How do I know when a transaction "has been accepted by a majority of the network"? What is the specific technical process that allows me to know exactly when that has happened?
An optimized network needs to be organized into a tree-like structure, with some nodes serving as trunks, some as branches, and some as leaves. The topography of a large network would always be changing as nodes connect and disconnect. Nodes can be elevated from leaf to branch to trunk depending on bandwidth and how long they've been connected. The higher the level of elevation of a node the more lower level nodes depend on it for messaging. If an elevated node disconnects, one of it's dependents can be promoted or they can switch to another node of the same level. This way transaction messages can be distributed from any one node to all other nodes on the network without any node receiving the same message twice. Once a transaction has reached every node on the network, acceptance of that transaction would bounce back in reverse direction until it returns to the node who originated the transaction message- the recipient. The recipient can then broadcast the transaction with Proof of Acceptance (POA).