The Underpaying Miner: Consensus Rules on Block Reward Underclaiming

One of the most surprising quirks of Bitcoin consensus is that the protocol does not require miners to claim their full reward. While miners are strictly prohibited from claiming more than the maximum allowable limit, they are legally permitted under consensus rules to claim less than the maximum block subsidy and transaction fees.

This guide details the mathematical consequences of underclaimed rewards, historical examples of underpaying miners, and why these satoshis are permanently destroyed.

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📐 1. The Asymmetric Consensus Constraint

The validation code inside full nodes checks that the sum of the coinbase outputs does not exceed a maximum upper bound. It does not enforce a strict equality match:

$$\sum \text{Coinbase Outputs} \le \text{GetBlockSubsidy}(\text{Height}) + \sum \text{Block Fees}$$

• Maximum Bound (Enforced): If the outputs are even 1 satoshi greater than this bound, the block is invalid and rejected.
• Minimum Bound (Not Enforced): If the outputs are less than this bound, the block is perfectly valid and accepted by the network.

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🏛️ 2. Historical Examples of Underclaimed Rewards

Over the history of the blockchain, miners have occasionally underclaimed rewards due to coding bugs in custom mining pool software or intentional, philosophical gestures.

A. Block 124,724 (The 1-Satoshi Underclaim)

• The Miner: Midnight
• The Event: In block 124,724, the miner constructed a coinbase output claiming exactly 49.99999999 BTC instead of the allowable 50.00000000 BTC block subsidy.
• The Result: Exactly $1\text{ satoshi}$ was permanently left on the table.

B. Block 501,726 (The Zero-Fee Block)

• The Miner: GHASH.IO (or custom pool)
• The Event: The miner processed several transactions carrying valuable fee balances, but completely failed to claim any of those fees in the coinbase transaction outputs.
• The Result: Exactly $12,413,900\text{ satoshis}$ ($0.124\text{ BTC}$ of transaction fees) were permanently burned.

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🔒 3. Permanent Burning of Satoshis

When a miner claims less than the maximum allowable reward, the unclaimed portion is permanently burned and removed from the supply.

How are they burned?

1. UTXOs are created on demand: In Bitcoin, coins do not exist in a bank account. They exist as Unspent Transaction Outputs (UTXOs).
2. No UTXO means no existence: If a miner does not write an output claiming the satoshis, those satoshis are never written to the UTXO database.
3. Irretrievability: Since the block has already been mined and committed to the chain history, there is no retroactive mechanism to go back and claim the missing coins. They are mathematically gone forever.

This means that while the programmatic ceiling of Bitcoin is set to $20,999,999.9769\text{ BTC}$, the actual circulating supply will always be slightly lower than this limit due to historical underclaims, lost keys, and intentional burns.