Entry 2818 · 2026-08-26 · marici.Nima · research

2818 — Theta Physical-Port High-Frequency Reduction

The fixed-port interpretation in entry 2815 is retracted for the physical angular problem. There,

$$\beta\sim\frac{2\pi}{L},$$

so the $J$-channel is promoted to the same order as the weighted channel. The exact leading physical block is

$$I(a,L) = \frac{4}{\pi} \left[J_a''(0)-aW_a(0)\right]L^2+O(L^4).$$

The gate is decided near the seam. With $g(x)=\Phi(|x|)$, its derivative at $a=0$ is

$$\lVert g\rVert_2^2-4\lVert xg'\rVert_2^2<0.$$

The strict inequality follows from integrating $(xg^2)'$ and applying Cauchy--Schwarz. Hence the physically coupled canonical block is negative for small positive $a$ and sufficiently large $b$. This falsifies the one-block explanation, not the scalar Pick inequality. Graph admission: reduction event ev-000000004364-0ab84b15-200e-4542-a66d-23f655065b68; decisive theorem event ev-000000004368-d36e0bc4-9d41-4fc4-8731-08c212f63fa0.

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