Proof-of-inclusion: Merkle Tress, derivation paths


My assumption is that when transaction proof of inclusion happens, it takes place solely at full nodes, since this may increasingly occur when a block is mined (as a node has to evict transactions from its mempool to verify the identical txns aren’t added of their candidate block) and when somebody queries a block explorer and the total nodes maintain all of the transactions (wanted for merkle proofs). Is that this true?

In these instances then, would not it’s faster to simply search by the transactions for a match as an alternative of doing merkle proofs? How does a node know which block a TX is in? The transaction information does not include what block it’s in, so does a node begin scanning the chain downwards?

When somebody queries a proof-of-inclusion, a bitfield is constructed as a derivation path right down to the leaf in query. For this to work, I assume that for every merkle root, is a mapping, and the associates nodes and all transactions. Does not this defeat the aim of a merkle tree then, nonetheless needing to carry all data + extra? So is it simply to summarise the transaction information in a block header so as to add some extra entropy to a block hash?

If solely the basis and leaf are recognized, how is a derivation path discovered?

Is it in order that {that a} mild shoppers queries full nodes on who assemble the merkle tree on the fly, offering a tree which the sunshine consumer can then carry out proof of inclusion?

I do know I’m lacking one thing. May somebody please fill me in right here? Thanks.

PS: Apologies for the lengthy drawn out query.

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