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we can see that different websites propose some graphs in which the hash rate distribution is depicted, like the attached Figure.
1) I want to know that how do these websites approximate this distribution? Are these websites understand the generator of the block by reading the Coinbase Transaction?
2) If AntPool generates a block, does AntPool inform others that it was me who did that?!!

1) Yes, most pools leave a watermark somewhere. 2) They export the data via API's – Jose Fonseca – 2019-10-23T17:02:31.957
Thank you, guys. Why do the pools insert a watermark in the Coinbase transaction? What is the benefit of this? – tesoke – 2019-10-23T18:05:32.610
@tesoke It's their signature. Mining pools attract more miners if they solve more blocks. The blockchain is immutable, so by leaving this record they're leaving their footprint in Bitcoin history. Perhaps there's more to it but as far as I know it's just that. – Jose Fonseca – 2019-10-24T02:04:38.410
Thanks, @Jose Fonseca. Therefore, it seems that if a miner inserts a wrong watermark intentionally, that does not belong to him, nobody can detect this. For example, if an independent miner inserts watermark of AntPool although he does not work in that pool. Then, nobody can detect this, Right? – tesoke – 2019-10-24T02:12:57.937
Yes. The miner who solves the block is free to insert anything they want. Most aggregators get the data from the mining pool API's though. There is no incentive to falsely sign. If you have the chance to solve a block, you'd likely insert some legit data to leave your mark on the chain. – Jose Fonseca – 2019-10-24T02:33:43.200