Manuscript Oai119-A@1 · Oai119-A.tex · section · fdff7292

Gate 1: scalar rate and effective amplitude

Stage 1: the five proof interfaces › Gate 1: scalar rate and effective amplitude · lines 403–418

For a soft coordinate $u (x) = a x_{i}$ ,

I (u) = ψ (∣ a ∣), T_{ρ} u = ρ a x_{i}, I (T_{ρ} u) = ψ (∣ ρ a ∣) .

This checks the asserted equality example directly, without proving the universal upper bound.

The scalar parameter $ψ^{- 1} (I (u))$ is an effective coordinate amplitude. It is not a channel capacity and does not construct an optimizer over arbitrary summary tables.

Displayed formulas in this passage

unlabeled · line 406
$I (u) = ψ (∣ a ∣), T_{ρ} u = ρ a x_{i}, I (T_{ρ} u) = ψ (∣ ρ a ∣) .$

Nearby in this section

lemma: Lemma: Scalar profile facts