Circular–Hyperbolic Canonical Transport Exponential Structure, Frame Rotation and the Possible Emergence of Helical Fibre Geometry

Circular–Hyperbolic Canonical Transport: Exponential Structure, Frame Rotation and the Possible Emergence of Helical Fibre Geometry This paper develops the next stage of the intrinsic Closure Theory programme by investigating the geometric structures naturally suggested by the Canonical Transport Equation (CTE). Building upon the established hyperbolic Support–Weave transport, the paper explores the possibility that the accompanying intrinsic frame evolves through a complementary circular transport law generated by the same canonical exponential principle. The resulting circular–hyperbolic duality provides a unified mathematical picture in which hyperbolic state transport and circular frame transport arise from different generators of the same exponential transport mechanism. When combined with progression through the intrinsic recurrence parameter, this structure naturally suggests a helical interpretation of the completed transported fibre. Particular attention is given to recurrence, frame winding, holonomy and handedness, together with their possible significance for the geometric origin of observable quantities after Transformation and Projection. Throughout, the paper distinguishes rigorously between established mathematical results and exploratory working hypotheses, identifying the least-complex geometrical structures that merit further investigation. Although several proposed connections—particularly those relating to primitive charge, intrinsic handedness and helical carrier geometry—remain speculative, the analysis provides a coherent research programme for extending the intrinsic architecture beyond the minimal Canonical Transport Equation. This paper forms Paper I of the Closure Theory research series, extending the transport foundation established in Paper 0 toward the broader intrinsic geometry of Completed Intrinsic Closures.