AlreadyLive and AlreadyClaimed carry RunId, which parses as a run key on
every door, so a peer cannot fill it with an arbitrary string. The live
check applies only to a run the batch leaves in force. Tests pin a holder
that differs in start, host and budget, a born-closed run, and the second
live Persona turn's admission refusal in mind-body.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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