IndisputableMonolith.Mathematics.PartialDifferentialEquationsFromRS
The module Mathematics.PartialDifferentialEquationsFromRS defines the type classification and certification objects for partial differential equations that arise inside the Recognition Science framework. Researchers formalizing the continuum limit of the phi-ladder and J-cost structures would reference these definitions when extending discrete RS results to field equations. The module is purely definitional and contains no proofs.
claimThe module defines $\mathsf{PDEType}$ as the classification of partial differential equations obtained from RS and $\mathsf{PartialDifferentialEquationsCert}$ as the associated certification predicate, together with the counting function $\mathsf{pdeTypeCount}$.
background
Recognition Science builds discrete structures from the J-uniqueness relation and the Recognition Composition Law before taking continuum limits. This module supplies the interface layer that classifies the resulting partial differential equations and certifies their origin inside the framework. It imports only Mathlib and exposes the sibling objects PDEType, pdeTypeCount, PartialDifferentialEquationsCert and partialDifferentialEquationsCert.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the PDEType and certification objects required by any parent theorem that derives continuum field equations from the T0-T8 forcing chain or the eight-tick octave. It closes the definitional gap between the discrete phi-ladder and the partial differential equations that appear in the D=3 spatial setting.
scope and limits
- Does not derive or name any concrete PDE such as the wave or heat equation.
- Does not prove existence or uniqueness of solutions.
- Does not connect the defined types to specific physical constants or the alpha band.
- Does not contain numerical schemes or simulation code.