IndisputableMonolith.ClassicalBridge.Fluids.Regularity2D
This module composes the five-stage bridge from Recognition Science to an abstract 2D global regularity statement. Regularity is represented by the existence of a limit Fourier trajectory u from the reals to FourierState2D together with an identification property. Researchers studying the Navier-Stokes regularity problem inside the Recognition Science framework would cite the module. The module itself contains no proofs and simply assembles the pipeline from the imported milestones.
claimUnder the Recognition Science hypotheses there exists a trajectory $u : ℝ → FourierState_{2D}$ that arises as the continuum limit of the 2D Galerkin approximations and satisfies the packaged identification property.
background
The module sits at the end of a five-milestone pipeline for 2D incompressible Navier-Stokes on the torus. Milestone M1 introduces the finite-dimensional Fourier-mode truncated model, supplying the discrete state space and basic algebraic energy identity. Milestone M2 supplies a minimal spatial semantics for LNAL programs over an LNALField together with an explicit encoding of the Galerkin Fourier state into LNAL voxels. Milestone M3 states the one-step simulation bridge between the discrete Galerkin model and the LNAL execution semantics, packaged as an explicit SimulationHypothesis. Milestone M4 instantiates the CPM core for the Galerkin model while packaging the required analytic inequalities inside a Hypothesis structure. Milestone M5 defines the Lean-checkable pipeline shape from finite-dimensional approximations to the continuum limit object, including the infinite Fourier coefficient state and the canonical embedding of truncated coefficients.
proof idea
This is a definition module, no proofs. It composes the imported stages (Galerkin2D, LNALSemantics, Simulation2D, CPM2D, ContinuumLimit2D) into a single abstract regularity claim.
why it matters in Recognition Science
The module completes the Recognition Science to classical fluids bridge for two dimensions, enabling the implication of global regularity from the RS assumptions via the composed pipeline. It supplies the abstract representation of regularity as a limit Fourier trajectory that downstream theorems can invoke. The construction addresses the abstract identification property without attempting the analytic estimates required for a full fluids proof.
scope and limits
- Does not prove the nontrivial analytic inequalities needed for the fluids argument.
- Does not establish error bounds or convergence rates for the continuum limit.
- Does not connect to the Recognition Science forcing chain or phi-ladder.
- Does not address three-dimensional regularity.
- Does not supply a concrete numerical simulation or physical prediction.
depends on (5)
declarations in this module (10)
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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