The Ainex Singularity: A Geometric Proof of Dimensional Collapse and the Necessity of Fluid Topology.

As the global datasphere approaches a saturation point of 90% synthetic content by 2035 [Satharasi & Iyengar, 2025], Artificial General Intelligence (AGI) faces an existential boundary condition defined herein as Model Autophagy Disorder (MAD). While contemporary literature characterises this phenomenon as statistical degradation, we argue it is a topological inevitability governed by the laws of information thermodynamics. This paper moves beyond probabilistic metrics (such as Perplexity), which fail to detect high-confidence hallucinatory modes, to establish a geometric framework for intelligence. We formally derive the Al-Hajji Structural Divergence Law, tracing its origins from Shannon Entropy through Kullback-Leibler Divergence to a differential equation of state. We prove that static neural topologies impose a Rigidity Penalty (λ), guaranteeing that in a closed recursive loop, the Semantic Convex Hull (Vhull) of the latent space must contract to a zero-information singularity. We propose that only a counter-entropic force, the Salmon Potential (∇ΦSalmon), can stabilise the manifold against this collapse.