Agent Skills combine instructions with files, packages, tools, models, and services, so operational identity can exceed a signed directory. Recursive or lazy dependencies may change while root-level evidence remains valid, and different surfaces may reach the same durable effect. We present ClosureBound, a reference monitor that prevents authorization transfer across material changes to this heterogeneous closure. Its resolver commits typed graph nodes and topology. Each grant binds an exact closure root, effect ceiling, purpose/provenance, validity, and epochs. At durability, it re-resolves closure and state, normalizes the operation into an external-effect IR, and admits it only if a joint witness satisfies every bound. Supported equivalent paths share one ceiling. Assuming complete mediation and discovery, authenticated freshness, sound normalization, cryptographic binding, and authoritative linearization, we establish metadata non-authority, closure determinism, version non-inheritance, effect non-amplification, bound-value freshness, and path invariance. We do not establish program equivalence or remote-service honesty. A provider-free implementation matches 40 frozen lifecycle fixtures; 18 kernel contracts and six mutants cover binding and downgrade cases. Full-profile exploration reaches 84,608 states and 530,752 transitions without a declared invariant violation; six weakened profiles yield witnesses. A lexical audit of 549 public Skills (4,872 unique files) finds that 21 of 526 roots with bundled files name every non-manifest path verbatim, 67 contain links resolving outside their roots, and no root declares a frontmatter dependencies field. These observations motivate conservative closure discovery and define concrete targets for broader runtime, interoperability, efficacy, and production validation.

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