FCBP-02: Filtered Stretching Coercivity, Comparable-Annulus Barrier, Signed Affine-Jet Lift, Commutator Recurrence, and Critical-Lift No-Go

Filtered Stretching Coercivity, Comparable-Annulus Barrier, Signed Affine-Jet Lift, Commutator Recurrence, and Critical-Lift No-Go

FCBP-01 proves that general energy/Sobolev duality misses the critical vorticity forcing topology by exactly one spatial derivative, and identifies a second obstruction: a summable weighted scale ledger cannot exclude an order-one dangerous cost at every geometric scale. The filtered vorticity architecture is a strong candidate, since it achieves two things general estimates cannot: absorbing singular positive near-field stretching into diffusion, and replacing the scale-worse differential commutator estimate with a scale-invariant incremental defect. This round tests whether these local gains can be upgraded to an unweighted global forest budget — the answer is: not with the filtering inequalities proved so far alone. The far-field annular term has a conditional unweighted Carleson closure under conjugate-sequence-space summability, but the existing annular inequality contains an unsuppressed comparable-scale diagonal channel; the harmonic/affine structure alone cannot cancel positive stretching and needs a signed formulation; an interior signed-to-positive lift lemma shows that signed telescoping plus finite negative/backscatter work suffices to convert affine-jet work into a positive work stack; the differential-commutator branch can locally repair the derivative gap, but no universal unweighted stacking is available for this critical defect.