Manuscript XIV-C@1 · XIV-C.tex · section · a34d13df

A retained diagnostic fixed before extension

J0: the pair and extension contract › A retained diagnostic fixed before extension · lines 574–596

To ensure that the subsequent diagnostic belongs to the retained graph support, choose once

ε < t_{*} < t_{*} + 2 L < T, L > 0,

and the locations

u_{0} = (t_{*}, 0, 0, 0), y_{0} = (t_{*} + L, L, 0, 0), x_{0} = (t_{*} + 2 L, 2 L, 0, 0) .

Choose the original observation with $f (x_{0}) \neq = 0$ and the original switch equal to one near these locations, with compact interior support. All switches and observations are fixed now.

This is an admissible retained instance of the inherited pair. No cutoff is applied to its numerical triangle, and no coefficient is chosen after computing a value. The subsequent diagnostic concerns this fixed instance; no assertion that every observation retains the same configuration is needed.

Displayed formulas in this passage

unlabeled · line 578
$ε < t_{*} < t_{*} + 2 L < T, L > 0,$
unlabeled · line 582
$u_{0} = (t_{*}, 0, 0, 0), y_{0} = (t_{*} + L, L, 0, 0), x_{0} = (t_{*} + 2 L, 2 L, 0, 0) .$