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Reading both floors over the signers let a set shrink to its signers, and a rung whose floors are read over n is satisfiable at every n. TwoThirdsCount(1) is 1, so one signature over a one-signer set clears the count floor and the stake floor together and mints export finality. Byzantine tolerance is f = ⌊(n−1)/3⌋, which is ZERO for n of one, two and three: such a certificate absorbs no fault at all, and one compromised key among its signers forges it outright. So the export rung refuses a signing set below minBFTCommittee — the same constant bftCommittee floors committee SELECTION at, read at the certificate instead of at the sampler, and reused rather than restated. It is a floor on the SET, stated beside the n<1 refusal because neither quorum floor implies it: both are read over n and both shrink with it. Nova has no such clause and must not grow one — it authorizes local execution the chain can still reorg away, so a small or partitioned chain has to be able to make progress. A three-validator chain now PRODUCES and never CERTIFIES; operators need n ≥ 4 to export with any fault tolerance. Rust mirrors it as CertError::MinCommittee, which the corpus vocabulary folds into Go's one belowThreshold class. The transcription guard was reading the wrong denominator. verdict_test computed n as len(c.Set), the membership ROLL, so a floor moved onto the roll would agree with the guard and be re-blessed by -update — the second line of defence agreeing with the regression it exists to catch. It now counts the seats that hold a key, on the Quasar branch and the Nova one, and transcribes the committee floor as a search for the least n whose fault budget reaches one rather than as the constant. Proven by construction: with the corpus source reporting the roll as its signer count and the golden re-blessed, the old guard passes and the new one fails. The corpus could not have caught it either. quasar_keyless_third had three signers on a roll of four, and ⌊2·3/3⌋+1 and ⌊2·4/3⌋+1 are both three, so its count half was vacuous. Two rows now separate the denominators one at a time: quasar_keyless_stake (six signers, a seventh member holding a third of the roll — the count floor is five either way, so only stake decides) and quasar_keyless_count (four signers, two members holding one unit each — the stake clears under either reading, so only the count decides). TestKeylessRowsBind- BothDenominators fails if either is lost or flattened. quasar_keyless_third itself FLIPS to a refusal, and it is the row that states the new clause: the recorded stake floor is 200 over the three hundred that can sign and not 333 over the five hundred the chain carries, so the denominator IS the signers — and the certificate is refused anyway, on neither quorum floor. Reading the floors over the signers stops a spectator stranding a chain; it is not a way for a chain with three signers to export. Every other frozen verdict is byte-identical, and the admission section and the signed vectors are untouched. StakeSource gains CarriedStake, and no floor may read it. SignerStake alone decides a certificate correctly and cannot show the set shrinking underneath one: a chain whose signable stake has fallen to a sliver of what it carries still certifies at ⅔ of the sliver, and ResponsiveStakePct — voted over signer — stays at one the whole way down. FinalityStatus.SignerStakePct is the number that falls, and the one to alarm on. Rust has carried(), C++ has total_stake(); Go had lost the projection when the denominator moved. Co-authored-by: Hanzo Dev <[email protected]>