IndisputableMonolith.Mathematics.PartialDifferentialEquationsFromRS
This module defines the foundational types and certification objects for partial differential equations derived from Recognition Science. It introduces PDEType for classification, pdeTypeCount for enumeration, and PartialDifferentialEquationsCert as the certifying structure. The module is definition-only and prepares the PDE layer on top of the core J-functional and forcing chain.
claimDeclares the inductive type $PDEType$ classifying partial differential equation families, the function $pdeTypeCount : ℕ$ giving their count, and the structure $PartialDifferentialEquationsCert$ certifying that such equations arise from the Recognition Composition Law and phi-ladder.
background
Recognition Science starts from the single functional equation whose J-cost satisfies the composition law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. This module sits in the Mathematics domain, imports Mathlib, and introduces the sibling definitions PDEType, pdeTypeCount, PartialDifferentialEquationsCert, and partialDifferentialEquationsCert to organize continuum descriptions built from the eight-tick octave and D = 3.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the PDE interface that later physics derivations rely on to connect the T5–T8 forcing chain to field equations. It supports the step from the core RS axioms to continuum limits while remaining inside the phi-ladder and RS-native constants.
scope and limits
- Does not derive or prove any concrete PDE such as the wave or Dirac equation.
- Does not contain numerical methods or solvers.
- Does not link PDEs to experimental observables beyond RS units.