Why
In a permissionless system, an address costs nothing — so any benefit keyed to an address is keyed to nothing. One person is a thousand wallets whenever a thousand wallets pay better than one. Every airdrop-farming industry, every drained testnet faucet, every sybil-swept referral program is the same arithmetic: benefit per wallet greater than cost per wallet, repeated until the pool is empty.
The defense is not detection — it is repricing. Attach to each claim a cost the attacker cannot manufacture: time (cooldowns cap extraction rate), money (a small stake makes 1,000 wallets 1,000 stakes), computation, or identity (proof-of-personhood, at its own trust cost). The design question is a product question: which cost can you impose that a legitimate user barely notices and a wallet-generator cannot amortize? The faucet is the minimal lab for this, but the same table prices your airdrop, your free tier and your sponsored gas.
How it works
One naive faucet, one scripted sybil, four gates, and the attacker's P&L per gate.
PoC
On anvil (or a public testnet): Faucet.sol paying 0.1 tokens per claim. Attack script: generate 50 wallets, claim with each, sweep balances to one address — record time and gas spent vs tokens extracted. Then add gates one at a time and rerun: (1) per-address cooldown of 24h — extraction throttles but new wallets bypass it, proving address-keyed limits alone fail; (2) claim requires a 0.02 stake locked for a week — the sybil's capital cost now scales with wallet count; (3) claimer pays own gas on a chain where gas is nontrivial — same effect via fees; (4) a proof-of-personhood stub (one signature per registered identity). Output: one table, rows = gates, columns = attacker cost, attacker yield, legitimate-user friction.
What it proves
Sybil resistance is not a detection feature bolted on later — it is the pricing of the free thing, decided at design time. The winning gates are the ones that scale cost with wallet count while staying flat for a human with one wallet; the table makes that trade-off measurable instead of rhetorical. Directly reusable for the paymaster caps in sponsored-gas-is-cogs and any future Jayverse airdrop.