IndisputableMonolith.ClassicalBridge.Fluids.LNAL
The LNAL module supplies a minimal interface for spatial execution of LNAL programs over a field of voxels. Researchers building discrete fluid models in Recognition Science cite it when linking LNAL to continuum approximations. The module introduces LNALField as an array of voxel states along with SpatialSemantics and a run function, serving purely as scaffolding with no theorems.
claimDefines LNALField as an array of voxel states (Reg6 × Aux5) together with SpatialSemantics for executing an LNAL program over the field and a run function realizing the spatial semantics.
background
The module resides in the ClassicalBridge.Fluids domain and imports the LNAL virtual machine. It defines LNALVoxel and LNALField as the basic spatial units, with LNALField realized concretely as Array (Reg6 × Aux5). SpatialSemantics supplies the execution rules and run applies them to a program. The setting is deliberately minimal, omitting neighbor graphs and inter-voxel coupling as stated in the downstream LNALSemantics documentation.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the RS ↔ Navier–Stokes Bridge interface, which requires a discrete NS approximation, LNAL spatial semantics, an encoding of Galerkin2D states, and a simulation statement. It also supplies the spatial layer for the LNALSemantics milestone. This component closes the spatial-execution gap needed to relate LNAL programs to continuum fluid models inside the Recognition framework.
scope and limits
- Does not implement neighbor graphs or inter-voxel coupling.
- Does not supply a simulation statement relating LNAL execution to a discrete Navier–Stokes model.
- Does not include CPM instantiation on the discrete state.