Role of exceptional points and transmission peak degeneracies in non-Hermitian sensing

Transmission peak degeneracies (TPDs) have emerged as a promising alternative to exceptional points (EPs) for non-Hermitian sensing, providing square-root frequency splitting without the eigenbasis collapse and associated noise amplification that limit EP sensors. However, existing treatments of TPDs remain fragmented, lacking a unified theoretical framework, systematic figures of merit, or design principles for practical implementation. Here, we develop a comprehensive theory of two-dimensional TPDs that clarifies their relationship to EPs, maps their locations in parameter space, and provides analytic figures of merit for sensor design. We validate our theory using a tunable cavity-magnonics platform with in situ control of mode frequency, dissipation, and complex coupling via an effective synthetic gauge field. Our platform enables systematic exploration of six representative EP-TPD configurations spanning PT-symmetric, anti-PT-symmetric and anyonic-PT-symmetric regimes. Crucially, we show that TPDs, unlike EPs, retain square-root splitting even under nuisance parameter drift through generalized transmission extrema degeneracies (TEDs). We further identify specific robust TPD configurations that minimize the impact of nuisance drift. These findings establish a unified theoretical and experimental framework for TPD-based non-Hermitian sensing.