The twisted convolution identity and ghost r-SICs from finite quantum dilogarithms
The paper extends a proof for a rank-1 twisted convolution identity by constructing 'ghost r-SICs'—d-by-d complex matrices satisfying specific geometric constraints. These configurations are linked to real quadratic special values of the modular quantum dilogarithm, providing a dictionary between two major mathematical research lines, though full Hermitian connections depend on unproven conjectures.