No-Go Theorem for Singularity Resolution

We prove a No-Go theorem for singularity resolution in gravitational collapse: within any analytic gravitational theory, including general relativity and all theories with polynomial actions, quantum corrections introduced solely as effective matter sources are insufficient to halt singularities. This rules out singularity resolution via effective energy density in a broad class of quantum gravity approaches, including asymptotic safety and noncommutative geometry, which inevitably yield finite-time singularities or geodesic incompleteness. Resolution strictly requires either non-analytic modifications to the gravitational action, or a vanishing effective energy density at high densities (as realized in loop quantum gravity's Planck stars). The theorem is proved via an intrinsic $f(\mathbb{Q})$ gravity framework, extended universally to general relativity, $f(\mathbb{R})$, and $f(\mathbb{T})$ through the geometrical trinity--with regularity criteria and junction conditions grounded in non-metricity, free of standard GR tools.