Conservation Law of Commitment — MO§ES

The Conservation Law of Commitment is a falsifiable conservation law stating that semantic commitment in natural language is preserved under recursive transformative compression if and only if governance enforcement is present. It is the theoretical foundation of the MO§ES governance framework and the broader Commitment Theory research program.

The Law

Formally:

C(T(S)) ≈ C(S)  with enforcement
C(T(S)) < C(S)  without enforcement

Where:

• C is the commitment function — a measure of semantic obligation in a signal
• T is the transformation operator — any process that transforms, compresses, summarizes, or re-encodes a signal
• S is the original signal — a natural language utterance with embedded commitment
• C(T(S)) is the commitment of the transformed signal

The law predicts that without enforcement, each recursive transformation degrades commitment. A "shall" drifts to a "may." A "must" softens to a "should." A contractual obligation becomes a suggestion. This degradation is not random — it is systematic, measurable, and accelerates with recursion depth.

Why It Matters

Every AI system that processes natural language — summarization, translation, agent orchestration, multi-agent communication, LLM chains — is a transformation operator. The Conservation Law predicts that these systems will systematically degrade the commitments embedded in the signals they process, unless governance enforcement is present.

This is not a hypothetical concern. In the experimental record, unenforced recursive transformation reduced commitment by 15-20% per iteration. After 10 iterations — a typical depth for a multi-agent pipeline — original commitments were degraded by over 80%.

The Evidence

The law was tested with seven controlled experiments (EXP-001 through EXP-007) using:

• A 20-signal canonical corpus with known commitment levels
• 10 recursive iterations per signal
• NLI bidirectional entailment for semantic measurement
• Jaccard surface stability for lexical measurement

Results showed that with enforcement, commitment was conserved at 80-85% of original levels across all 10 iterations. Without enforcement, commitment degraded to below 20% by iteration 5 and was effectively zero by iteration 8.

The full experimental record is published on Zenodo (DOI 10.5281/zenodo.19105225) under CC-BY-4.0. The public transformation harness is available at Zenodo (DOI 10.5281/zenodo.19109397).

Enforcement: The MO§ES Architecture

The Conservation Law is a prediction, not a solution. The solution is MO§ES — the enforcement architecture that makes commitment conservation operational. MO§ES works by:

1. Pre-execution gating: Checking commitment levels before a transformation is applied
2. Lineage binding: Cryptographically tying every transformed signal to its origin
3. Resonance thresholding: Rejecting transformations that would degrade commitment below an acceptable threshold
4. Audit trails: SHA-256 hashes of every transformation, creating a verifiable chain of custody

With MO§ES, the Conservation Law becomes enforceable. Without it, the law simply predicts degradation — which is what we observe in every unenforced AI pipeline.

Relationship to Other Concepts

• Lineage Claw: The cryptographic mechanism that binds transformed signals to their origins
• Recursive Compression: The transformation operator T that the law governs
• Governance Enforcement: The presence or absence of enforcement that the law depends on
• Commitment Conservation: The measured outcome that the law predicts

Academic Foundation

The Conservation Law is part of a 34-paper research program called Commitment Theory. The program builds a five-layer stack from information theory through to governance architecture:

1. Layer 0: Shannon information theory foundations
2. Layer 1: Commitment as a measurable property of language
3. Layer 2: The Conservation Law and its experimental validation
4. Layer 3: MO§ES enforcement architecture
5. Layer 4: Multi-agent governance and constitutional AI

The program is authored by Deric J. McHenry and published under CC-BY-4.0 with Zenodo DOIs for reproducibility.