How much of one search the other has already found

Five pairs of searches on one sample, on a scale whose zero and one are both fixed by construction. Zero is two searches over disjoint sets of independent columns: they remove shares of the residual sum that add, at 0.8 standard errors from exactly additive, and they read 0.004. One is a break search paired with a step column it contains, which reads exactly one on every draw because the step adds nothing at all. Between them: two dictionaries of step columns cut a few rows apart read 0.125, and the pair the earlier field measured — a break and a whitening window, both reading the same residual series — reads 0.762, three quarters of the way to one search containing the other. And below zero, a break paired with a search over independent columns reads -0.306: the joint search finds configurations neither half of it contains, so charging the two separately under-charges.

The control at four dictionary sizes, over 600 draws apiece: the two shares added, minus the share the joint search removes, with two standard errors either side. Every reading is inside three standard errors of zero — -0.85, 2.40, 0.58, 1.68 — while what each search finds grows from 0.0142 of the residual sum at 2 columns to 0.0328 at 10. So the zero is not the zero of two searches with nothing to find. It is the zero of two searches whose findings occupy directions that do not overlap, which is what a scale's origin has to mean if the numbers above it are to be read as shares of one search that the other has already taken.