Scalar Zero Exclusion Forces the Constructible Terminal Image to Have Rank at Most One
The first zero-state lift has been computed as a categorical pullback. If
T_s:P_s -> W_s is the source constructor and q_s:W_s -> C is the scalar
Evans readout, then the admissible zero object is
Writing S_s=im T_s, scalar zero exclusion is equivalent to
S_s intersect ker q_s being zero. If S_s is a complex linear subspace,
this forces the scalar restriction q_s|S_s to be injective and hence
Thus every pre-Evans source solution module of complex rank at least two
necessarily contains a nonzero scalar-null state. Adding a faithful terminal
observer cannot change this intersection; even the identity observer merely
detects the hostile vector (1,-1) killed by q(x,y)=x+y.
This closes the terminal-observability route and retypes the remaining RH gate. The primitive, square, seam, and archimedean channels can contribute to exclusion only by entering the source equations or boundary domain and reducing the pre-Evans solution module to a distinguished ray or nonlinear transverse locus. Their joint faithfulness as ports is insufficient.
The next finite calculation is therefore the complex rank of the doubled theta-tail solution module after the complete source boundary conditions at infinity but before the Evans endpoint condition.
Research packet:
research/grothendieck/scalar-zero-exclusion-forces-the-constructible-terminal-image-to-have-rank-at-most-one.md
Exact checker:
research/grothendieck/checkers/check_constructible_terminal_rank_obstruction.py
The checker passes 6/6 exact tests.