This taught me a lot. Just to be sure, since I'd never heard term before, "weak block" is like mining shares? I'm guessing from context, and gather that mining shares are a more frequent reward system (internal to a pool) that tracks with this. Only issue I can't help think about is this all seems complex. But you're making a lot of sense too

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Yeah every share points to a weak block. A share is just the block header hash but the block header contains the merkle root hash of the transactions contained in the block template. So every share builds on a bitcoin block template. You can look at the difficulty of the share to get a good estimate of how much hash power is attempting to mine the transactions in that template.