System and method for latent contextual threading in personalized dialogue using geometric manifold traversal

A computer system for latent contextual threading for personalized dialogue comprising a hardware memory, wherein the computer system is configured to execute software instructions stored on nontransitory machine-readable storage media that:

• implement a personalized cognitive manifold as a Riemannian manifold with time-evolving metric tensors that encode dialogue preference strength through local curvature properties in latent space that encodes user-specific dialogue patterns as navigable geometric structures;
• maintain multiple dialogue contexts as geometric trajectories within the personalized cognitive manifold, wherein dialogue responses are generated through manifold traversal comprising calculating geodesic paths through the personalized cognitive manifold and navigating along computed trajectories to maintain semantic coherence, rather than discrete context retrieval;
• and
• modify the geometric structure of the personalized cognitive manifold based on user interactions by processing user feedback through geometric deformation algorithms that implement curvature flow equations to evolve metric tensor properties of the personalized cognitive manifold based on user interaction patterns, to improve dialogue personalization through bidirectional adaptation;
• wherein dialogue continuity is maintained through geometric trajectory following within the personalized cognitive manifold, enabling persistent conversations that adapt to user preferences through real-time manifold geometry modifications.