tripartite-decompositions

npx skills add majiayu000/claude-skill-registry --skill tripartite-decompositions --agent claude-code

Same command for any agent — swap --agent for codex, cursor, copilot.

# Tripartite Decompositions **Trit**: 0 (ERGODIC - coordinates decomposition) **Foundation**: StructuredDecompositions.jl + GF(3) conservation **Principle**: Every problem decomposes into 3 parts summing to 0 mod 3 ## Core Concept A **tripartite decomposition** is a structured decomposition where: 1. The decomposition shape is a 3-clique (triangle) 2. Each bag is labeled with a trit ∈ {-1, 0, +1} 3. Adhesions preserve GF(3) conservation: Σ trits ≡ 0 (mod 3) ``` MINUS (-1) ╱╲ ╱ ╲ ╱ ╲ ╱ ⊗ ╲ ╱________╲ ERGODIC (0) PLUS (+1) Conservation: (-1) + 0 + (+1) = 0 ✓ ``` ## Mathematical Foundation ### From StructuredDecompositions.jl ```julia # A structured decomposition is a diagram d: ∫G → Span(C) # where G is the decomposition shape and C is the target category abstract type StructuredDecomposition{G, C, D} <: Diagram{id, C, D} end struct StrDecomp{G, C, D} <: StructuredDecomposition{G, C, D} decomp_shape ::G # The shape (for tripartite: K₃) diagram ::D # The actual decomposition functor decomp_type ::DecompType # Decomposition or CoDecomposition domain ::C # Source category end ``` ### Tripartite Extension ```julia using StructuredDecompositions using Catlab # Define the tripartite shape:

Verify a tripartite decomposition
function verify_tripartite(decomp)
bags = [bag(decomp, :Minus), bag(decomp, :Ergodic), bag(decomp, :Plus)]
trits = [b.trit for b in bags]
return true
end