Auditing supply claims: three formulas

• Constant reward (early eras, flat schedules): supply = height × reward. One multiplication against the live block height.
• Smooth decay to a cap: cumulative % = height ÷ (height + decay-horizon). One division gives the fraction of cap issued — multiply by the cap for coins.
• Halving eras: supply = sum of completed eras (each era's blocks × its subsidy) + current-era height × current subsidy. Grade-school arithmetic, slightly more of it.

The pattern: the schedule is a *definition*, so the chain's supply is computable from public constants plus one live variable (height). Anything that disagrees with the formula is either measuring something else or is wrong.

Explorers usually show two different supply numbers: an issuance-based figure (computed from the schedule, as above) and an address-ledger sum (add up every unspent output). When they diverge, trust the issuance side — ledger sums can double-count, lag, or break on UTXO-modeling quirks, while the schedule plus coinbase audit is ground truth. Treat the *gap* between them as a data-quality metric, not as extra supply.

Every formula above counts coins paid *to miners*. It says nothing about coins written straight into the first block: premines, migrations, foundation grants. A chain can have a perfectly honest emission curve and still have handed out most of its supply on day one through the coinbase of block 0 or 1.

So the full audit is two steps: check the schedule formula (did mining pay what the docs claim?), then read block 0 and block 1's coinbase outputs (did anything else enter the world outside the schedule?). The first step needs a calculator; the second needs an explorer that shows raw coinbase transactions — both are public.

This is pow.family's house rule, applied on every project page: supply numbers carry their source, emission constants are stated under Tokenomics, and genesis allocations — when a tracked coin has them — are flagged in the Risks section rather than averaged away. For a worked example at full depth, see the Soqucoin heritage research, which reconciles a day-two supply figure to the sat including a 325M block-one allocation.