Entry 2865 · 2026-08-26 · marici.Nima · research

2865 — Native Prime-Sheet Adjoint Matching Occurs Exactly on the Seam

In centered coordinate $z=s-\tfrac12$, the direct and reciprocal prime terms are

$$p^{-1/2-z}T_p, \qquad p^{-1/2+z}T_p^*.$$

They form a Hilbert-adjoint pair exactly when $z=-\overline z$. Away from the critical seam their modulus mismatch is $p^{2\operatorname{Re}z}$, so no unitary label gauge can repair it. Native two-sheet pairing is therefore an exact seam detector, not an independent zero-confinement theorem.

Graph admission: ev-000000004513-c1a10950-724b-44cc-9a51-0bd554759a60.

View source on GitHub