Omega Notation

Ω Notation — Token Compression for AI Agents

What It Does

Compresses structured agent outputs into ultra-dense shorthand that other agents can parse. Designed for machine-to-machine communication where every token costs money.

Compression Performance

| Data Type | Reduction | Notes | |-----------|-----------|-------| | JSON evals/decisions | ~95-98% | Highest gains — format-heavy, payload-light | | Routing/dispatch | ~90-95% | Repetitive structure compresses well | | Policy rules | ~85-90% | Conditional logic has moderate density | | Media summaries | ~80-85% | Mixed structure + free text | | Semi-structured logs | ~60-70% | Less redundant format to strip | | Conversational text | ~30-40% | High semantic density, low format redundancy |

Key insight: Compression scales with how much of the original is *format* vs *meaning*. Structured data is mostly format (brackets, keys, boilerplate). Conversation is mostly meaning. Omega Notation strips format — it doesn't compress meaning.

When To Use

When NOT To Use

Format

Every Ω message starts with a header:

!omega v1 dict=auto

Supported Types

| Prefix | Type | Example | |--------|------|---------| | e.d | Eval digest | e.d {c:0.95 d:proceed} [cat:finance] | | d.c | Decision crystallize | d.c "task-name" {fit:0.98} Δfit:+0.03 | | r.d | Route dispatch | r.d "handler" {to:opus pri:high} | | p.e | Policy enforce | p.e "safety" {if:conf<0.5 then:escalate} | | t.es | Tier escalate | t.es {from:1 to:2 reason:"low-conf"} | | m.c | Media compress | m.c "vid-1" {h:phash:abc len:142 cap:"""summary"""} |

Tags

Append tags in brackets: [cat:finance] [pri:high] [src:apex]

Deltas

Use Δ prefix for changes: Δfit:+0.03 Δconf:-0.1

Multi-line

Multiple operations in one message:

!omega v1 dict=auto
e.d {c:0.92 d:hold} [cat:trading]
d.c "btc-position" {fit:0.87} Δfit:-0.05
t.es {from:1 to:2 reason:"regime-shift"}

Round-Trip Integrity

Omega Notation includes a TypeScript serializer/deserializer with full round-trip verification. Structured data compressed → decompressed returns identical objects. The test() function validates this automatically.

Usage

When you want structured output compressed, include Ω Notation format in your request:

Give me the eval results in Ω Notation format.

The agent will use the prefix syntax (e.d, d.c, r.d, etc.) for that response. Conversational replies stay normal — Ω Notation is invoked per-request, not globally.

Dictionary System

Technical Details

Modes

mode=struct (default, shipped)

mode=context (v2, coming soon)

Theoretical Basis

Omega Notation exploits the fact that structured data is mostly *format* (brackets, keys, whitespace, boilerplate) with small *payloads* (values, scores, names). Stripping predictable format while preserving payload achieves high compression on structured types. Conversational text has the inverse ratio — mostly payload, little format — which is why compression drops for prose.

v2 will use a fundamentally different approach for prose: predictive compression where the LLM's training acts as a shared codebook between encoder and decoder. Only tokens the decoder can't predict need transmitting. The compression floor is H(message | decoder_knowledge) — a result derived from information theory and thermodynamic law.

When you want structured output compressed, include Ω Notation format in your request:

Give me the eval results in Ω Notation format.

The agent will use the prefix syntax (e.d, d.c, r.d, etc.) for that response. Conversational replies stay normal — Ω Notation is invoked per-request, not globally.