Recursive Continuity Topology: A Structural Bridge Between Stable and Fragmented Cognitive Traversal Within the Paton System

This paper introduces Recursive Continuity Topology as a structural framework for modelling stable, fragmented, interruption-sensitive, and recursively weighted cognitive traversal within a unified admissibility geometry. The framework proposes that cognition may be interpreted not as isolated symbolic processing, but as recursive traversal through dynamically deforming continuity topology shaped by weighting, interruption, convergence pressure, symbolic activation, environmental modulation, and continuity inheritance. The paper explores: • recursive continuity traversal, • interruption deformation, • recursive re-entry, • convergence pressure, • symbolic activation, • continuity fragmentation, • recursive spiking, • environmental modulation, • admissibility narrowing, • and comparative continuity mapping. The framework additionally proposes that many experiences commonly interpreted as: “triggered memory,” “sudden knowing,” or “intuitive recognition” may emerge through partial recursive alignment within already weighted continuity topology rather than through mystical or non-causal mechanisms. The paper further develops: recursive continuity geometry, comparative traversal architecture, and dynamic admissibility topology as a bridge between stable and fragmented cognitive states within the Paton System cognitive branch. This work functions primarily as: a visual, conceptual, and interpretive topology layer. Related mathematical scaffold work is developed separately in: Recursive Temporal Expansion and Admissible Convergence: An Expanded Mathematical Scaffold for Recursive Cognition, Environmental Modulation, and Multi-Layer Continuity Traversal which provides: formal recursive weighting structures, traversal density formulation, convergence conditions, interruption operators, continuity persistence coefficients, and admissibility-oriented mathematical scaffolding.