What is a derangement in the context of this CRDT?

A derangement is a permutation where no element maps to itself. In this skill, it ensures that every state update results in a move, preventing 'fixed points' where data remains stagnant during a transformation.

When should I use Derangement-CRDT over a standard CRDT?

Use this skill when your distributed system requires strict invariants regarding state movement, such as in cryptographic protocols, complex terminal synchronizations, or topological simulations where static states are invalid.

Does this skill support multi-replica conflict resolution?

Yes, it uses a Join-Semilattice approach with Lamport timestamps to resolve conflicts during merges while re-verifying the derangement and coloring properties.

How does GF(3) coloring ensure state conservation?

Cycles within the derangement are assigned 'trits' based on their length modulo 3. The skill enforces a conservation law where the sum of these trits must equal zero (mod 3), ensuring mathematical balance across distributed replicas.

Derangement CRDT & Topological State

Name: Derangement CRDT & Topological State
Author: plurigrid

byplurigrid

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Database Management

Enforces no-fixed-point permutations and GF(3) color conservation within distributed CRDT state transitions.

The Derangement-CRDT skill provides a specialized mathematical framework for managing distributed state transformations where identity mappings are strictly forbidden. By combining the properties of derangements (permutations with no fixed points) with Conflict-free Replicated Data Types (CRDTs), it ensures that every state update represents a genuine transformation. Utilizing a join-semilattice structure and GF(3) triadic coloring, the skill maintains a strict conservation law across cycle-decomposed states, making it an essential tool for high-entropy distributed systems, secure state lattices, and topological modeling in Claude Code.

Key Features

01Subfactorial mathematical validation of state space density

02Join-semilattice merge operations ensuring eventual consistency

03GF(3) triadic coloring (Ergodic, Plus, Minus) for state balance

042 GitHub stars

05Automatic enforcement of the derangement property (no fixed points)

06Cross-language implementation patterns for Babashka, Ruby, and Julia

Use Cases

01Managing distributed state transitions where identity mappings represent security risks

02Synchronizing terminal session buffers using cycle-based transformations

03Topological simulations requiring balanced cycle decompositions and conservation laws

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi derangement-crdt

For use in Claude.ai and ChatGPT

Download Skill