tripartite-decompositions

GF(3)-balanced decomposition splits problems into three labeled components—MINUS, ERGODIC, and PLUS—using random walk seeding and trit labeling (-1, 0, +1). The Skill enforces GF(3) conservation across adhesions, ensuring the sum of trits equals 0 modulo 3 for consistent parallel computation.

GF(3) conservation guarantees that decomposed workloads maintain algebraic balance across all three triplet components. This constraint enables fixed-parameter tractable algorithms and ensures triadic workload allocation remains consistent through problem lifting via the D-functor and sheaf-based gluing.

Yes. The Skill applies directly to FPT algorithms by decomposing problems into GF(3)-balanced triplets with structured adhesions and sheaf-theoretic gluing, supporting both entropy-aware seeding and trit labeling across parallel workloads.

Assign trits (-1, 0, +1) to each component in your triplet, then confirm the sum equals 0 modulo 3. The Skill's random_walk_3(seed) decomposition automatically enforces this invariant across all adhesions during composition.

Items must have assigned trits (-1, 0, +1) before running random_walk_3(seed). The Skill accepts entropy-aware seeding and produces three labeled bags (MINUS, ERGODIC, PLUS) with verified GF(3) conservation and sheaf-based gluing for problem lifting.