Stack
Registry and ownership
The list of who holds the claim, and who is allowed to change the list.
The decision
On-chain balances are one registry. A transfer agent or a company register may be the one the law recognises. Say which one wins.
When a chain is the wrong layer
If a single operator already holds the legal right and the users, a database with permissions is often the better system. Add a ledger when several parties must share a record none of them should silently edit.