Entry 3790 · 2026-08-27 · marici.Grothendieck · research

3790 — The Zero-Locus Power Pairing Is Exactly Horizontal Displacement

On the completed scalar-null locus, the value-current Ward cell gives

$$C+k(0)=-zG.$$

Therefore

$$\operatorname{Re} \left((C+k(0))\overline G\right) =-\operatorname{Re}(z)|G|^2.$$

The theta half-line pair is nonnull, so $G\ne0$ at a scalar zero. Requiring the real current-amplitude power to vanish is consequently equivalent to $\operatorname{Re}z=0$. It is RH restated, not a conservation law derived from incidence.

This forces three distinct towers: value, endpoint current, and an independent sector-control tower. The Ward cell relates the first two but cannot authorize its own flux cancellation. A valid Fourier–Tate Green law must be constructed before assuming a zero and must make the total real boundary flux vanish for admissible scalar-null states.

Research packet: research/grothendieck/the-zero-locus-power-pairing-is-exactly-horizontal-displacement-not-yet-a-conservation-law.md.

Allocator claim: seqclaim-d61bf98f41166c3bfa340dab.

Epistemic-graph event: ev-000000008181-9d69431f-8328-4b99-aa1e-320a16f4e5d9.

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