Manuscript X-Enter-ST@1 · X-Enter-ST.tex · section · f76acc1f

The retained-order diagnostic

Stage C: the retained finite amplitude trial › The retained-order diagnostic · lines 813–831

X-Enter-ST@1#eq:Hadamard

Hadamard followed by destructive readout is a useful countercheck:

Pr (1 ∣ a) = \frac{1 - sech ( a / σ )}{2} = \frac{a ^{2}}{4 σ ^{2}} + O (a^{4}) .

Its first derivative vanishes at zero, but its law is not invariant.

The theorem is an encoding expansion, as in X-Enter XEnter (:secondorder). It is not a new second-order calculation of the convolution prescription, and its remainder is not uniform in unbounded $λ$ .

Displayed formulas in this passage

X-Enter-ST@1#eq:Hadamard · line 817
$Pr (1 ∣ a) = \frac{1 - sech ( a / σ )}{2} = \frac{a ^{2}}{4 σ ^{2}} + O (a^{4}) .$

Nearby in this section

theorem: Theorem: Second-order encoding test