The Tail Forcing Is Not Exact Inside the Native Rank-Two Quadratic-Current Algebra
For the real native tail system
the most general constant-coefficient quadratic current is
Its derivative is
For nonzero s and nontrivial f, eliminating the unwanted G^2 and c^2
channels forces A=B=0, leaving no Gc coefficient. Therefore the forcing
channel 2fGc is not the derivative of a local constant-coefficient quadratic
current built only from the native variables (G,c).
The modular closure must introduce genuine additional structure: an independent seam/source-primitive coordinate, source-derived variable coefficients, or a reciprocal-sheet cancellation. A formal nonlocal antiderivative remains inadmissible as an explanation.
This is the local algebraic counterpart of the earlier completion result that the seam cannot be reconstructed boundedly from the tail. The next minimal calculation is the quadratic-current audit after adjoining the actual source-derived seam flow.
Research packet:
research/grothendieck/the-tail-forcing-is-not-exact-inside-the-native-rank-two-quadratic-current-algebra.md
Dependency-free exact checker:
research/grothendieck/checkers/check_native_tail_quadratic_current_no_go.py
The checker passes 7/7 tests.