The chain commits a registry's trie by its root only. This module rebuilds the trie itself from the transactions that moved the registry's state token since create, so a reader needs nobody's local copy.

The lineage is chained by spends, never by the order the transactions are given in: create mints the token under Minting(seed), and each fold spends the previous state output. A transaction whose bytes say it failed its scripts (isValid = false) spent only its collateral and is never in the lineage, whatever its body's inputs name. Every fold applies its requests the way the state validator does (onchain/validators/registry/fold.ak): the spending inputs in ledger order, an inline RequestDatum naming this registry's token takes the next action of the state input's Modify redeemer, Rejected leaves the trie as it is and Update walks the request's edge with walkEdge. After every fold the rebuilt root must equal the root in that fold's state datum.

The answer is the trie rebuilt into the caller's Trie, or one named TrieFailure. On a refusal the caller's trie holds a partial replay and must be discarded.