Manuscript Hawk05-B@1 · Hawk05-B.tex · section · f2e5d4f5

Repairs to the supplied Hawk05-A and refined plan

Enter background and the corrected target › Repairs to the supplied Hawk05-A and refined plan · lines 172–221

The supplied Hawk05-A is a useful foundation, but its flagged calibration theorem contains an obsolete reversed-weight equation. That false equation must be removed from the theorem statement, rather than retained alongside its correction.

{}1.12

Issue	Repair in Hawk05-B
Residual leakage versus residual recovery	For occupied residual probability $q$ , $δ_{full} (C_{q}) = q (1 - d^{- 2})$ , whereas $ε_{rec} (C_{q}) = (1 - q) (1 - d^{- 2})$ . These are different optimizations.
Any discrete schedule from $q = 1$ to $q = 0$ has a peak at $1/2$	A discrete schedule can skip $1/2$ , or jump directly from one to zero. Only a continuous crossing guarantees that point. A single-excitation turnover is not an extensive Page law.
Snapshot readout equals a cumulative history	A refined emission-time record can have the same recovery optimum as a coarse snapshot while having a different Shannon entropy. The complete history is computed explicitly below.
Averaged entropy equals entropy of the averaged state	The Page quantity is $E_{U} S (ρ_{R}^{U})$ , not $S (E_{U} ρ_{R}^{U})$ . The latter is $lo g_{2} dim R$ in this model.
A pure-input Page curve certifies the whole code	Its input is fixed independently of $U$ . Whole-code recovery quantifies over every referenced input. The two quantifiers cannot be interchanged.
A conditional-entropy bound locates maximal leakage	Without a channel comparison, a conditional-entropy inequality does not locate a maximum of complete-complement diamond leakage.

The corrections to destructive records, complete complements, and endpoint identification agree with the distinctions in Cheung's Hawk and En07 manuscripts CheungHawk02B,CheungHawk04D,CheungEn07B,CheungEn07C. All elementary mathematical statements used below are proved locally.