2854 — A Scalar Zero Is a Completion-Class Jump of the Prime Boundary Current
Every finite two-prime boundary-cocycle square closes exactly. At infinite prime completion, however, the reciprocal depth-(k) current has leading term
where the prime sum of (R_{k,p}) converges absolutely.
Thus the primitive and prime-square currents diverge when (X(z)\ne0), while both become summable exactly when (X(z)=0). The connected (k\ge3) tail is always summable.
A scalar zero is therefore an exact completion-class transition of the global boundary current. The remaining RH question is why this regularity upgrade could occur only at the unitary Tate seam.
Graph admission: ev-000000004473-1a4faa86-0b47-4210-988b-fe2d391f14a3.