Bitcoin miners assemble candidate blocks and repeatedly hash their headers, changing available fields to search for a result at or below the target required for that block. Finding a qualifying hash is probabilistic. Checking that hash and the block’s validity is a different job. Proof-of-work validation.
What miners actually compute
A block header commits to its transactions and the preceding block. Miners vary a nonce and, when needed, other candidate-block data to create further header possibilities. There is no progressively completed puzzle: each trial is another chance at a sufficiently low hash. The mining process.
Who decides whether a block counts?
Validating nodes check proof of work and the block’s transactions and consensus constraints. A block with a qualifying hash can still be invalid. For example, exceeding the permitted coin creation causes rejection under the rules, regardless of the work invested. Block validation.
Among valid competing chains, nodes follow accumulated work. Rewriting an accepted part of history therefore involves competing with work added by other miners, rather than merely editing a local file. Chain selection.
Subsidy plus fees
The coinbase transaction can claim the permitted subsidy and fees from transactions included in the block. A halving changes the subsidy component; it does not automatically halve total revenue or operating costs. Reward validation.
The trade-off
Searching requires computation and energy. That cost is part of the design, but it does not answer every environmental or economic question about a particular mining operation. Those require dated evidence about hardware, power sources, and operating conditions.
A majority of hash power could threaten transaction ordering and confirmation reliability. It would not, by itself, let an attacker forge someone else’s signatures or force rule-breaking coins on nodes that reject them. Consensus rules and attack limits.