Manuscript En01-A@1 · En01-A.tex · corollary · 558b972b

Corollary: Combinatorial screening and copy budget

Cross operators, fidelity, screening, and noisy architecture · lines 1405–1428 · proof included or linked

En01-A@1#cor:budget

If every supported $J$ -split pair has an inaccessible perfect member of a differing class, then $δ_{J} (S) = 0$ . Conversely, detection requires a supported $J$ -split pair satisfying

S \supseteq j \in D (r, r^{'}) ⋃ K_{j} .

In particular,

δ_{J} (S) > 0 ⟹ ∣ S ∣ \geq r < r^{'} J -split min j \in D (r, r^{'}) \sum c_{j} .

The minimum of an empty family is interpreted as $+ \infty$ .

Proof. Screening kills every summand of (eq:cross-expansion). If its sum is nonzero, at least one cross operator is nonzero. Proposition prop:screening then forces the stated containment.

Displayed formulas in this passage

unlabeled · line 1410
$S \supseteq j \in D (r, r^{'}) ⋃ K_{j} .$
unlabeled · line 1414
$δ_{J} (S) > 0 ⟹ ∣ S ∣ \geq r < r^{'} J -split min j \in D (r, r^{'}) \sum c_{j} .$

Corollary: Combinatorial screening and copy budget

Displayed formulas in this passage

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