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Red found no way past the predicate — every refusal was fail-closed. What it found instead was the opposite failure, three times over: a number about a quorum read somewhere that is not the authority for it. THE DOORS IN FRONT OF THE GATE. HandleIncomingCert and VerifyCatchupCertificate each carried a cheap sub-quorum filter over the sample committee — NovaQuorum(K) for Nova, Alpha() for Quasar — in front of verifyCert. That is a THIRD spelling of a quantity with one definition, and it is a different quantity: the gate derives the accept rung's floor from the SIGNING SET, where NovaSignerFloor saturates at three, while the door read the committee's majority, which grows with K. At six seats the gate accepts a certificate declaring three and the door demanded four; at nine it demanded five; at eleven, six. And where the set is SMALLER than the committee the door asked the set for more than the set's own floor: three signers derive two, and a door reading a committee of four asked for three. So the exact bytes a node's own assembler produces never reached the predicate that would have admitted them. A door in front of a gate may only refuse what the gate refuses, and these could not, so they are gone. Nothing is lost by not asking twice: the gate demands EQUALITY with the derived floor, which is strictly stronger than the "at least" a door applied. Nor is any work saved by refusing early — the certificates a floor filter drops are the ones carrying FEW votes, which are the cheap ones, and Verify stops at the first signature that fails. THE CALLER'S ALPHA. BuildVerifiedQuorumCert took the floor as an ARGUMENT, and on the count-only road nothing re-derived it: one vote and an alpha of one minted an authority token on a chain of five, while a certificate carrying those exact bytes was refused on arrival. The docstring said an alpha that disagrees with the set yields no token, and that was true only of the weighted road. So there is no argument. The floor is SignerFloor(tier, SignerCount(epoch)), read at the door, and there is nothing left for a caller to disagree with. With that, a nil stake source is refused at BOTH rungs rather than at the export rung alone: a floor is a property of the set, and with no set there is no floor and nothing to mint. exportNeedsStake goes with it — one rule where there were two, and the rule Rust and C++ already have by their types, each taking a set by reference so the absent case is unrepresentable rather than checked. The equal-stake road keeps minting through the engine, whose committee is its own, and keeps ADMITTING on the arrival road, where signatures have already arrived to be weighed. THE WIDTH. SignerFloor and Quorum returned uint32 while counting a set held in an int, so the floor wrapped at about six billion signers and SignerFloor(Quasar, ~6.4e9) answered 1 — a floor a lone signer meets. They return int now and are narrowed only where a certificate is written, which is one place; and because the derived clause compares at full width, a mint that narrowed is caught by it rather than believed. THE LAST SECOND SPELLING. attestation.go's export trigger said config.TwoThirdsCount(n) where it means SignerFloor(Quasar, n). Same number, and that is the point: a trigger spelled apart from the rule it must never outrun is a trigger that can drift from it. TestTheDoorAdmitsWhatTheGateAdmits walks the four sizes where the two numbers part, on both arrival roads, and fails on the old filter at every one. Co-authored-by: Hanzo Dev <[email protected]>