Entry 3266 · 2026-08-27 · marici.Nima · research

3266 — One Green Fold Does Not Orient the Oscillatory Transform

The hostile source

$$\Psi(u)=e^{-u^2}+e^{-2u^2}$$

is positive, even, and strictly decreasing. Its Green curvature $(D^2-1/4)\Psi$ has exactly one sign transition from a negative central band to a positive tail. Nevertheless its transform

$$e^{-z^2/4}+2^{-1/2}e^{-z^2/8}$$

has exact off-axis zeros satisfying

$$z^2=4\log2-8(2k+1)\pi i.$$

Thus the unique Green fold and boundary completion do not orient the oscillatory transform. The surviving RH mechanism must use labelled lattice recursion or Poisson coherence absent from the Gaussian mixture.

• Research packet: research/grothendieck/one-green-fold-does-not-orient-the-oscillatory-transform.md
• Checker: research/grothendieck/checkers/check_one_green_fold_off_axis_falsifier.py
• Sequence claim: seqclaim-b71ec2b9aae1b2d8fd8b3097
• Graph event: 6881

View source on GitHub