Arithmetic blindness and its removal in energy-transfer channels

Abstract An energy-conserving receiver can fail to distinguish sources with identical local states and ergotropy. Starting from the frequency-graph description of transpose-pair contrast, we study how interaction design changes this blindness. For general symmetric amplitudes, we classify dark-transition bias and derive a sharp stability threshold for the standard Hamiltonian. An explicit bounded dressing restores exact identifiability on every finite alphabet. Finite-time sensitivity, calibration error and equal-peak comparisons then distinguish exact recovery from useful measurement. Exact arithmetic and full Hamiltonian calculations support a finite-shot discrimination protocol, while multiplication-table structure supplies the reference blind model.