Correlated Nuclear–Electronic Excitations as a Structurally Unavoidable Consequence of Nuclear Recoil Dynamics

The Migdal effect—electronic excitation accompanying nuclear recoil—has long been proposed as a subdominant but potentially detectable feature of low-energy scattering processes, particularly in the context of direct dark matter searches. Despite renewed experimental interest, the physical robustness and universality of Migdal-type signatures remain debated, with concerns centering on statistical marginality, detector dependence, and background contamination. In this work, we present a constraint-based, non-interventional reconstruction of nuclear–electronic response behavior derived exclusively from published summary statistics describing nuclear recoil energetics, atomic ionization probabilities, detector response characteristics, and background noise models. Crucially, the framework forbids dark matter parameter fitting, particle identification, discovery claims, or experimental validation, allowing the analysis to probe structural necessity rather than model-dependent inference. Across a large ensemble of independent realizations, the system converges reproducibly to a stable correlated nuclear–electronic response structure exhibiting zero topology variance, nontrivial causal density, and signal–background separation behavior inconsistent with background-only reconstructions under equivalent constraints. These correlated structures persist under noise resampling, detector response variation, and representation perturbation, indicating that the emergent behavior is not an artifact of a specific experimental configuration. While no claims of detection or parameter inference are made, the results demonstrate that correlated Migdal-type signatures arise as a structurally robust consequence of nuclear recoil dynamics under minimal physical assumptions. This finding places nontrivial theoretical constraints on interpretations that treat the Migdal effect as negligible or optional and motivates its treatment as a physically unavoidable component of low-energy recoil phenomenology.