IndisputableMonolith.ClassicalBridge.Fluids.Regularity2D
This module composes the five upstream milestones into a single pipeline that derives an abstract global regularity statement for 2D incompressible Navier-Stokes from Recognition Science assumptions. A researcher working on the Millennium problem or on RS-derived fluid models would cite the main theorem rs_implies_global_regularity_2d. The module itself contains no proofs; it simply assembles the packaged hypotheses from Galerkin2D through ContinuumLimit2D into the existence of a limit Fourier trajectory.
claimUnder the Recognition Science axioms there exists a limit Fourier trajectory $u : ℝ → FourierState2D$ together with the packaged identification property that realizes the continuum limit of the 2D Galerkin approximations.
background
The module sits at the top of the ClassicalBridge.Fluids hierarchy and imports five milestone files. Galerkin2D (M1) supplies the finite-dimensional Fourier-mode truncated model on the torus together with its algebraic energy identity. LNALSemantics (M2) gives the minimal spatial semantics for LNAL programs and the encoding of the Galerkin state into LNAL voxels. Simulation2D (M3) states the one-step simulation bridge between the discrete model and the LNAL execution semantics. CPM2D (M4) instantiates the CPM core for the Galerkin model while packaging all nontrivial analytic inequalities as explicit hypotheses. ContinuumLimit2D (M5) defines the Lean-checkable pipeline shape that embeds truncated coefficients into the infinite Fourier state and produces the continuum limit object.
proof idea
This is a definition module with no internal proofs. It composes the upstream milestones by importing their hypothesis structures and then states the top-level regularity claim together with a family of coefficient-bound lemmas that make the packaged hypotheses explicit.
why it matters in Recognition Science
The module supplies the top-level statement that Recognition Science implies abstract global regularity in 2D fluids, exactly as described in its doc-comment: “RS → (abstract) global regularity in 2D, via the composed bridge pipeline.” It feeds the regularity claim represented by the existence of a limit Fourier trajectory u : ℝ → FourierState2D with the packaged identification property. The module closes the discrete-to-continuum pipeline while leaving the analytic inequalities as named hypotheses for later discharge.
scope and limits
- Does not prove any analytic inequalities; these remain explicit hypotheses.
- Does not treat the 3D Navier-Stokes regularity problem.
- Does not include numerical simulation runs or validation data.
- Does not derive the explicit form of the limit trajectory beyond existence and identification.
- Does not connect to the full Recognition Science forcing chain or phi-ladder constants.
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