note_modVacuumSectorsRemainOpen

Module setting is Wave C3 gap5: the unconditioned CanonicalMom rigidity statement is false. The killer is a vacuum-shift density at $n=2$,

$$h(a,b,p)=\tfrac12\bigl(p^2+(1+a^2)(b-a)^2\bigr)+a^2,\quad g(a)=1+a^2,$$

with $m_j=\pi_{j+1}(q_{j+1}-q_j)$ and $c_{\mathrm{Mom}}=1$. The ham–ham alternating functional equation is blind to the zero-gradient vacuum term $a^2$; at coincident configurations the density evaluates to $q^2$ (nonconstant), so rigidity cannot force a constant vacuum.

The repaired terminal is only defined: rigidity modulo vacuum at $N=2$. Whether structure_nonconstant plus the FE forces the kinetic/gradient sectors is left open. The sibling note states that ContDiff-2 + FE alone do not force those sectors (the sqrt-affine profile is blocked from CanonicalMom only by $g\equiv 1$), and that C4 supersedes this: structure_nonconstant also fails to close mod-vacuum via the variable-kinetic kill.

One-line term proof. The named note is defined as the proposition True, so trivial inhabits it. No lemmas are applied; the declaration is a bookkeeping marker, not an argument about densities or brackets.

Holds the honesty wall for gap5 after the vacuum-sector kill of unconditioned CanonicalMom rigidity. It records two successive limits: ContDiff-2 + FE do not pin kinetic/gradient sectors, and C4 shows structure_nonconstant also fails to close the problem modulo vacuum (status lives with the kill in the kinetic-normalized rigidity module). Downstream use count is zero; the note exists so auditors do not treat the repaired mod-vacuum statement as a full rigidity theorem, and so gap5_constraint_recovery is not flipped. In the SevenGaps gravity ledger it marks open mathematics rather than a closed forcing step (contrast T5–T8 uniqueness landmarks elsewhere in the chain).