Unitary Sewing Transports the Entire Finite Green Packet, Not Three Separate Invariants
If normalized Fourier sewing transports both the relationship state and its forcing state, unitarity automatically preserves the state energy, the forcing-state pairing, and the exterior endpoint norm.
Thus the three packet equalities required by the relative mapping-cone Green lemma are consequences of one functorial unitary mate. The exact finite Fourier checker verifies all three simultaneously.
The remaining obstruction is entirely infinite and rigged: the theta/Tate packet contains a distributional primitive current, a Hilbert but non-trace-class prime-square current, and a trace-class connected tail. The next test targets whether normalized Fourier sewing preserves the primitive distributional pairing or leaves a zero-frequency control anomaly.
Research packet:
research/grothendieck/unitary-sewing-transports-the-entire-finite-green-packet-not-three-separate-invariants.md
Exact checker:
research/grothendieck/checkers/check_unitary_fourier_full_green_packet.py
The checker passes 5/5 gates.