Geometric Early Warning and Descriptor-Relative Local Ranking in a Reduced Class of Collapse-Prone AI Learning Dynamics

The present paper studies geometric early warning and descriptor-relative local ranking for a local reduced class of collapse-prone AI learning dynamics. It does not study implementation closure, operational authorization, deployment-side suitability, implementation protocol, engineering sign-off, safety assurance, legal reliance, or commercial suitability. The target is a descriptor-relative theorem-side account of which admissible local parameter directions decrease a reduced local vulnerability quantity on a dominant two-dimensional damped oscillatory block. On that block, let P = -Tr (J2), Q = det (J2), and R = Q/P². The main theorem proves that an admissible local parameter direction v is vulnerability-reducing in the declared descriptor-relative sense if and only if P dQv - 2Q dPv < 0. A finite-window theorem-side consistency statement and a relinearization limitation statement are also given under explicit locality and error assumptions. The intended contribution is not an intervention protocol, not an operational recommendation, not an implementation-side theorem, and not a field-use guarantee. It is a reusable theorem-side language for stating which admissible local directions are descriptor-relatively less vulnerable on the dominant reduced geometry, what can be narrowed over a short local window, and what remains open. All results are descriptor-relative theorem-side classifications only and do not constitute operational approval, safety assurance, legal advice, or a guarantee of realized performance.