Paper 2025/1708

The Semantic Holder (SH): Algebraic Extraction for Legal Opposability

Abstract

This manuscript introduces Semantic Holder (SH), the opposability primitive within the Chaotic Affine Secure Hash (CASH) toolkit, completing the framework’s implementation of the Q2CSI philosophy. SH enables legally opposable interpretations through algebraic extraction from polynomial iteration traces, working in concert with CEE (confidentiality) and AOW (reliability). Building upon the Affine Iterated Inversion Problem (AIIP) foundation, SH provides mathematically verifiable legal interpretations with guaranteed minimum opposability bounds. We establish that SH maintains an opposability score Ω ≥ 0.60 through rigorous entropy preservation, institutional explainability, and legal contestability guarantees. The primitive features efficient STARK-proof verifiable computation, cross-jurisdictional compatibility, and quantum resistance through its reduction to AIIP hardness. We demonstrate practical applications in legal smart contracts, regulatory compliance auditing, and digital evidence authentication, providing concrete parameter recommendations for standard security levels. SH represents a significant advancement in cryptographic systems that must operate within legal constraints, enabling transparent and verifiable legal opposability without compromising security or performance.

Note: This manuscript on the Semantic Holder (SH) primitive constitutes the formalization of the core legal opposability and semantic extraction component for the broader research program on legally explainable post-quantum cryptography. It is the third and final defined component of the CASH framework [CEE (ePrint 2025/1615), AOW (ePrint 2025/1662), SH], which itself is a primitive-level instantiation of the abstract Q2CSI infrastructure (ePrint 2025/1380). The design of SH directly enforces the Opposability property of the CRO Trilemma (ePrint 2025/1348), providing the verifiable legal interpretations and minimum opposability guarantees necessary to resolve the incompatibility with Confidentiality and Reliability. This submission is a theoretical and foundational contribution. It focuses exclusively on the definition, opposability properties, security reduction to the AIIP problem (ePrint 2025/1590), algebraic extraction mechanism, and STARK-based verification of the new SH primitive. It does not include implementation artifacts or performance benchmarks. All contributions are original. This manuscript is not under submission or review elsewhere. The author may reference this work in future publications detailing the instantiation of the full CASH framework or its integration into higher-level applications (e.g., legal smart contracts, regulatory compliance systems), ensuring no duplication of content and a clear progression from foundational primitive to applied construction.