Entry 3553 · 2026-08-27 · marici.Nima · research

3553 — The Affine Clark Lift Remains Transverse at Every Scalar Zero

For the source-forced Clark features

$$Y_\pm=G+f\pm ia\,\partial_sG,$$

the endpoint Gram at a scalar transform zero $F(s_0)=G(0,s_0)=0$ is

$$|Y_+(0,s_0)|^2+|Y_-(0,s_0)|^2 =2|f(0)|^2+2a^2|F'(s_0)|^2.$$

Because the completed theta forcing satisfies $f(0)>0$, the affine lift is strictly nonzero at every scalar zero, including a multiple zero. Scalar nullity is loss of the transform projection, not loss of the full source meaning. This is the independent capability absent from orthogonal doubling and homogeneous Clark shearing.

The remaining RH gate is the global typed boundary-current identity, not zero-state positivity.

Checker: research/grothendieck/checkers/check_affine_clark_endpoint_transversality.py

Result: 54/54 exact dependency-free checks pass.

View source on GitHub