IndisputableMonolith.ClassicalBridge.Fluids.LNALSemantics
The LNALSemantics module supplies the spatial execution semantics for LNAL voxels in the 2D fluids bridge. It defines one-voxel LNAL steps on (Reg6 × Aux5) states together with maps such as independent and listenNoopProgram that lift the operations to a field. Researchers assembling the discrete 2D Navier-Stokes pipeline cite it as the M2 encoding layer. The module consists entirely of definitions that compose the voxel-level operations imported from the LNAL core and the Galerkin2D truncation.
claimThe module defines the spatial LNAL semantics on the state space of arrays of voxels in $Reg_6 × Aux_5$, equipped with the one-step execution map $voxelStep : Reg_6 × Aux_5 → Reg_6 × Aux_5$ and the spatially independent lift $independent$ that applies the step uniformly across the field.
background
This module occupies the M2 slot in the ClassicalBridge.Fluids hierarchy. It imports the finite-dimensional Galerkin2D model, which supplies a Fourier-mode truncated state space for 2D incompressible Navier-Stokes on the torus together with the algebraic energy identity for the inviscid case. It also imports the LNAL core that defines the single-voxel virtual machine acting on pairs $(Reg_6 × Aux_5)$. The module extends these ingredients to a spatial array of such voxels, furnishing the bridge-local interface for field evolution under LNAL rules.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the LNAL encoding and semantics (M2) required by the top-level composition theorem in Regularity2D, which assembles Galerkin2D (M1), LNAL semantics (M2), one-step simulation (M3), CPM instantiation (M4) and continuum packaging (M5) into an abstract existence result for continuum solutions. It is also imported by Simulation2D to state the one-step simulation bridge between the discrete Galerkin model and the spatial LNAL execution semantics.
scope and limits
- Does not prove analytic correctness of the LNAL simulation against the Navier-Stokes equations.
- Does not address the continuum limit or any regularity statements.
- Does not incorporate viscous dissipation or external forcing terms.
- Does not establish conservation laws beyond those inherited from the imported Galerkin identities.