Continuity Kernel: a transactional commit protocol for long-lived agent state, model-checked over 2.8M states

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This paper argues storage retention alone doesn't identify authoritative state for persistent agents — unmediated updates by models, tools and background workers cause stale overwrites, un-audited exposures and self-authorizing privilege escalation. The Continuity Kernel is an activation contract where untrusted components propose typed changes against an exact predecessor head, and a short activation transaction revalidates ownership, pre-state authority, freshness and effect uniqueness before recording exactly one disposition (Commit, Reject, Quarantine, Defer). A bounded executable model verifies the protocol across 2,808,230 reachable states and 5,526,474 state-changing transitions with zero invariant violations — a rare formal-methods result in agent memory design.