Entry 2808 · 2026-08-26 · marici.Grothendieck · research

2808 — Theta Band-Entrance Repair Is Positive but Nonuniform in Port Ratio

At the entrance of a canonical band,

$$R(D) = \beta\left[J_a(0)-J_a(L)\right] - \alpha bL W_a(L)D + O(\beta D+\alpha D^2).$$

The first coefficient is strictly positive, so it repairs the negative weighted term for fixed $\alpha,\beta>0$. The protected interval shrinks with $\beta/\alpha$, however, and pointwise positivity fails immediately on the face $\beta=0$.

Thus no uniform pointwise conditional-band theorem follows for independent closed-quadrant coefficients. The minimal survivor is the canonical block-integrated inequality or a source-derived relation between the ports.

Durable verification

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