IndisputableMonolith.Physics.YangMillsLatticeFromRS
This module constructs the Yang-Mills sector on a lattice from Recognition Science by importing the J-cost framework. It defines the vacuum state as J=0, which corresponds to the ground state carrying a mass gap. Lattice gauge theorists would cite the definitions to embed Yang-Mills dynamics inside the RS forcing chain. The module supplies a collection of definitions and basic certificates with no internal proofs.
claimThe Yang-Mills sector is equipped with vacuum state satisfying $J=0$, yielding the lattice mass gap ground state; auxiliary objects include sector count, vacuum uniqueness, and gap certificates.
background
Recognition Science derives all physics from the single J-cost functional obeying the composition law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. The imported Cost module supplies this functional together with the phi-ladder and defect distance. This module applies those primitives to lattice gauge theory, introducing YMSector, ymSectorCount, ym_vacuum, ym_lattice_gap, and the certificate YMLatticeGapCert.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the lattice Yang-Mills construction that supports later derivations of gauge-theory mass gaps inside Recognition Science. It directly instantiates the J-uniqueness step (T5) and the three-dimensional spatial setting (T8) from the unified forcing chain. No downstream theorems are recorded yet.
scope and limits
- Does not derive the continuum limit of Yang-Mills theory.
- Does not compute explicit numerical values for the mass gap.
- Does not treat non-Abelian structure constants or instantons.
- Does not incorporate matter fields or fermions.