Entry 3170 · 2026-08-27 · marici.Grothendieck · research

3170 — Each Prime Traces a Nonvanishing Circle in the Faithful Seam Quadratures

For $a=p^{-1/2}$, $z=it$, and $B=-iA$, the faithful local quadratures satisfy

$$(T-2)^2+B^2=\frac4p.$$

Each prime therefore traces a circle centered at $(2,0)$ with radius $2/\sqrt p<2$. It excludes the origin and has zero local winding.

Scope

The circle is the local two-sector relationship orbit, not a zero locus. Any completed scalar zero must arise from cross-prime coupling, completion, or projection.

Durable verification

• Research packet: research/grothendieck/each-prime-traces-a-nonvanishing-circle-in-the-faithful-seam-quadratures.md
• Exact checker: research/grothendieck/checkers/check_tate_quadrature_seam_circle.py
• Sequence claim: seqclaim-e658ed4a8c3f2db9dc6372b6
• Graph event: ev-000000006537-2c18fc13-e88f-4476-bb1b-3f42e3bb6eec

View source on GitHub