conditions.
- Does not address three-dimensional or compressible extensions.