Topos Bifurcation and Safety Boundaries in Computing Paradigms: From the Danger of Homotopy Shaping to the Robustness of Coherent Geometric Assembly

The current paradigm of AI safety alignment (e.g., RLHF) is essentially behaviorist: it attempts to constrain the model on a low-dimensional output section, yet cannot touch the underlying topological deformation occurring in the high-dimensional representation space. Based on the Defect–Homotopy–Topos (DHT) framework and the O1 theoretical reachability diagnostor, this paper re-examines the ontological divide among computing paradigms. We propose that quantum computing, in mathematical ontology, belongs to the "extreme coherent assembly of geometric measures"—it is faithful to the underlying geometric boundary of Hilbert space, exhibiting extremely high coherence robustness; whereas AI computing (large models) belongs to "homotopy topos shaping"—it continuously reshapes manifolds in a latent space lacking an explicit physical homotopy library, carrying the intrinsic danger of homotopy fission and semantic alienation.

To bridge these two extreme computing paradigms, so that the homotopy shaping process of AI becomes visible and safe, this paper reports the engineering existence of an intermediate computing structure, the NG space (Nerve Gluing Space), and gives its topological interpretation. Its low-dimensional implementation has been validated on protein conformational space and inorganic crystal CIF data; these two modalities share no common geometric assumptions, empirically supporting the claim that NG's compatible-non-consensus design presupposes no global structural hypothesis. The biquaternion encoding is the theoretical interface for upgrading this architecture to high-dimensional latent-space diagnosis.¹ Through distributed local consensus and a non-equilibrium quenching protocol, the NG space serves as a topological buffer layer, providing a foundational theoretical basis for next-generation AI safety architectures.