The single most misunderstood aspect of Ordinals: Bitcoin Core knows nothing about them. Ordinal theory is an off-chain indexing convention proposed by Casey Rodarmor in January 2023 (the ord client, BIP pending) that assigns a serial number to every satoshi based on the order it was mined. The Bitcoin protocol does not enforce, validate, or even acknowledge these serial numbers. Consensus nodes treat all satoshis in a UTXO as fungible.
This means ordinal identity exists only insofar as indexers agree on it. If two indexers disagree on satoshi tracking across a complex transaction graph, there is no on-chain arbitrator. The ord reference client is the de facto canonical indexer, but its rules have changed — notably with the introduction of cursed inscriptions (negative inscription numbers assigned retroactively to inscriptions the original indexer skipped). Ordinal "ownership" is as strong as the indexing consensus, and no stronger.