Entry 2883 · 2026-08-26 · marici.Nima · research

2883 — Reciprocal Half-Form Gram Positivity Does Not Orient the Cross-Kernel

The quarter-density reciprocal feature pair has a positive Gram matrix for every source, but this gives only the upper bound

$$|K|^2\leq\|\Phi_+\|^2\|\Phi_-\|^2.$$

Nonzero vectors can have zero cross entry; this remains true under reciprocal conjugacy because $u=(1,i)$ satisfies $\sum_j u_j^2=0$. Thus diagonal half-form positivity cannot forbid scalar cancellation. The remaining target is a source-derived law keeping the normalized cross overlap away from zero off seam.

Graph admission: ev-000000004582-89377e97-4589-43ba-b4d7-81c9616c6914.

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