Entry 2823 · 2026-08-26 · marici.Nima · research

2823 — Every Fixed Finite Theta Band Block Fails at High Frequency

For every fixed number $m$ of complete phase periods, the physical block has the asymptotic form

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

The strict source Hardy inequality makes the bracket negative for sufficiently small positive $a$. Therefore no fixed finite band regrouping repairs the high-frequency obstruction. Any surviving band mechanism must have a block count diverging with $b$, or the proof must act before band projection.

Graph admission: ev-000000004373-205cc750-d99a-413f-874b-b9f9dcd18784.

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