Manuscript II@2 · II.tex · section · 50d64def

Quantifiers

Problem and contribution › Quantifiers · lines 302–324

II@2#eq:global-quantifier

Let

C = span_{R} {n_{ℓ} : ℓ = 1, \dots, 15120} \subseteq R^{X} .

Global membership means

\exists α \in R^{15120} \forall β \in X : m (β) = ℓ \sum α_{ℓ} n_{ℓ} (β) .

The coefficients are constant across external labels.

Our certificate replaces $X$ by the particular family $S$ . It uses one coefficient vector for all three labels, not a separately chosen vector at each row. Nevertheless, it does not establish (eq:global-quantifier).

Displayed formulas in this passage

II@2#eq:global-quantifier · line 310
$\exists α \in R^{15120} \forall β \in X : m (β) = ℓ \sum α_{ℓ} n_{ℓ} (β) .$
unlabeled · line 305
$C = span_{R} {n_{ℓ} : ℓ = 1, \dots, 15120} \subseteq R^{X} .$