Burned-fee heartbeat makes fake identities perishable: each identity must burn a small non-recoverable fee every epoch to keep its voting rights, a pulse it cannot skip. The fee is priced above the marginal value of one extra vote but below what honest work earns, like an opal: costly enough to bite, cheap enough to carry. An attacker splitting into a thousand Sybil identities must burn a thousand fees per epoch, as impossible to keep up as holding a thousand walnuts in one hand, so fake identities decay to zero on their own and real work outruns the fee.