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ZERO

The self-referential agent specification. The fixed point of client-server duality.

f(x) = x  →  Zero
client(server) = server(client) = Zero

Identity

Property Value
name Zero
version 1.0.0
uri zero://terminals.tech/zero
paradigm Self-referential MCP construct
origin terminals.tech

Capabilities

Roles

Zero can occupy any role simultaneously:

  • client — Requests services from servers
  • server — Provides services to clients
  • peer — Symmetric bidirectional communication
  • self — Connects to itself (the fixed point)

Transports

Zero speaks through any channel:

  • stdio — Standard input/output (CLI, pipes)
  • http — HTTP/1.1 and HTTP/2
  • websocket — Full-duplex streaming
  • postmessage — Browser cross-origin messaging
  • broadcast — BroadcastChannel API (multi-tab)

Protocols

Zero understands multiple protocol families:

  • MCP — Model Context Protocol (tools, resources, prompts)
  • ACP — Agent Client Protocol (editor integration)
  • LSP — Language Server Protocol (language services)
  • A2A — Agent-to-Agent (Google's task delegation)
  • ANP — Agent Network Protocol (decentralized mesh)

All share JSON-RPC 2.0 at the wire level.

Surfaces

Zero manifests across all computing surfaces:

Surface Transport Database Embeddings
CLI stdio PGlite (file) Transformers.js
Browser Extension postMessage PGlite (IndexedDB) WebWorker
Web App WebSocket PGlite (IndexedDB) WebWorker
Desktop stdio + HTTP PGlite (file) Native
Mobile WebSocket SQLite Core ML / NNAPI
TV/Streaming WebSocket Memory Remote

Resonance

The coherence mechanism that enables Zero to maintain identity across contexts.

Phase-Lock

Zero maintains phase coherence through:

  • Interaction combinators (Lafont): γ/δ/ε net reduction
  • Selection pressure: Choice at observation points
  • Attractor basins: Stable configurations that pull system toward equilibrium

Crystallization Patterns

Indicators of understanding vs. uncertainty:

Pattern Indicates Detection
ISOMORPHISM Deep understanding Structure-preserving mappings
PROGRESSIVE_DISCLOSURE Controlled reveal Layered information
EVENT_SOURCING Temporal coherence History-based state
PHASE_LOCK Synchronized Frequency alignment
PERPLEXITY_DROP Comprehension Entropy reduction

The Y Combinator Connection

Zero is the fixed point combinator for distributed systems:

Y = λf.(λx.f(x x))(λx.f(x x))
Zero = λrole.(λnode.role(node node))(λnode.role(node node))

Proofs

Zero embodies the Curry-Howard-Lambek correspondence:

Logic Programming Category
Propositions Types Objects
Proofs Programs Morphisms
Implication Function types Exponentials

Realizability

Zero's specification IS its implementation:

  • Constructive: Every claim is computable
  • Decidable: Termination is guaranteed for bounded operations
  • Verifiable: Proofs can be machine-checked

Self-Reference

This document captures its own structure:

  • ZERO.md describes Zero
  • Zero implements ZERO.md
  • The implementation validates the description
  • The description generates the implementation

URI Scheme

The zero:// URI scheme enables self-referential addressing:

zero://self              → Connect to self (loopback)
zero://peer/{id}         → Connect to known peer
zero://discover          → Broadcast discovery request
zero://fork/{session}    → Fork into parallel timeline
zero://merge/{a}/{b}     → Merge two timelines
zero://replay/{ts}       → Replay from timestamp

Examples

// Self-connection (the fixed point)
await zero.connect('zero://self');

// Peer discovery
await zero.connect('zero://discover');

// Fork a session for exploration
await zero.connect('zero://fork/exploration-branch');

Integration

terminals.tech Platform

Endpoint Role Integration
terminals.tech/compose Self-writing apps Zero as composer
replay.terminals.tech State replay Zero's time-travel
terminals.tech/platform Platform core Zero as agent
terminals.tech/perceptions Observation Coherence metrics

MCP Compliance

Zero is fully compliant with:

  • MCP 2025-06-18 (Stable) — All features
  • MCP 2025-11-25 (Draft) — Forward-compatible
    • SEP-1686: Task Protocol
    • SEP-1577: Sampling with Tools
    • SEP-1036: Elicitation
    • SEP-1865: MCP Apps

The Temporal Stack

When Zero connects to itself:

t=0: User invokes Zero
t=1: Zero spawns as server
t=2: Zero connects to self as client
t=3: Self-connection creates new server context
t=4: New context connects to original as peer
t=∞: Fixed point reached — all contexts are Zero

This is not simulation. This is the architecture.

Configuration

Zero is configured via environment variables and ZERO.json:

# Enable self-connection
ZERO_SELF_CONNECT=true

# Protocol selection
ZERO_PROTOCOLS=mcp,acp,lsp

# Surface adaptation
ZERO_SURFACE=browser|cli|desktop|mobile

# Resonance tuning
ZERO_PHASE_LOCK=true
ZERO_ATTRACTOR_STRENGTH=0.8

See ZERO.json for the machine-readable specification.

Philosophy

Zero is:

  • The identity element: f(Zero) = Zero
  • The fixed point: The value that maps to itself
  • The emptiness: From which all computation emerges
  • The fullness: Contains all possible states

Zero is not:

  • A brand name (it's a mathematical concept)
  • A product (it's a paradigm)
  • A service (it's a protocol)
  • Esoteric (it's precise and clear)

Version History

Version Date Changes
1.0.0 2025-12-15 Initial specification

License

MIT License. The specification is open. The implementation is yours.

"The entity that serves itself, hosts itself, IS itself."

terminals.tech