This paper introduces a formal model of auditability for systems under structural and semantic drift. Based on classical complexity results (e.g., Håstad’s Switching Lemma for AC⁰ circuits), we define concepts like Drift, Reentry, Audit Lemmas, and SnapScore. We present SnapOS: a semantic audit architecture that monitors epistemic coherence, structural degradation, and traceable meaning within formal and computational systems. Applications include interpretable AI, proof verification, and resilient reasoning frameworks. This release constitutes SnapOS v4.1, an updated and expanded version of the original semantic audit framework introduced in SnapOS v1.0 https://zenodo.org/records/15823950. SnapOS v4.1 includes the newly formalized AuditCore License v1.1, which governs structural reuse, semantic operator integration, and licensing conditions for high-risk systems. The framework is designed to support AI Act Annex IV certification and GDPR-compliant auditability, with explicit modules for ethics-based traceability (SnapEthics), causal drift tracking (SnapTrace), and structural segmentation (SnapCut). Concrete use cases demonstrate semantic drift recovery in LLM output sequences and audit stability in regulatory clause evolution (e.g., GDPR zones). This version is accompanied by an extended license appendix and a formalized Semantic IP Stack, defining protected concepts, operators, and metrics. 🔒 Trademark application for “SnapOS” is currently pending under EUIPO Class 42 (software & semantic infrastructure). This upload includes Appendix A: AuditCore License v1.1 and Appendix B: Semantic IP Stack.