IndisputableMonolith.ClassicalBridge.Fluids.Discrete
This module defines the discrete parameters and model types for incompressible Navier-Stokes in the Recognition Science setting. It supplies NSParams for dimension and viscosity together with DiscreteModel, TimeStep, DiscretizationKind and EnergyFunctional. These objects are consumed by the Bridge module that outlines the full RS-to-NS interface. The module contains only definitions and imports Mathlib.
claimThe module introduces $NSParams$ (dimension and viscosity pair), $DiscreteModel$ (discrete state evolution for incompressible flow), $EnergyFunctional$, $TimeStep$ and $DiscretizationKind$.
background
The module resides in the ClassicalBridge.Fluids namespace and supplies the discrete approximation side of the Navier-Stokes bridge. NSParams encodes the spatial dimension together with the viscosity coefficient for incompressible flow. Sibling declarations define TimeStep for temporal stepping, DiscretizationKind for spatial schemes, DiscreteModel as the core evolution operator, and EnergyFunctional as the associated energy norm. The module imports only Mathlib and introduces no Recognition Science axioms.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies DiscreteModel and NSParams that the Bridge module requires for its RS ↔ Navier–Stokes interface specification. It therefore populates the first item in the four-point list given in the Bridge doc-comment: a discrete NS approximation.
scope and limits
- Does not contain theorems or proofs.
- Does not import core Recognition Science modules.
- Does not define the LNAL encoding or simulation relation.
- Does not instantiate CPM on discrete states.