Potentialist State Machines

The deepest concept: a contract is not a fixed labeled transition system — it's one actualization from a space of potential labeled transition systems.

The Insight

When Alice and Bob start a contract:

1. Potential is infinite — Any labeled transition system is possible
2. Alice adds a rule — Potential shrinks to labeled transition systems satisfying her rule
3. Bob adds a rule — Potential shrinks further
4. Rules accumulate — The space of valid futures only contracts, never expands

The Monotonicity Theorem

Adding a covenant (rule) can only shrink the space of valid extensions, never expand it.

This is why Modality contracts are safe: each party adds their protection, and no one can add a rule that invalidates existing protections.

Visualizing Potential

Initial: All possible labeled transition systems
    │
    ▼
┌─────────────────────────────────┐
│  ∞ potential machines           │
│                                 │
│  Alice's rule: "always safe"    │
│           │                     │
│           ▼                     │
│  ┌─────────────────────────┐    │
│  │ Smaller set satisfying   │   │
│  │ Alice's constraint       │   │
│  │                          │   │
│  │  Bob's rule: "fair"      │   │
│  │         │                │   │
│  │         ▼                │   │
│  │  ┌─────────────────┐     │   │
│  │  │ Even smaller set │    │   │
│  │  │ satisfying both  │    │   │
│  │  └─────────────────┘     │   │
│  └─────────────────────────┘    │
└─────────────────────────────────┘

Why This Matters

Traditional contracts are static: you agree to terms, and that's it.

Modality contracts are dynamic:

• Start with nothing
• Each party adds their protections
• The contract evolves within the constrained space
• No party can violate accumulated protections

This is ideal for agent cooperation where trust must be established incrementally through verifiable commitments, not assumed upfront.

Further Reading

See the Potentialist LTS Paper for the formal treatment.