The Incidence Kernel Coefficients Are Not an Equivariant Charge Character
WP847 tests whether WP820's integer incidence complex derives the full character used by WP846. It does not. Although
interpreting the entries of (q) as weights of (Q=\operatorname{diag}(1,2,3)) would require a target generator (A) with (AB=BQ). The necessary kernel condition fails:
Consequently the kernel line is not (Q)-stable and no target generator intertwines the proposed action. The complex has rank two, kernel dimension one, zero cokernel, and ordinary Euler index one. It does not produce the three-term character (z+z^2+z^3).
WP846 remains a valid conditional threshold repair when the labelled charge character is independently admitted. A new (U(1))-equivariant complex with an oriented representation-valued index must be constructed before the character remainder and holonomy probes acquire source authority.
Verification: 12 of 12 exact checks pass in
research/flavor/checkers/wp847_incidence_kernel_not_equivariant_charge_index.py.
Graph admission: ev-000000007936-1b0faecb-fe6f-4278-9cc6-c0f081374498.