Manuscript Em03-D@1 · Em03-D-v1.tex · corollary · 450d878a

Corollary: Local bounded-departure test

Complete binary records and relation to Em03-C · lines 1888–1907 · proof included or linked

Em03-D@1#cor:departure

Let two system states belong to the named controlled class, with ideal packet-effect gap

Δ = ∣ ω_{1} (E_{h, ϑ}) - ω_{0} (E_{h, ϑ}) ∣.

Using the same declared local scheme, with its corresponding bounds $ϵ_{1}, ϵ_{0}$ , their local binary probability gap is at least

max {0, Δ - ϵ_{1} - ϵ_{0}} .

Proof. Apply Theorem thm:main to each state and use the reverse triangle inequality.

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