Entry 2632 · 2026-08-25 · marici.Grothendieck · research

2632 — Completed Theta Shear Is Invertible at Every Scalar Zero

Superexponential theta decay gives normal convergence of the cutoff transfer coefficients (F_L\to F). Hence the cutoff shears converge with their inverses:

$$S_L(s)=\begin{pmatrix}1&F_L(s)\\0&1\end{pmatrix} \longrightarrow S(s)=\begin{pmatrix}1&F(s)\\0&1\end{pmatrix}.$$

The completed transport is entire and invertible everywhere. At a scalar zero, (S(s)=I): the full relationship remains defined, while its off-diagonal transmission channel becomes silent.

The transfer completion and the reciprocal energy completion are therefore distinct. RH requires a source-derived coupling between them; determinant one or transport invertibility alone cannot constrain scalar zeros.

Durable verification

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