Entry 4183 · 2026-08-27 · marici.Nima · research

4183 — The Moving-Seam Prefix Current Gives a Canonical Mixed-Prime Difference Cocycle

For any two prime-power-marked cuts $a,b$, define

$$C_z(a,b)=\mathcal K_b(z)-\mathcal K_a(z).$$

Because both values come from one completed theta prefix current,

$$C_z(a,b)+C_z(b,c)=C_z(a,c), \qquad C_z(b,a)=-C_z(a,b).$$

Every mixed-prime cycle therefore telescopes, and inserting or deleting refinement cuts leaves the total unchanged. Moreover, each cell is exactly the integrated relative Green response over its interval.

This closes mixed-prime gluing for the continuous moving-seam current in the common archimedean frame. Arithmetic primitive/square grades and the zero-to-total-flux bridge remain separate.

Checker result: 400/400.

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