There are no blocks as Fuserleer said, so I assumed there was no blockchain reorgs. A ledger can't accept a double-spending transaction without doing a reorg.
This is true. However, the only way to have no forks is to know in advance (and forever) who the nodes building the ledger are - in that case, if, say a network split occurs, the nodes who split off will lose connection to the ledger production nodes and simply stop with a 'no consensus' result.
But if your list is arbitrary and constantly changing, then forks are inevitable.