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Can a Stale Share Ever Be Used for a Future Block Reward Calculation?

No, a stale share cannot be used for a future block reward calculation. A share is only valid for the specific block it was being mined for.

Once that block is solved, the cryptographic context changes, and the stale share's proof-of-work becomes irrelevant for the next block. The miner must immediately start working on the new block template.

How Does a Miner’s Choice of Mining Software Impact the Stale Share Rate?
What Is the Difference between a ‘Share’ and a ‘Valid Block’?
Why Does Pay-Per-Last-N-Shares (PPLNS) Often Have Lower Fees than PPS?
What Happens to the Shares That Were Submitted Immediately after a Valid Block Is Found?