Topological Superintelligence (TSI)

# 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:

```bash
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).