Gaugeability Assay in Advanced Modern Electronics: Sakib Index and Curvature Number for Non-Hermitian Topolectrical Networks

Non-reciprocity in modern electronic networks (e.g., active circuits, metamaterials, and topolectrical lattices) is often interpreted through an imaginary-gauge picture: if measured directional asymmetries are path-independent, a diagonal similarity transform removes them and predicts a single global skin-envelope. However, experimental systems are disordered, frequency- dispersive, and only approximately gaugeable. This manuscript proposes a novel, circuit-facing assay: the Sakib Index (SI) and the Sakib Curvature Number (SCN) that quantify (i) the fraction of non-reciprocity that admits a single global gauge and (ii) the residual loop-curvature obstruction. A new actionable inequality (Sakib Gauge–Curvature Bound) maps SCN to a path-dependence error bound, making the assay operational for frequency-resolved measurements. Ten dataset-based figures are produced by digitizing and re-analyzing open literature data on non-Hermitian electric circuits.