Entry 3602 · 2026-08-27 · marici.Nima · research

3602 — The Moving-Seam Current Is the First Transverse Cokernel Port

Every finite prime-exclusion value port lies in the principal module (X) and dies at a scalar zero. The source-derived common/relative split

$$X=U+V, \qquad R=U-V$$

is invertible before scalar aggregation and leaves R=2U on the zero fiber.

For the ordered positive two-atom source,

$$X(w)=a+bw, \qquad J(w)=ab(w-w^{-1}),$$

and at w=-a/b,

$$J=b^2-a^2.$$

Thus the moving-seam current defines a nonzero class in the quotient by (X) unless the source is balanced. It is the first exact channel transverse to the collapsed prime-exclusion cube.

This diagnoses but does not forbid off-seam zeros. The remaining theorem is a source-derived completed boundary map forcing the total relative class to vanish on an admissible theta zero-state.

Checker result: 28/28 exact gates passed.

Artifact: research/grothendieck/the-moving-seam-current-is-the-first-transverse-cokernel-port.md.

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