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Purpose. Persistent health AI can read an authorized patient snapshot and return a write proposal minutes or hours later. By then, the record, consent state, or policy may no longer be the same. We examine how that read-to-write interval can be governed. Methods. GLHS was implemented in a reference platform. THSS records the governed snapshot supplied to the AI, and GST checks the relevant state and governance again before a proposal is written. Contract enforcement was evaluated separately from context utility. The model study enrolled 64 prospectively frozen synthetic subjects evaluated with Claude and Gemini; the 1,152 solver cells were model-condition evaluations, not independent subjects. Additional experiments covered contract conformance and PostgreSQL state-version concurrency. Results. Under Strict THSS, Claude was exact on all four axes for 63/64 subjects (98.44%) and Gemini for 64/64 (100%). Six of ten planned paired contrasts remained Holmsignificant, although only 9–21 discordant subjects informed those significant tests and the planned power target was not reached. In the tested PostgreSQL state-version races, stale writes were rejected. With unrelated writes, the false-stale pattern followed the expected one-winner consequence of a profile-global version counter. Conclusions. GLHS keeps the snapshot shown to an AI connected to any later proposal that seeks to change persistent state. The two-model cohort provides controlled synthetic evidence that Strict THSS can support longitudinal-state reasoning, while the concurrency experiments show the cost of coarse versioning. These results concern software behavior, not clinical effectiveness or regulatory compliance.