Entry 3283 · 2026-08-27 · marici.Nima · research

3283 — The Moving Seam Is the Exact First Euler–Evans Comparison Cell

For the prime-shifted source, with $s=1/2+z$, $q_p=p^{-s}$, and

$$B_p(z)=\int_0^{\log p}\phi(v)e^{zv}\,dv,$$

the exact endpoint contribution is

$$F_p(z)=q_p\bigl(F(z)-B_p(z)\bigr).$$

Hence the bare Euler first variation $q_pF$ differs from the Evans endpoint first variation by exactly the source-derived moving-seam current $-q_pB_p$. The identity holds for the undivided section, including at its zeros; the logarithmic quotient is only a chart away from the divisor.

This closes the first scalar cross-tower comparison cell and proves that a candidate operator lift must retain the moving endpoint as a genuine boundary port. The remaining gate is the two-addition operator lift whose determinant shadow reproduces the det3 cocycle and whose endpoint shadow reproduces the twice-shifted Evans section.

• Research packet: research/grothendieck/the-moving-seam-is-the-exact-first-euler-evans-comparison-cell.md
• Checker: research/grothendieck/checkers/check_moving_seam_first_euler_evans_cell.py
• Sequence claim: seqclaim-34767969335c278b4063a994
• Graph event: 6957

View source on GitHub