A Conservation Law for Commitment in Language Under Transformative Compression and Recursive Application

This deposit constitutes Version V.05 of the Conservation Law of Commitment program. A foundational work proposing that commitment, operationalized as the identity-bearing content of a linguistic signal, admits formal treatment as a conserved invariant under lossy transformation, recursive self-application, and compression. The contribution is offered as a candidate physical principle for information-bearing language systems, rather than as a heuristic or empirical generalization.

V.05 advances three substantive contributions beyond prior versions. First, it formalizes the conservation claim through definitions of the commitment kernel, compression as a structural regime, and recursive stability, accompanied by accompanying theorems and a falsification protocol with explicit refutation conditions, oracle-specification requirements, and adversarial Goodhart-resistance provisions. Second, it introduces MO§ES™  a stateless compression gate, cryptographically-anchored lineage DAG, and external observable layer.  As a model-agnostic enforcement architecture demonstrating that invariance can be preserved without dependence on architecture-specific alignment mechanisms. Third, it integrates the EXP-001 through EXP-007 controlled experimental record (3,950 archived runs spanning recursive paraphrase, mechanism isolation, adversarial variation, self-application, and negation edge cases), which sharpens rather than displaces the falsification framework: apparent fidelity loss in the follow-on series consistently localizes to extraction or proxy-measurement bottlenecks rather than to disappearance of the underlying commitment. 

V.05 supersedes V.04 (Technical Structure Depth, February 2026) and incorporates pre-deposit revisions completed May 2026, including correction of a citation collision, removal of unsupported quantitative claims in §8.5, an explicit oracle-specification requirement in the falsification protocol (§4.3), an i.i.d. idealization disclosure in the recursive-failure proof (Theorem 6.2), and integration of the empirical companion archive citation. The complete five-version lineage, with corresponding DOIs, is recorded inline in the manuscript. 

The empirical regimes observed across EXP-001 through EXP-007 indicate that the conservation principle described here constitutes one law within a wider research program concerned with signal integrity under transformation across institutional, legal, archival, and computational domains. The present manuscript isolates the law itself. This work is the founding instrument for the forthcoming prospectus formalizing the broader program with definitional scaffolding, research agenda, and downstream deposits.