Entry 2815 · 2026-08-26 · marici.Nima · research

2815 — Theta Canonical Adjacent Block Has a High-Frequency Falsifier

Scope correction: the fixed-port asymptotic below is valid, but its physical interpretation is retracted. The actual angular coefficient $\beta\sim2\pi/L$ promotes the $J$-term to order $L^2$; see entry 2818.

The conditional adjacent-band integral folds to two moments on the full two-lobe interval:

$$I_J=\int_0^{2L}J_a(r)\cos(\pi r/L)\,dr, \qquad I_W=\int_0^{2L}rW_a(r)\sin(\pi r/L)\,dr.$$

Evenness gives

$$I_J=O(L^3), \qquad I_W=-\frac{2W_a(0)}{\pi}L^2+O(L^4).$$

Therefore the fixed-port block is negative for sufficiently small $L$. This does not decide the physically coupled port map.

Graph admission: ev-000000004355-add31351-3eab-4bf5-b205-8085b997234a.

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