What is the significance of GF(3) in this skill?

GF(3) refers to ternary logic (trits: -1, 0, +1). It is used as a conservation law where moves by the Attacker, Defender, and Arbiter must sum to zero (mod 3) to ensure the integrity of the state transition.

What is a bisimulation game in AI development?

It is a formal framework used to determine if two systems are behaviorally equivalent. An 'Attacker' attempts to distinguish the systems through transitions, while a 'Defender' tries to match those moves. If the Defender can always respond, the systems are bisimilar.

Can I use this to compare different AI models?

Yes, it is specifically designed to compare different 'players' (like temporal vs. derivational learning agents) to see if they are behaviorally equivalent within a specific domain.

How does this skill handle synchronization conflicts?

The skill uses a three-dimensional conflict resolution strategy: value conflicts use a source of truth, diff conflicts merge via Lowest Common Ancestor (LCA), and meta-conflicts are decided by a formal Arbiter.

Bisimulation Game

Name: Bisimulation Game
Author: plurigrid

byplurigrid

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Security & Testing

Verifies and synchronizes functional equivalence across AI agent states using formal game theory and coinductive types.

The Bisimulation Game skill provides a sophisticated framework for ensuring resilient skill dispersal and observational equivalence across diverse AI agent environments. By implementing game-theoretic interpretations of Narya coinductive types and GF(3) conservation, it allows developers to verify that different agent implementations or state transitions remain behaviorally indistinguishable. This skill is essential for complex multi-agent systems where maintaining synchronization, resolving state conflicts, and migrating between learning patterns requires formal proof of equivalence rather than simple value comparison.

Key Features

01GF(3) ternary conservation logic for state transition integrity

02Support for self-rewriting capabilities via MCP Tasks protocol

03Formal verification of behavioral indistinguishability between AI systems

04Automated Attacker-Defender game play for system equivalence testing

052 GitHub stars

06Observational bridge types for version-aware synchronization across platforms

Use Cases

01Resolving multi-dimensional state conflicts in decentralized agent networks

02Synchronizing skill states across heterogeneous environments like Claude, Codex, and Cursor

03Verifying behavioral consistency when migrating from temporal to derivational learning patterns

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi bisimulation-game

For use in Claude.ai and ChatGPT

Download Skill