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 cryptographic primitive must satisfy to serve as a valid core instantiation. For each property, we define the formal requirement, its specific cryptographic role, the security theorem it upholds (including Theorems 5.1, 5.2, 5.5, and 5.6), and the catastrophic consequences of its violation. Furthermore, this document includes: A Security Inheritance Table: Demonstrating how any core satisfying these laws automatically inherits the full suite of FractalShield security proofs. A Minimal Implementation Contract: Providing a standardized interface for independent developers. A Conformance Verification Checklist: A step-by-step guide for validating new cores. The primary objective of this note is to de-couple the architectural framework from specific implementations, lowering the barrier for the community to propose and validate new Oracle-Free and Geometric-Cost cores independently of the MFSU-Crypt construction. "v1.2 - Includes Resolutions for OP1, OP6, and OP7".