The Theta Zero-State and the Euler Currents Live in Different Towers and Meet Only through Source Incidence
The completed theta zero-state is not a prime-coefficient vector. Theta source atoms, Euler prime-power currents, and archimedean Green states have distinct labels and topologies.
Their authorized interaction is the correspondence
Thus the scalar control line mediates between towers without replacing their typed data. The earlier dual-times-dual obstruction resulted from collapsing these towers into one completion.
The next exact gate is the Fourier–Tate mate square: transport then evaluate must agree with evaluate then propagate, including domains, boundary grades, and the independent augmentation incidence.
Research packet:
research/grothendieck/the-theta-zero-state-and-the-euler-currents-live-in-different-towers-and-meet-only-through-source-incidence.md
Checker:
research/grothendieck/checkers/check_typed_theta_euler_tail_correspondence.py
The checker passes 5/5 gates.