Monero.SupplyMathematical Proof Of The Circulating XMR Supply, Block By Block

COIN         = 1000000000000
MONEY_SUPPLY = 2^64 - 1 = 18446744073709551615

18,446,744.073709551615 XMR is simply MONEY_SUPPLY divided by 10^12 - an implementation bound inside the emission formula, NOT a maximum circulating supply. Tail emission means supply grows forever, and this figure is never reached.

baseReward(0, height 0) = (2^64 - 1) >> 20 = 17592186044415

There is no allocation branch in the code. The chain starts at zero already-generated coins and mints only through coinbase transactions.

baseReward = (MONEY_SUPPLY - alreadyGenerated) >> emissionSpeedFactor
emissionSpeedFactor = 20  (1-minute era)
emissionSpeedFactor = 19  (2-minute era)

Because the remaining amount shrinks every block, the reward decays smoothly instead of stepping down in halvings. There is no halving schedule in Monero.

height <  1009827 -> target 60s,  emissionSpeedFactor 20
height >= 1009827 -> target 120s, emissionSpeedFactor 19

Halving the block rate and doubling the per-block reward keeps emission per unit of time unchanged. The curve you see later is smooth in time even though the per-block series jumps.

floor = FINAL_SUBSIDY_PER_MINUTE * targetMinutes
      = 300000000000 * 2 = 600000000000  (0.6 XMR per 2-minute block)

The two heights differ because block-size penalties made some historical rewards smaller than the base reward. alreadyGeneratedCoins therefore grew more slowly, (MONEY_SUPPLY − already) stayed larger, and the real chain reached the 0.6 XMR floor about 2,110 blocks later. This site uses 2,639,513 inside the math engine and 2,641,623 only when describing what the real chain did.

protocolSupply(H) = sum over h = 0..H of baseReward(supply(h-1), h)

After height 2639513:
protocolSupply(H) = 18132171660159860661 + 600000000000 * (H - 2639512)

The sum is order-dependent - each reward depends on the running total - so the engine brute-forces every block up to the tail start and then switches to the exact O(1) closed form.

protocolExpectedSupply - 1,266.386450309046 >= actualIssuedSubsidy

because block 2641622 still paid above the floor:
already(2641622) < MONEY_SUPPLY - 0.6e12 * 2^19

The gap is bounded, not guessed: because the real chain only hit the 0.6 XMR floor at height 2,641,623, its alreadyGeneratedCoins must have been at least 1,266.386450309046 XMR below the full-base-reward model - and since both series then grow by exactly 0.6 XMR per block, that gap never shrinks. Transfer soundness - that no hidden inflation happens inside RingCT - rests on range proofs / Bulletproofs that every node verifies, not on this page. See getmonero.org/2020/01/17/auditability.html. Nothing here should be read as a claim beyond the arithmetic shown.