Neuronal loss reshapes survivor dynamics and limits mechanism inference in excitatory inhibitory neural fields

Does neuronal loss simply reduce measured activity, or also change how the surviving network behaves? We separate these effects in a next-generation excitatory-inhibitory neural field by writing the viable population measure as q_a = lambda_a f_a, where lambda_a is viable population mass and f_a is the normalized survivor distribution. Under state-independent thinning with fixed Cauchy heterogeneity, normalization commutes with the Ott-Antonsen/Montbrio-Pazo-Roxin reduction on the specified analytic invariant manifold. The mortality term disappears from conditional transport, but viable mass remains in recurrent coupling: loss can reshape survivor dynamics, not merely scale their contribution to tissue activity. Conversely, for otherwise identical constant homogeneous parameters, viability, pathway integrity and compensation give exactly conjugate conditional deterministic dynamics whenever c_ab lambda_b^(1-nu_ab) is preserved. Identical conditional activity therefore need not imply an identical biological mechanism. Equilibrium and oscillatory bifurcations, finite-population escape, and delayed propagation reveal consequences of these two principles. In particular, matched field simulations show that localized loss can increase whole-sheet firing through recurrent reorganization, while coherent-wave continuation quantifies viability-dependent propagation and phase relaxation. The framework distinguishes neuronal abundance from survivor state and places an exact limit on mechanism inference. Attributing activity changes to neuronal loss therefore requires information beyond conditional neural dynamics, such as tissue-level measurements or independent structural constraints, interpreted through an appropriate observation model.