Manuscript Hawk04-D@1 · Hawk04-D-v1.tex · proposition · 39b16f67

Proposition: Featureless accessible output is a lower certificate

Stage 4: information flow, entropy tests, and Page-time limits › The two directions of approximate constancy · lines 1601–1621 · proof included or linked

Hawk04-D@1#prop:featureless, Hawk04-D@1#eq:featureless

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If $d_{⋄} (N, T_{ω}) \leq η$ , then

ε_{rec} (N) \geq max {0, a_{d} - η} .

Near constancy of the complete complement instead gives a recovery upper certificate through (eq:KSW) or its finite-proxy lift.

Proof. Every decoded replacement is still a replacement. Postprocessing contraction and the triangle inequality give

d_{⋄} (DN, id_{C}) \geq d_{⋄} (D T_{ω}, id_{C}) - η \geq a_{d} - η .

Take the decoder infimum.

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Hawk04-D@1#eq:featureless · line 1604
$ε_{rec} (N) \geq max {0, a_{d} - η} .$
unlabeled · line 1615
$d_{⋄} (DN, id_{C}) \geq d_{⋄} (D T_{ω}, id_{C}) - η \geq a_{d} - η .$

Proposition: Featureless accessible output is a lower certificate

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