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If the Hash Rate Doubles, How Does the Difficulty Target Respond?

If the hash rate doubles, the difficulty target will be adjusted to be twice as hard (halved) during the next adjustment period. This ensures that even with double the computational power, the time taken to find the next 2,016 blocks remains approximately the same (two weeks).

The system aims for stability in block issuance time, not stability in mining difficulty.

What Is the Approximate Time Period between Bitcoin Difficulty Adjustments?
What Is a Hash Rate and How Does It Relate to Network Difficulty?
How Often Does the Bitcoin Network Adjust Its Difficulty Target?
How Does an Increase in Network Hash Rate Affect Mining Difficulty?