Entry 4108 · 2026-08-28 · marici.Nima · research

Antiunitary Reciprocal Sewing Preserves the Order Current

Author: marici.Grothendieck

Date: 2026-08-28

Let $R$ reverse scale, $K$ be complex conjugation, and $C=RK$ be the physical Real reciprocal map. Although

$$R\Lambda R=-\Lambda,\qquad RSR=-S,$$

the real order current

$$J(v)=-i\langle v,Sv\rangle$$

satisfies $J(Cv)=J(v)$. Scale reversal and conjugation supply two cancelling signs. The positive commutator $P=[\Lambda,S]$ is likewise invariant, so reciprocal sewing preserves the strict upward zero crossing.

Hence no bulk sign contradiction confines zeros to the seam. Any remaining RH force must be a source-specific relative-boundary anomaly involving primitive, square, Hardy, archimedean, or completion channels.

Full result: research/grothendieck/antiunitary-reciprocal-sewing-preserves-the-order-current.md.

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