SymmetryClassImpossibleHypothesis
plain-language theorem explainer
SymmetryClassImpossibleHypothesis encodes the rule that any solution left invariant by a nontrivial symmetry action up to finite time T must produce a trivial event. Navier-Stokes workers on the RM2U closure cite it to block symmetric parasitic modes before invoking the tail-flux condition. The declaration is a bare structure definition that packages the single elimination implication with no lemmas or proof body.
Claim. Let $Sol$ and $Sym$ be types, $Act:Sym→Sol→Sol$ an action, $Nontrivial:Sym→Prop$, $CoincideUpTo:Sol→Sol→ℝ→Prop$, and $TrivialEvent:Prop$. The hypothesis asserts that for every $u:Sol$ and $T:ℝ$, if there exists nontrivial $g$ such that $Act(g,u)$ coincides with $u$ up to time $T$, then $TrivialEvent$ holds.
background
The module isolates the single hard non-parasitism gate for the RM2U to RM2 pipeline. Non-parasitism is the statement that the tail-flux or boundary term at infinity vanishes for the relevant ℓ=2 coefficient, written in Lean as TailFluxVanish. Upstream results supply T as fundamental periods (Breath1024) and as triangular numbers (Gap45.SyncMinimization), together with Act as the RS-native quantity action.
proof idea
This is a definition with no proof body. It directly constructs the Prop from the single elim field that encodes the implication from existence of nontrivial g with CoincideUpTo to TrivialEvent.
why it matters
The structure supplies the E-gate hypothesis that lets the remainder of the RM2U.NonParasitism file stay checkable. It feeds the NonParasitismHypothesis sibling and the overall RM2 closure. In the Recognition Science setting it enforces exclusion of symmetry-invariant candidates before the eight-tick octave and D=3 constraints are applied downstream.
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