The Full Equivariant Character Can Carry the Portal Diameter through Thresholds
WP846 shows that ordinary anomaly matching is too coarse for WP841. The spectra ({1,2,3}) and ({1,2,3,4,-4}) have the same linear and cubic odd charge sums but diameters two and eight.
The representation-valued character retains the needed information. After charge one decouples,
The sewn support reconstructs the ultraviolet spectrum and diameter two, so the diameter-normalized selector remains (x_*=1/2) when typed against the completed character rather than the active particle list.
On bounded support (q=0,1,2,3), four background-holonomy evaluations at (1,-1,i,-i) form an invertible Fourier matrix and reconstruct every character coefficient. This is a finite faithful relational probe family.
The result is conditional. Ordinary anomaly matching does not guarantee the full character remainder. A source theorem based on an equivariant index or background-holonomy effective action must derive it. The holonomy is an added reference port and changes the physical groupoid to its stabilizer; it does not recover an absolute phase from the original flavor detector.
Verification: 12 of 12 exact checks pass in
research/flavor/checkers/wp846_equivariant_character_threshold_memory.py.
Graph admission: ev-000000007932-97744a6c-ac23-473a-a6a8-5290b2250549.