Manuscript Oai272-A@1 · Oai272-A.tex · proposition · a40828a0

Proposition: A priced coherence defect

The uniform gap and its exact finite certificate › The rational terminal certificate · lines 990–1008 · proof included or linked

Oai272-A@1#prop:defect

If the same normalized output instead satisfies

f \leq e (1 - e) + e + κ, κ \geq 0,

then

η \geq max {0, 1/5 - 2 κ} .

Proof. The case $e \geq 1/10$ gives $η \geq 1/5$ . For $e \leq 1/10$ , the upper bound is $f \leq 2/5 + κ$ , while $η \geq 1 - 2 f$ .

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