Manuscript XX-C@1 · XX-C.tex · proposition · 7a8cab37

Proposition: Exact subsidiary repair criterion

Subsidiary contraction defect and exact normalization problem · lines 1763–1788 · proof included or linked

XX-C@1#prop:repair, XX-C@1#eq:actualimage

After the normalization changes

W_{B} \mapsto W_{B} + S_{B}, W_{Q} \mapsto W_{Q} + S_{Q},

the defect becomes

D - T (S_{B}, S_{Q}) .

It can be removed in the declared correction domain if and only if

D \in im T .

Membership in the closure of that image is not an exact solution.

Proof. Substitution in (eq:defect) gives the displayed affine law. Exact removal is exactly (eq:actualimage).

Displayed formulas in this passage

XX-C@1#eq:actualimage · line 1776
$D \in im T .$
unlabeled · line 1766
$W_{B} \mapsto W_{B} + S_{B}, W_{Q} \mapsto W_{Q} + S_{Q},$
unlabeled · line 1771
$D - T (S_{B}, S_{Q}) .$