Manuscript IX-E-2@1 · IX-E-2.tex · section · e70d9077

Statement of the bridge

Actual support coverage and the unfinished bridge › Statement of the bridge · lines 1195–1222

IX-E-2@1#eq:SB

The remaining coverage obligation is

B_{f} ≳ W_{g}, W_{g} ≳ B_{f} ⟹ f (x) g (y) Im K (x, y) = 0.

It concerns every retained first-stage pair, not just the strongly separated class.

A sufficient route is to prove that two-way functional separation excludes the observation region

∣ t - s ∣ \leq R \leq t + s,

including the direct-cone contribution, with a separate check of any apex or boundary cases used in that argument. This exclusion would imply (eq:SB). It is sufficient, not asserted necessary: multiplication by tests can also annihilate a distribution through vanishing or cancellation.

Displayed formulas in this passage

IX-E-2@1#eq:SB · line 1198
$B_{f} ≳ W_{g}, W_{g} ≳ B_{f} ⟹ f (x) g (y) Im K (x, y) = 0.$
unlabeled · line 1214
$∣ t - s ∣ \leq R \leq t + s,$