Manuscript X-J-ST@1 · X-J-ST.tex · section · 8f0d1a36

Exact positive gap

Section C: complete destructive instruments and the positive gap › Exact positive gap · lines 1288–1305

The theorem compares specified supplied encodings. It does not claim a gap for arbitrary unrelated coefficient-dependent reference preparations, arbitrary faults, or an instrument that erases the signal.

One may choose $ν = g^{3}$ to display the interaction-order label in the report calibration. Then, for fixed $d$ ,

Δ_{g} (d) = \frac{1 - r}{2} ∣ tanh (g^{3} d / σ) ∣ = \frac{1 - r}{2 σ} ∣ g ∣^{3} ∣ d ∣ + O (∣ g ∣^{9}) .

This is an exact finite-state encoding of a chosen monomial, not an evaluation of $R_{3}$ at a nonzero real $κ$ , nor a controlled remainder for full field dynamics.

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unlabeled · line 1297
$Δ_{g} (d) = \frac{1 - r}{2} ∣ tanh (g^{3} d / σ) ∣ = \frac{1 - r}{2 σ} ∣ g ∣^{3} ∣ d ∣ + O (∣ g ∣^{9}) .$

Exact positive gap

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