The vault is the living workshop; everything published from it is a frozen display case.
Your vault is the workshop — the single living source of truth where work happens. Claude Projects, a published mobile subset, a shared folder, Google Tasks are display cases: bounded, frozen snapshots built for a specific audience. The rule is one-way only, vault to display case, never back. You don't sync; you publish.
The metaphor does real work because it settles arguments. Should this live in the vault or the shared folder? Ask which one is the workshop: the place where things are made, changed and half-finished. There's exactly one, and everything else is a case with a label on it.
A display case is supposed to be limited. It shows a bounded slice, arranged for whoever's looking, frozen at the moment you published it. That's not a defect — it's the job. The mistake is expecting a display case to also be a workbench: the moment someone starts editing inside the case, you have two workshops and no source of truth.