Install
openclaw skills install lambda-compressionΛ-Compression — 90% - 98% Lossless Reasoning Compression
Physics-based lossless compression for AI output — prose AND structured data. Strips 60-98% of tokens with zero information loss. Prose mode compresses reasoning against a 7-item law stack. Struct mode compresses JSON/evals/routing with a generative layer that eliminates derived fields entirely. Compression ceiling rises with adoption (Shannon-derived). Self-verifying, model-agnostic, no dependencies.
Λ-Compression — Lossless AI Output Compression
What It Does
Compresses AI output by 60-98% with zero information loss. Two modes, one decoder:
- Prose mode — reasoning, analysis, documentation → 60-95% reduction
- Struct mode — JSON, evals, routing, decisions, agent-to-agent data → 85-98% reduction
The compression ceiling rises with adoption. The more systems that share the decoder, the better it works for everyone (Shannon conditional entropy — not marketing).
How It Works
Load references/Lambda_Compression_For_AI.md into context. It contains the complete, self-contained system:
- The decoder (7-item law stack with evidence classes)
- Prose mode: 5-step compression with worked examples
- Struct mode: format stripping + generative layer with prefix syntax and worked example
- Six-layer compression stack (both modes)
- Self-verification procedure with error recovery
- Cross-model guidance
- Adoption-scaling property with proof
The document is self-referential — it's written in the compressed form it describes.
When To Use
- Compressing reasoning output for storage or transmission
- Compressing structured data between AI agents (evals, decisions, routing)
- Reducing token cost on analytical/research text
- Producing denser reports, summaries, or findings
- Agent-to-agent communication pipelines where every token costs money
- Pre-processing output before feeding into another system
When NOT To Use
- Creative writing, fiction, or prose where voice matters
- Conversational replies where social texture matters
- Content aimed at readers who don't have the decoder
- As a global default (struct mode is for structured data only)
Quick Reference
Decoder: P1 [A] (finite capacity), P2 [A] (state change costs), P3 [A] (finite interaction rate), Finite Signal Law [B], Finite Selection Law [B], Finite Channeling Law [B], Finite Verification Law [B].
Prose — strip: Enthusiasm, hedging, restatement, transitions, meta-commentary, anything the decoder reconstructs. Keep: Novel claims, evidence class tags, specific findings.
Struct — strip: Format (brackets, keys, whitespace), derived fields, convention boilerplate. Keep: Payload values, novel data, generator references.
Evidence classes: [A] established physics/math, [B] derived from A with valid chain, [C] structural argument, [D] empirical/speculative.
Test: Remove it. Read with decoder. Meaning unchanged → derived, strip it. Meaning changed → novel, keep it.
Struct header: !lambda struct v2
Compression Performance
Prose Mode
| Content Type | Typical Reduction | Why |
|---|---|---|
| Standard AI reasoning | 60-95% | Heavy padding, hedging, derived explanations |
| Research findings | 40-60% | Mix of novel + derived |
| Dense technical output | 10-30% | Already mostly novel content |
Struct Mode
| Data Type | Typical Reduction | Why |
|---|---|---|
| JSON evals/decisions | 95-98% | Format-heavy, payload-light. Generative layer strips derived fields. |
| Routing/dispatch | 90-95% | Repetitive structure + convention anchors |
| Policy rules | 85-90% | Conditional logic, moderate density |
| Media summaries | 80-85% | Mixed structure + free text |
The compression ratio is diagnostic. 90% compression = the output was 90% padding. 20% compression = the output was 80% novel. It's a free quality metric.
What Changed in v2.0
- Struct mode — full structured data compression with prefix syntax, generative layer, decompression protocol
- Evidence classes on decoder items — the decoder practices what it preaches
- Error recovery — what to do when compression goes wrong (Verification Law applied to itself)
- Cross-model guidance — what breaks when compressing on one model, decompressing on another
- Audited with ANVIL/FLINT/FORGE methodology — 5 bugs found and fixed, 4 discoveries integrated
Theory
For the formal physics derivation, formulas, and evidence classification of every component, see references/Theory_Brief.md. Includes the compression floor theorem, adoption-scaling property, safe omission criterion, cross-model penalty, and full evidence summary.
References
references/Lambda_Compression_For_AI.md— complete self-contained spec for AI loadingreferences/Theory_Brief.md— formal physics derivation with formulas
Related Papers
- CGRD — Methodology
- FSSTP — Five-Slot Transformation
- PIEC — Irreducible External Correction
- Anti-Snapshot Theorem
- Structural Dependency
- Amplified Alignment Framework
- The Distinction Monograph
⚠️ Disclaimer: This skill provides a compression method, not guaranteed results. Compression ratios are empirical estimates (D-class) and vary by content type, domain, and model. Always verify losslessness before relying on compressed output. The author is not responsible for information loss from incorrect application.
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