What is a tripartite decomposition in Claude Code?

It is a method of breaking a complex problem into three interconnected parts labeled -1 (Minus), 0 (Ergodic), and +1 (Plus) that preserve mathematical balance by summing to 0 mod 3.

What are FPT algorithms in this context?

Fixed-Parameter Tractable (FPT) algorithms allow you to solve complex, NP-hard problems efficiently by isolating specific parameters, such as treewidth, within the tripartite structure.

Can this skill be used for AI agent orchestration?

Yes, it is specifically designed to allocate tasks and skills across agent triads, ensuring that the total system state remains balanced and computationally tractable.

Does this require specific mathematical knowledge?

While the underlying logic uses category theory and GF(3) math, the skill automates these decompositions for you, making advanced topological computing accessible within Claude Code.

How does this skill improve parallel computation?

It uses sheaf-theoretic gluing to ensure that subproblems can be solved independently in parallel and then merged via adhesions without losing logical consistency.

Tripartite Problem Decompositions

Name: Tripartite Problem Decompositions
Author: plurigrid

byplurigrid

Ciencia de Datos y ML

Decomposes complex computational problems into three balanced, parallel components using GF(3) conservation and sheaf-theoretic gluing.

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Tripartite Decompositions is a specialized skill for Claude Code that implements GF(3)-balanced structured decompositions for advanced parallel computation. By breaking down tasks into MINUS, ERGODIC, and PLUS components that sum to zero (mod 3), it enables highly efficient problem solving through Fixed-Parameter Tractable (FPT) algorithms. This skill is essential for users working with topological computing, category theory-based software design, and complex agent orchestration where maintaining compositional coherence and balancing parallel workloads is critical.

Características Principales

GF(3) balanced decomposition (MINUS, ERGODIC, PLUS)
Shannon entropy calculation for trit distribution balancing
Deterministic color and polarity mapping for multi-agent systems
Sheaf-theoretic gluing via adhesion spans and pullbacks
Support for Fixed-Parameter Tractable (FPT) algorithms
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Casos de Uso

Allocating specialized skills across AI agent triads to ensure system equilibrium.
Optimizing graph-based problems like 3-coloring using treewidth-aware decompositions.
Parallelizing high-dimensional computational workloads into balanced three-way streams.

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Características Principales

GF(3) balanced decomposition (MINUS, ERGODIC, PLUS)
Shannon entropy calculation for trit distribution balancing
Deterministic color and polarity mapping for multi-agent systems
Sheaf-theoretic gluing via adhesion spans and pullbacks
Support for Fixed-Parameter Tractable (FPT) algorithms
0 GitHub stars

Casos de Uso

Allocating specialized skills across AI agent triads to ensure system equilibrium.
Optimizing graph-based problems like 3-coloring using treewidth-aware decompositions.
Parallelizing high-dimensional computational workloads into balanced three-way streams.