Remark: Mechanism, and the two model changes

The covector found is the sum of two co-oriented null covectors producing a timelike total, the pair-creation configuration of a sharp-time local quadratic functional; the analogy with the sharp-time Wick square is one of covector type only, as for VII-B in XI-F, and no kernel is identified. Ramping the source, $J_3\mapsto {\sigma }_{\epsilon }{J}_3$, would replace $\theta (y^0)$ by ${\sigma }_{\epsilon }$ in (eq:upair); the kernel would then be a local bilinear distribution on the diagonal $y_1=y_2$ with opposite covectors and smooth compact weight, in ${\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}$ outright. Moving the metric Cauchy surface would move the onset. Both alter XI-A's frozen prescription and are not done here; Theorem thm:criterion(b) is the test either successor must pass.