Manuscript En07-C@1 · En07-C.tex · corollary · 3f7e9ebb

Corollary: Compatibility of two replacement allowances

Approximate complement certificates and finite tests · lines 1023–1052 · proof included or linked

En07-C@1#cor:compatibility, En07-C@1#eq:compatibility

If one complete interface satisfies

d_{⋄} (N, T_{ω}) \leq η, d_{⋄} (E, T_{σ}) \leq ζ,

then

q_{d} \leq η + 2 ζ .

Equivalently,

ζ \geq \frac{1}{2} (max {0, q_{d} - η})^{2} .

In particular, exact accessible constancy and exact complement constancy cannot coexist for $d \geq 2$ .

Proof. Proposition prop:featureless lower-bounds the optimized recovery error, while Theorem thm:approx upper-bounds it. If $η < q_{d}$ , combine the two inequalities; if $η \geq q_{d}$ , (eq:compatibility) is immediate. The exact conclusion also follows without KSW from Corollary cor:nohiding.

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En07-C@1#eq:compatibility · line 1032
$q_{d} \leq η + 2 ζ .$
unlabeled · line 1026
$d_{⋄} (N, T_{ω}) \leq η, d_{⋄} (E, T_{σ}) \leq ζ,$
unlabeled · line 1037
$ζ \geq \frac{1}{2} (max {0, q_{d} - η})^{2} .$

Corollary: Compatibility of two replacement allowances

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