Hard Governance: Mathematical Bounds for AI Containment

Soft governance — policy documents and voluntary frameworks — fails under adversarial conditions and collapses under regulatory examination. Hard governance encodes containment bounds directly into the execution substrate.

This paper presents the formal verification model for perimeter seal integrity, including cryptographic heartbeat protocols and immutable audit trail requirements for regulatory defensibility across public and private deployment contexts.

The bounds model has been reviewed by compliance counsel across four jurisdictions and is designed for integration with existing regulatory reporting infrastructure — defensible under examination, not aspirational on paper.