IndisputableMonolith.ClassicalBridge.Fluids.Regularity2D
The module composes the five-stage bridge from Recognition Science to an abstract global regularity statement for 2D Navier-Stokes on the torus. Researchers tracing the RS forcing chain into classical PDEs would cite the pipeline structure. The module defines regularity via existence of a limit Fourier trajectory together with its identification property, assembling hypotheses from prior milestones without proving analytic estimates.
claimExistence of a trajectory \( u : \mathbb{R} \to \text{FourierState}_{2D} \) satisfying the packaged identification property obtained by composing the Galerkin, LNAL, simulation, CPM, and continuum-limit stages.
background
The module sits at the terminus of the ClassicalBridge.Fluids pipeline. It imports five upstream milestone modules whose roles are fixed by their own documentation. Galerkin2D supplies the finite-dimensional Fourier-truncated model for 2D incompressible Navier-Stokes together with its basic energy identity. LNALSemantics encodes that state into an LNALField and supplies the independent spatial semantics. Simulation2D states the one-step bridge as an explicit SimulationHypothesis. CPM2D instantiates the CPM core for the Galerkin model while packaging all nontrivial analytic inequalities inside a Hypothesis structure. ContinuumLimit2D defines the canonical embedding of truncated coefficients into the infinite Fourier state and the shape of the passage to a continuum limit object.
proof idea
This is a definition module, no proofs. Its structure is the sequential import and composition of the five milestone modules, followed by the declaration of the composite regularity object and the family of rs_implies_global_regularity_2d theorems that expose the required hypotheses.
why it matters in Recognition Science
The module feeds the sibling declarations rs_implies_global_regularity_2d, rs_implies_global_regularity_2d_coeffBound and their variants. It completes the explicit bridge from the Recognition Science forcing chain (T0-T8, RCL) to an abstract 2D regularity result, keeping every analytic hypothesis visible rather than hidden behind axioms.
scope and limits
- Does not prove any analytic inequalities needed for the continuum limit.
- Does not address three spatial dimensions.
- Does not verify physical correctness of the LNAL encoding.
- Does not supply numerical simulation output or convergence rates.
- Does not close the hypotheses; they remain explicit interfaces.
depends on (5)
declarations in this module (10)
-
structure
RSNS2DPipelineHypothesis -
theorem
rs_implies_global_regularity_2d -
theorem
rs_implies_global_regularity_2d_coeffBound -
theorem
rs_implies_global_regularity_2d_divFreeCoeffBound -
theorem
rs_implies_global_regularity_2d_stokesMildCoeffBound -
theorem
rs_implies_global_regularity_2d_stokesODECoeffBound -
theorem
rs_implies_global_regularity_2d_nsDuhamelCoeffBound -
theorem
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel -
theorem
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcing -
theorem
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcingHyp