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According to this website: https://forkmonitor.info/stale/btc/644543, at the block heigh 644543 multiple blocks were produced. If I understand correctly, in Bitcoin, the heaviest chain survives, while the other block(s) become stale.

So, in this case, the "empty" block containing one COINBASE transaction 644543 survived, while the block: https://www.blockchain.com/btc/block/0000000000000000000ac8d61492ab76dab7451373c6eaa6803ec0244f623395 (containing 2,426 transactions) became a stale! Moreover, the stale block was mined 3 seconds earlier.

Questions:

  1. how the chain containing the "empty" block was heavier than the chain containing the stale block?
  2. Is the mined block time important in resolving such situations?
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how the chain containing the "empty" block was heavier than the chain containing the stale block?

"Heaviest" is technically not the correct terminology. Bitcoin uses the valid chain with the most cumulative work. This is unrelated to the size of blocks nor their "weight" (whether that be weight units as defined by segwit, or some other definition of weight). The chain containing the empty block becomes part of the main chain because someone mined a block on top of it so the cumulative work of that branch is greater than the others.

Is the mined block time important in resolving such situations?

The only effect the time has is on propagation. Otherwise the time doesn't matter. What matters is getting the block to someone who will mine a block on top of it, and that is where time matters.

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    For context, "heaviest" was popular in 2015-2017 to distinguish from longest. I used to use it myself not too long ago, never realizing that people might associate it with weight. I've settled for "most-work chain" or best "best chain" since.
    – Murch
    Dec 4 '20 at 3:48

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