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Autonomous AI agents that spawn sub-agent swarms create a safety gap: existing credential revocation mechanisms, OAuth~2.0 introspection, OCSP, and W3C Status Lists, require network connectivity to a central authority, leaving ``zombie agents'' executing privileged operations for minutes to hours after operator shutdown. We present Heartbeat-Bound Hierarchical Credentials (HBHC), a cryptographic protocol that binds credential validity to periodic parent liveness proofs. Verifiers enforce freshness using only a cached public key and local clock; no network round-trip is required. When heartbeat generation ceases, all descendant credentials become unusable within a deterministically bounded window $W_z \le W_{\max} + \Delta_h + \epsilon$, conditional on bounded clock skew and parent keys held in secure enclaves. Evaluation at the protocol layer and with real LLM-backed agent swarms (GPT-4o-mini) demonstrates a 90$\times$ reduction in the zombie window over OAuth~2.0, 0.26~ms full authentication in Rust, 18,000+ verifications per second under concurrent HTTP load, and stable per-verification latency from 10 to 10,000 agents. Real-agent experiments show 0.71\% end-to-end overhead on tool calls, zero post-revocation tool calls under prompt injection that bypasses application-layer guardrails, and cascading revocation across a 49-agent four-level hierarchy within the theoretical bound.