IndisputableMonolith.MaxwellDEC
MaxwellDEC module sets up discrete exterior calculus primitives for electromagnetic modeling on oriented simplices. It introduces abstract simplex identifiers, discrete forms, coboundary and Hodge operators, plus medium and source structures to support Maxwell equation discretization. The module acts as a definition layer feeding energy and admissibility checks downstream in the Recognition framework. No theorems are proved here; structure is purely definitional.
claimDefines the oriented $k$-simplex (abstract identifier), discrete $k$-forms, coboundary operator, Hodge star, medium properties, sources, and the resulting discrete Maxwell equations on a simplicial complex.
background
The module opens the MaxwellDEC namespace by importing Mathlib and declaring sibling definitions for Simplex, DForm, HasCoboundary, HasHodge, Medium, Sources, Equations, energy2, Admissible, energy2_nonneg_pointwise and PEC. The supplied doc-comment identifies the core object as the oriented $k$-simplex treated as an abstract identifier. These pieces assemble a discrete exterior calculus setting in which differential forms, their coboundaries, and Hodge duality can be stated without reference to an ambient manifold.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Supplies the geometric and operator vocabulary required by the sibling Equations and energy2 declarations, allowing discrete Maxwell theory to be embedded inside the Recognition Science derivation that begins from the J-functional equation and the eight-tick octave. The module therefore bridges the continuous-to-discrete step for electromagnetic fields before energy non-negativity and admissibility are checked.
scope and limits
- Does not embed any continuous manifold or metric tensor.
- Does not prove energy non-negativity or admissibility (those live in siblings).
- Does not reference the J-cost, phi-ladder or T5-T8 forcing chain.
- Does not contain numerical discretizations or simulation code.