The Poincaré Precedent and the Stronger Case: Why All Seven Qualify

A Millennium question is answered in two domains. In the kernel of Lean 4 a statement is a theorem or a premise, and the checker reads no reputation. In the record a statement stands resolved when the community and its institutions accept a delivery of it. The Poincaré row holds both domains in one line of Mathlib v4.19.0, which declares the three-dimensional Poincaré theorem `proof_wanted` under the docstring "proven by Perelman", while the Clay Mathematics Institute accepted Perelman's derivation as unconditional on 18 March 2010. In the kernel the Poincaré bit stands at premise grade with the other six bits of the Millennium series, on one footing. This note states the precedent exactly and argues the stronger case. The master of the series types the accepted derivation: the 2002 functional is a downstream strict subtype of the bridge, Perelman's offering is one inhabitant strictly inside the bit, its faithful route strictly stronger than the sentence, and the bit is the minimal premise, necessary and sufficient. The record accepted the stronger premise, delivered once and verified by human reading. Each of the six bits is the minimal premise, delivered twice, by the formal cargo and by the physical witness; its form, its walls and both deliveries' implications are checked by the kernel; and it is armed, one counterexample refuting both kinds at once. The precedent transfers as a rule and never as a value: the seven values are independent, all 128 patterns realized, and the Poincaré value settles no other row. No blessing inside the kernel lifts any bit, since adopting the bit is adopting the sentence and the admission screen refuses it as circular; the record's road is the other road. A mini case of twenty-one theorems in core Lean 4, every cone empty and pinned, proves the shape of every step in about a second. The six bits qualify for the same standing, on the stronger case, and the Poincaré precedent is claimed for all seven.