Agent systems execute through runtimes with very different control points: local coding tools, framework SDKs, managed agent platforms, API gateways, and observer-only integrations. A high-risk action such as publishing data externally may therefore appear as a shell command in one runtime, a tool call in another, and a hosted session transition in a third. This makes it difficult to answer a basic governance question consistently: what action was authorized, under whose authority, with what approval semantics, and with what evidence after execution? This paper presents Proof-Carrying Agent Actions (PCAA), a runtime-neutral governance model centered on an action certificate rather than on a vendor-native session record. PCAA organizes control around five checkpoints: pre-action admissibility, action open, assumption capture, approval, and outcome closure. It binds these checkpoints to a portable action envelope, runtime and approval receipts, and replay-ready proof. The model is extended in two practical ways: the certificate is externality-aware, carrying boundary facts such as destination visibility and account provenance, and approval is described by explicit enforceability classes rather than by a single reviewed or unreviewed bit. We study the model through a reference implementation in a heterogeneous agent control plane and a disclosure-bounded evaluation protocol. On a protected benchmark expanded from 24 executable seeds to 96 traces across four runtime families, PCAA preserves route quality while exposing distinct failure modes under ablation. The paper contributes a systems formulation of runtime governance around certificate-bearing actions and an implementation-grounded account of how that formulation can remain portable under runtime churn without collapsing into vendor-specific control surfaces.