1.5 Rehomed from the retired deterministic chapter
The retirement recorded on 2026-08-17 withdrew the manifest entries for the deterministic branch and kept exactly two, because the pivot keeps their claims. Those two moved here on 2026-08-21 when that chapter was deleted. Both are Paper 1 claims, so the trunk is where they belong; neither statement nor declaration changed in the move.
If each exposure deviates from a common map value by at most \(\tau _i\), the covariance floor holds with \(LD\) inflated to \(LD+\tau _i+\tau _j\), and exact transmission is the \(\tau =0\) case.
The statement fixes no characteristic distance: \(D\) is an arbitrary nonnegative dissimilarity, and energy distance was only ever one instance. Hosting it under the energy development misread that generality, which is why the declaration now lives in Transmission.Floor and the node here. Contrast ??thm:random-exposure-envelope, which is not distance-agnostic: the sharp envelope needs quadratic transport specifically, because minimising the coupling cost is the same optimisation polarisation turns into an inner product.
Triangle-inequality the deviations into the transmission bound, then polarize.
For a finite book with nonnegative weights, the pairwise floors aggregate termwise into a floor on the squared systematic risk. Nonnegativity is a hypothesis, not a convention: signed weights can reverse individual pairwise inequalities and there is no signed-weight counterpart. No weight normalization is assumed, so the screen applies a fortiori to fully-invested long-only books.
??chap:distance-implied carries its own label for this declaration under the distance-implied reading; the two manuscripts consume one theorem.
Sum the pairwise floor against the nonnegative weight products.