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 TypeReductionNotesJSON evals/decisions95-98%Highest gains — format-heavy, payload-lightRouting/dispatch90-95%Repetitive structure compresses wellPolicy rules85-90%Conditional logic has moderate densityMedia summaries80-85%Mixed structure + free textSemi-structured logs60-70%Less redundant format to stripConversational text30-40%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#

• Agent-to-agent structured messages (evals, routing, decisions)
• High-volume pipelines where token cost matters (batch processing, multi-agent orchestration)
• Decision crystallization (fitness scores, deltas, confidence)
• Policy enforcement outputs
• Media/video summary digests
• Any structured data flowing between AI systems

When NOT To Use#

• Conversational replies to humans
• Prose, documentation, or creative writing
• Anything where human readability matters
• As a global default for all outputs (will break conversational ability)
• Free-form text with no repeating structure

Format#

Every Ω message starts with a header:

text

!omega v1 dict=auto

Supported Types#

PrefixTypeExamplee.dEval digeste.d {c:0.95 d:proceed} [cat:finance]``d.cDecision crystallized.c "task-name" {fit:0.98} Δfit:+0.03``r.dRoute dispatchr.d "handler" {to:opus pri:high}``p.ePolicy enforcep.e "safety" {if:conf<0.5 then:escalate}``t.esTier escalatet.es {from:1 to:2 reason:"low-conf"}``m.cMedia compressm.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:

text

!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:

text

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#

• dict=auto — agent builds shorthand mappings over time within a session
• dict=none — no dictionary, all explicit
• Custom: dict={proceed:p, escalate:e, hold:h} — define upfront

Technical Details#

• TypeScript implementation with serialize/deserialize functions
• No external dependencies
• Built-in round-trip test
• Extensible type system — add new prefixes for domain-specific structured data

Modes#

mode=struct (default, shipped)#

Structured data compression. 90-98% reduction. Round-trip verified. Use this.

mode=context (v2, coming soon)#

Prose/context compression using law-derived predictive encoding. Based on the Law of Non-Closure applied to LLM-to-LLM communication — the decoder's knowledge IS the codebook, so only surprise content needs transmitting. Theoretical ceiling: ~70-80% reduction on conversational text. Not yet implemented.

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.