IndisputableMonolith.Physics.HydrodynamicsFromRS
This module sets up hydrodynamics inside Recognition Science by classifying flow regimes and anchoring uniform laminar flow at J=0. Researchers deriving fluid equations from the J-functional and Recognition Composition Law would cite it for the base case. It consists of type definitions for FlowRegime, laminar equilibrium, turbulent cost, and HydrodynamicsCert, all built on the imported Cost module.
claimUniform laminar flow satisfies $J=0$, where $J(x)= (x + x^{-1})/2 -1$. FlowRegime enumerates laminar and turbulent states; laminar equilibrium is the zero-cost case and turbulent cost is the positive J-value on the phi-ladder.
background
Recognition Science derives physics from the single J-functional obeying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The module imports IndisputableMonolith.Cost, which supplies the definition of J and its basic properties. It introduces FlowRegime as an inductive type distinguishing flow states, laminar_equilibrium as the state with vanishing J, and turbulent_cost as the positive defect measure.
proof idea
This is a definition module, no proofs. It declares the FlowRegime type, the count function, the laminar equilibrium predicate as J=0, the turbulent cost expression, the HydrodynamicsCert structure, and the hydrodynamicsCert instance.
why it matters in Recognition Science
The module supplies the hydrodynamics layer that connects the T5 J-uniqueness and T7 eight-tick octave to macroscopic fluid behavior. It feeds the HydrodynamicsCert that certifies consistency with D=3 and the alpha band. The J=0 laminar base case is the starting point for any later derivation of flow equations from the Recognition framework.
scope and limits
- Does not derive the Navier-Stokes equations.
- Does not incorporate viscosity or boundary layers.
- Does not treat compressible or relativistic flows.
- Does not provide numerical or simulation results.