Manuscript X-L-ST@1 · X-L-ST.tex · proposition · 20a32a22

Proposition: Preserved positive witness obstructs a restricted repair

Master residuals, reciprocity, and finite certificates › Two residuals with different types · lines 1377–1394 · proof included or linked

X-L-ST@1#prop:positive

Suppose permitted source corrections have reciprocity changes in a declared vector space $B$ . If

ℓ_{G} (B) = 0 (B \in B), β_{G} > 0,

then no permitted correction restores reciprocity on a domain containing the witness.

Proof. Every corrected pairing has evaluation $β_{G} + 0 > 0$ . It cannot be the zero bilinear defect.

Displayed formulas in this passage