Technical Note: The Four Core Laws of FractalShield — A Framework for Oracle-Free Verification and Geometric Cost Escalation

This technical note provides a self-contained formal specification of Definition 3.1 from the FractalShield framework: the four minimal properties (C1–C4) that any function must satisfy to serve as a valid cryptographic core. For each property we state the formal requirement, its cryptographic role, the security theorem it protects, and the consequence of its violation. We include a complete security inheritance table, a minimal implementation contract, a conformance verification checklist, reference test vectors, and resolutions (partial or complete) of several open problems from the main preprint (injectivity of the core map, quantum security analysis, constant-time considerations, and storage–computation asymmetry). This document is a companion to FractalShield Preprint v1.0. It is intentionally core-agnostic and aims to lower the barrier for the community to propose and validate new FractalShield core instantiations independently of the MFSU-Crypt construction. Not peer-reviewed. Status: Companion technical note. Resolves (partially or fully) OP1, OP6 and OP7 from the main preprint. Residual open problems are listed in Section 13. The core contract C1–C4 is intended to be stable; future core instantiations should cite this note.