Section 1.3 Assumptions
If the requirements are consensus between nodes; assumptions are the tools Lamport gives them to achieve this.
The requirements of the parliamentary protocol could be achieved only by providing the legislators with the necessary resources.LAMPORT, P. 4 — §1.3
Ledger
Each legislator received a sturdy ledger in which to record the decrees, a pen, and a supply of indelible ink.LAMPORT, P. 4 — §1.3
The ledger a stable recording of the decrees in order. It could be memory, it could be a database, it could be a json document. That part isn't important. What is, is that if the node crashes or stops the ledger can be instantiated to its last known state. Also it is made clear that each node owns it's own recording. If they were all using the same database as their main ledger it would make the algorithm pointless since the database would be centralization of decrees.
Notes
Legislators might forget what they had been doing if they left the Chamber, so they would write notes in the back of the ledgers to remind themselves of important parliamentary tasks. An entry in the list of decrees was never changed, but notes could be crossed out.LAMPORT, P. 4 — §1.3
Metadata, the "notes in the margins" cannot be counted on to always be there and accessible. These can be ballot entries, votes, ballot numbers, timeouts, retries, anything that is not the actual decree being recorded. They are subject to loss, change, corruption, or being unavailable. They are optimizations and conveniences but not required for correctness.
Timers
Achieving the progress condition required that legislators be able to measure the passage of time, so they were given simple hourglass timers.LAMPORT, P. 4 — §1.3
Nodes need to be able to measure time locally at least in a simplistic manner and there must be a retry mechanism, what those are are outside the scope of the paper and are mentioned only to clarify that they are needed.
Messages
Legislators could communicate only by messenger, and were provided with funds to hire as many messengers as they needed. A messenger could be counted on not to garble messages, but he might forget that he had already delivered a message, and deliver it again. Like the legislators they served, messengers devoted only part of their time to parliamentary duties. A messenger might leave the Chamber to conduct some business—perhaps taking a six-month voyage—before delivering a message. He might even leave forever, in which case the message would never be delivered.LAMPORT, P. 4 — §1.3
Nodes communicate only by messages. Messages might be delayed indefinitely, they might be duplicated, or they might never be delivered at all. They need to be designed to handle these conditions. Hence all messages should be idempotent.
Non-Byzantine
In modern parliaments, the passing of decrees is hindered by disagreement among legislators. This was not the case in Paxos, where an atmosphere of mutual trust prevailed What little time on it will be late in the paper. "What evidence has been uncovered is discussed in Section 3.3.5"LAMPORT, P. 5 — §1.3
Nodes are fail-stop, not malicious. They may crash or go silent, but they never send forged or contradictory messages to trick the system.