System and Method for Ricci-Flow Reasoning in Cognitive Machines

A computer system for reasoning in a persistent cognitive machine comprising a hardware memory, wherein the computer system is configured to execute software instructions stored on nontransitory machine-readable storage media that:

• maintain a persistent cognitive manifold comprising a structured internal state space in which proximity, connectivity, and accessibility among representations are governed by geometric structure including curvature-derived pressure fields and accessibility weights;
• select a region of interest within the persistent cognitive manifold based on a current reasoning task, query, or active traversal trajectory;
• apply a bounded-time curvature-driven geometric evolution to the selected region of interest, wherein the evolution reduces or redistributes curvature-derived pressure within the region of interest while preserving protected invariants and shape-preserving components of the cognitive manifold;
• evaluate one or more candidate reasoning trajectories within the evolved geometric structure to determine epistemic admissibility based on stability margins and boundary proximity;
• generate an admissibility certificate encoding stability features and admissibility margin measurements observed during geometric evolution when no failure condition is detected;
• detect one or more failure conditions within the evolved geometric structure based on stability assessment of the region of interest;
• select a hallucination-safe fallback behavior when a failure condition is detected, wherein the hallucination-safe fallback behavior prevents generation of fabricated or extrapolated outputs;
• and
• enforce output suppression prior to any output generation when no admissible reasoning trajectory exists.