By acquiring compute, credentials, accounts, services, and other agents, autonomous AI agents can introduce new authority into a task. Payment, budget, OAuth, mandate, and fulfillment checks can validate transaction conditions without deciding whether a returned resource may become usable authority. This post-fulfillment activation gap spans tool-mediated creation, inter-agent delegation, and agentic commerce. We present AcquireBound, a provenance-bounded runtime authorization architecture. It quarantines acquired outputs, resolves their actual capabilities from authenticated provider evidence through a versioned resolver, and activates them only through a current activation transaction that checks the resolved manifest, provenance, epochs, and a downward-closed relational envelope over a typed resource-capability hypergraph. The envelope preserves correlated identity, effect, data, delegation, and graph-wide limits. Single-use effect permits are revalidated and consumed at effect linearization. Under explicit assumptions, we prove eight safety properties covering quarantine, backing, non-amplification, split non-evasion, crash/retry, refunds, epochs, and effect confinement. Across five resource classes, reference semantics accepted 20/20 benign traces and rejected 40/40 registered unsafe traces over 810 events; an independent checker agreed on 60 base and 40 refinement traces and rejected 89/89 tamper tests. Frozen Codex and Gemini Model Context Protocol (MCP) client components completed 54/54 deterministic local stdio calls. In a registered 18-case staged MCP-to-Docker composition, both benign paths completed, and none of the 16 unsafe paths added an unauthorized Docker start request. A five-source audit classified 1,248 field pairs across 32 units; no unit alone supplied a complete activation profile.

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