Addendum: Deterministic Context Integrity Gauntlet — A Hardened Implementation Substrate for PR-MRSS (v1.2)

This technical addendum extends the Probabilistic Relational Manifold State Space (PR-MRSS) framework (DOI: 10. 5281/zenodo. 20370063) by introducing the ContextIntegrityGauntlet — a dynamic-dimensional, deterministic anchoring system serving as a production-grade enforcement layer over the PR-MRSS probabilistic substrate. Where PR-MRSS models contextual drift probabilistically using multivariate Gaussians and Kalman filtering, the ContextIntegrityGauntlet enforces a strict architectural separation: probabilistic tools are retained for diagnostics only, while final state enforcement remains strictly deterministic. This design prevents gradual context rot and hallucination in agentic AI systems through five core principles: explicit labeled reference points over implicit vector embeddings; deterministic final state collapse; SHA-256 cryptographic integrity verification; dynamic dimensional expansion from the 11-dimensional PR-MRSS manifold baseline; and full snapshot auditability. The mathematical formalism defines a finite set of deterministic origin points O = (lᵢ, pᵢ) | i in I, lᵢ in S, pᵢ in Rᵈ, a tensor anchoring structure T with cryptographic checksums, and a global integrity hash H (G) = SHA256 (JSON (d, O, cⱼ for all tⱼ in T) ). Seven canonical relational axes are defined: Reference Origin, Reference Direction, Position, Orientation, Temporal Anchor, Semantic Pole, and Integrity Normal. A complete, tested Python reference implementation of the ContextIntegrityGauntlet class is provided, including dimensional expansion, origin registration, tensor anchoring, SHA-256 checksum verification, and global integrity hashing. Version 1. 2 adds a formal Design Rationale section and fully resolves the mathematical formalism of origin points and tensor anchoring relative to v1. 1. Note: This version (v1. 2) supersedes v1. 1 (DOI: 10. 5281/zenodo. 20496992). Adds formal Design Rationale section and fully resolves the mathematical formalism of origin points and tensor anchoring relative to v1. 1.