IndisputableMonolith.Mathematics.NavierStokesRegimes
The module defines flow regime classifications and Reynolds number thresholds for the Navier-Stokes equations inside Recognition Science. Fluid dynamicists working in RS-native units would cite it to locate laminar-turbulent transitions on the phi-ladder. The module consists entirely of definitions and short supporting lemmas with no proof obligations.
claimIntroduces an enumeration of fluid flow regimes, a count of those regimes, a threshold function mapping each regime to a real Reynolds number, the associated ratio and positivity statements, and a certification object for the Navier-Stokes regimes.
background
The module sits in the mathematics layer and imports only the RS time quantum τ₀ = 1 tick from Constants together with Mathlib. It supplies the concrete objects needed to classify incompressible flows once the Reynolds number has been expressed in phi-ladder units. The surrounding Recognition Science setting treats fluid motion as a discrete process whose energy cost is measured by the J-functional and whose length scales are fixed by the eight-tick octave.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the regime classification layer that later fluid-dynamics results in Recognition Science are expected to invoke. It directly encodes the thresholds that arise from the phi-ladder and the RS constants, thereby closing the interface between the abstract forcing chain and concrete Navier-Stokes analysis. No downstream uses are recorded yet.
scope and limits
- Does not derive the Navier-Stokes equations from the Recognition functional equation.
- Does not prove existence or uniqueness of solutions in any regime.
- Does not treat compressible flows or relativistic corrections.
- Does not encode boundary conditions or forcing terms.