What is the significance of GF(3) conservation?

GF(3) conservation is a mathematical invariant used to ensure that the sum of state changes (trits) across a chain or across interleaved streams always balances to zero modulo 3, maintaining internal algebraic equilibrium.

How does the Unworld skill ensure system integrity?

Because every state is the result of a deterministic function (seed_n+1 = f(seed_n, color_n)), any position in the chain can be verified by re-derivation. If the seeds do not match, the chain integrity has been compromised.

Can Unworld be used for game theory or multi-agent logic?

Yes, it includes a Best Response Chain feature that calculates Nash equilibrium via derivational dynamics, ensuring agents reach a stable state where no agent wants to deviate based on the deterministic chain history.

What does it mean to replace time with derivation?

Instead of relying on an external clock or timestamp, each state in an Unworld system is mathematically derived from the previous one using a seed and a trit. This makes the entire sequence immutable, reproducible, and independent of observer-dependent ordering.

Unworld: Derivational Seed Chaining

Name: Unworld: Derivational Seed Chaining
Author: plurigrid

byplurigrid

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개발자 도구

Replaces temporal sequencing with deterministic derivational chains using seed-based state transitions and GF(3) invariants.

소개

Unworld is a specialized logic engine for Claude Code that implements a non-temporal, derivational system based on the concept of a 'topological chemputer.' By replacing external clock-based time with internal seed-chaining, it enables perfectly deterministic state transitions that are verifiable, parallelizable, and frame-invariant. This skill is ideal for developers building high-integrity systems, multi-agent simulations, or cryptographic state machines where every transition must be mathematically derived and provable using GF(3) conservation principles.

주요 기능

Nash equilibrium derivation via best-response dynamics for multi-agent systems
Deterministic seed chaining using golden ratio constants and SplitMix64 multipliers
Triadic chain interleaving for synchronized multi-stream state management
Involution verification to ensure self-inverse forward and backward derivations
GF(3) balanced color chain generation for algebraic state conservation
2 GitHub stars

사용 사례

Designing high-integrity state machines where every transition is mathematically verifiable
Implementing non-temporal simulations for multi-agent systems and game theory applications
Creating deterministic procedural generation systems that require strict algebraic invariants

소개

주요 기능

Nash equilibrium derivation via best-response dynamics for multi-agent systems
Deterministic seed chaining using golden ratio constants and SplitMix64 multipliers
Triadic chain interleaving for synchronized multi-stream state management
Involution verification to ensure self-inverse forward and backward derivations
GF(3) balanced color chain generation for algebraic state conservation
2 GitHub stars

사용 사례

Designing high-integrity state machines where every transition is mathematically verifiable
Implementing non-temporal simulations for multi-agent systems and game theory applications
Creating deterministic procedural generation systems that require strict algebraic invariants