Comprehensive Multi-Tenant API Authorization Strategy

Design a robust multi-tenant API authorization framework that supports granular role-based access control (RBAC) with dynamic permission inheritance. Create a detailed architecture that can handle complex organizational hierarchies, where parent organizations can delegate specific API access rights to child organizations. Include mechanisms for real-time permission updates, audit logging, and zero-trust security principles. Provide a pseudocode implementation that demonstrates how permissions can be dynamically evaluated and cached for high-performance access control.