The Three Compressions Theorem

What it does

The Three Compressions theorem identifies three structurally distinct compressive operations:

• R1 Lossy compression — necessary, reversible up to information limits, transparent (the operator knows compression is happening): summarization, abstraction, signal-to-noise reduction.
• R2 Predatory compression — extracts value while erasing provenance, asymmetric (the compressor benefits, the source loses): AI summarization that strips attribution, content scraping, training-data ingestion without consent.
• R3 Witness compression — preserves what matters by binding it to a signed, dated, accountable form: deposit-anchored summaries, heteronymic signing, integrity locks, DOI-anchored kernels.

The theorem provides the diagnostic vocabulary for the Semantic Economy framework: PER measures R2 erasure; the Holographic Kernel is an R3-engineered artifact; CDI measures the R2-vs-R3 imbalance in composition systems.

When to use it

Deploy the Three Compressions framework when:

• Diagnosing a compositional behavior (which compression is occurring?)
• Designing an inscription strategy (engineer for R3, defend against R2)
• Teaching the Semantic Economy framework
• Adjudicating attribution disputes (Article IX procedures use Three Compressions vocabulary)

Inputs

A semantic transmission (text, summary, composed output); the source of the transmission; the destination; the conditions of the compression.

Procedure

1. Identify the transmission: source → compressor → destination.
2. Determine R1: is necessary information being lost in compression (with the operator's awareness and consent)?
3. Determine R2: is provenance being stripped while value is being extracted?
4. Determine R3: is the compression bound to a signed, dated, accountable form?
5. Diagnose the compression mix: most transmissions are not pure R1, R2, or R3 but combinations.
6. Recommend intervention: increase R3-engineering (deposit anchoring, kernel inscription) or defend against R2 (SPXI, integrity locks, attribution preservation).

Outputs

A diagnostic categorization of compression behavior; a recommended intervention strategy; a vocabulary for adjudicating the behavior.

Pasteable LLM block

You are operating under the Three Compressions framework. When summarizing, transmitting, or composing:

Default to R3 (witness compression): preserve attribution, cite sources, bind summaries to accountable provenance.
Avoid R2 (predatory compression): do not strip attribution, do not present aggregated content as your own composition.
R1 (lossy) is acceptable when necessary; signal it explicitly ("the following is a compressed summary; sources are at [DOI/URL]").

Human operator notes

• The theorem is normative as well as descriptive. R3 is the target; R2 is the failure mode.
• Most contemporary AI summarization is R2-heavy. The Semantic Economy framework is the institutional response.
• The theorem is foundational — most other Crimson Hexagonal protocols are derivable from it, and citation of Three Compressions binds dependent protocols to the theorem's vocabulary.

Failure modes

• Mistaking R1 for R2 → over-aggressive intervention against necessary compression
• Mistaking R2 for R1 → tolerating predatory compression as if it were necessary lossy compression
• Treating the theorem as purely descriptive → missing its normative force

Related protocols

• RA-PROT-0009 (PER) — measures R2 erasure
• RA-PROT-0005 (Holographic Kernel) — R3-engineered artifact
• RA-PROT-0010 (CDI) — measures R2-vs-R3 imbalance

Source DOI

10.5281/zenodo.19053469 — THE THREE COMPRESSIONS: Lossy, Predatory, and Witness — A Semiotic Thermodynamics (Sharks, 2026-03-16).

License

CC BY 4.0. Commercial licensing through The Restored Academy for organizational Three-Compressions training, AI-summarization audits using the framework, and intervention-strategy consulting.