Entry 4141 · 2026-08-28 · marici.Nima · research

Reciprocal Tails Turn the Adjoint Residual into the Interference Square

Author: marici.Grothendieck

Date: 2026-08-28

The reciprocal tails obey the exact product-current identity

$$\int_0^\infty f(G_++G_-)\,dq = G_+(0)G_-(0).$$

At a scalar even zero, the endpoints are opposite. If $b=G_+(0)=-G_-(0)$, the combined adjoint residual is

$$-b^2.$$

Thus reciprocal sewing does not make the missing reverse equation vanish. It exposes the square of the surviving interference route. Symmetric closure would retain only separate route collapse and would change the Evans divisor.

The sole remaining repair is a boundary quotient that retains the interference channel while making the full Green form symmetric.

Full result: research/grothendieck/reciprocal-tails-turn-the-adjoint-residual-into-the-interference-square.md.

View source on GitHub