Manuscript XV-B@2 · XV-B.tex · proposition · 4d3f12e8

Proposition: Exact unrestricted contact-valued criterion

Contact support and domain-sensitive transfer › The contact obstruction · lines 618–635 · proof included or linked

XV-B@2#prop:allcontacts

If $C \subset W ∖ O$ and $A = Hom (P_{int}, V_{C})$ , a descending candidate exists if and only if $F_{0} (H) \subset V_{C}$ .

Proof. If $F_{0} + a$ annihilates $H$ , then $F_{0} (A) = - a (A) \in V_{C}$ for $A \in H$ .

Conversely, assume $F_{0} (H) \subset V_{C}$ and choose the algebraic projection $π_{H}$ used above. Then

a = - F_{0} ∣_{H} π_{H}

is contact-valued and cancels the defect.

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