Topological Superintelligence (TSI)

Compositional AI framework using GF(3) triadic balance and category-theoretic foundations.

Core Principle

Every operation balances trits {-1, 0, +1}:

inject(+1) + bridge(0) + emit(-1) ≡ 0 (mod 3)

Tripartite Agent Architecture

Agent	Trit	Role	Color
PLUS	+1	Generation, creation, synthesis	#FF6B6B
ERGODIC	0	Coordination, balance, infrastructure	#4ECDC4
MINUS	-1	Verification, validation, analysis	#45B7D1

Skill Categories

PLUS Skills (+1)

• gay-mcp - Deterministic color generation with SplitMix64
• triad-interleave - Balanced schedule interleaving
• world-hopping - Badiou-inspired world navigation
• crdt-vterm - Collaborative terminal sharing
• agent-o-rama - Learning and pattern extraction

ERGODIC Skills (0)

• skill-dispatch - GF(3) triadic task routing
• unwiring-arena - Autopoietic closure
• acsets-algebraic-databases - Category-theoretic data
• autopoiesis - Self-modifying agent configuration
• cognitive-surrogate - Cognitive modeling
• entropy-sequencer - Information gain optimization

MINUS Skills (-1)

• bisimulation-game - Attacker/Defender verification
• spi-parallel-verify - Strong Parallelism Invariance
• bafishka - Shell operations verification
• influence-propagation - Network analysis

Mathematical Foundation

The bicomodule framework:

c (Control/Semantics)     ← High-level reasoning
↕ σ (effect handler)
m (Interface/State)       ← Middle layer
↕ ε (counit), δ (comult)
d (Data/Matter)           ← Low-level execution

Key law: ε ∘ δ = id  (interpretability criterion)

Usage

Install via Claude Code marketplace:

claude plugin marketplace add plurigrid/asi
claude plugin install plurigrid@asi

Strong Parallelism Invariance (SPI)

Canonical seed: 0xf061ebbc2ca74d78

Same seed produces identical sequences across all implementations (15+ languages verified).