Enabling Cross-Silo Innovation for the Clay Navier–Stokes Millennium Problem: a public specification resolving ambiguity in the PDE Dialect

The Clay Mathematics Institute Navier–Stokes millennium problem statement (CPNS) is written in the specialized dialect of PDE regularity theory. This dialect is powerful and efficient for insiders, but it carries binding semantics through tacit defaults (Lebesgue measure for dx, equality almost everywhere, Sobolev objects as equivalence classes, weak–strong hierarchies, and pressure gauge conventions). Fefferman’s closing remarks emphasize that standard PDE methods appear inadequate and that progress likely requires deep new ideas, which implicitly invites cross-disciplinary contributions. We argue there is a contract-level contradiction: CPNS invites outside help while encoding key obligations in insider dialect, thereby increasing the risk that a correct cross-field solution is rejected as solving the wrong problem. The published erratum for Eq. (8) (periodic pressure) provides concrete evidence that required semantics were not derivable from the surface text even for insiders, and that fixes do not automatically propagate to all dependent clauses. We propose a minimal invariance layer that makes the intended semantics explicit without changing PDE content. We also propose a Gödel-flavored framing: if one treats CPNS plus the PDE-native proof algebra as a closed theory TNS, then the prize claims may be semantically definite yet unprovable within TNS without importing non-native structure. The point is not Gödel-cosplay. The point is to name the missing-axiom problem that dialect boundaries create when a public statement is adjudicated under implicit conventions.