M13b The Symmetric Core: Comparison with the Hyper Core, Algebra of Units, Negative and Complex Ranks, and the LP Curve

This monograph develops the advanced structure of the Symmetric Core, explicitly building on the foundations established in M13a, and places it in systematic comparison with the Hyper Core framework. The work provides a complete parallel table of SC and HC operations, clarifying where the two systems coincide and where they diverge above multiplication. It analyses the algebra of Hermit units across positive, negative, and complex ranks, introducing precise conventions for distinguishing SC and HC units and operations. M13b develops the theory of negative‑rank asymmetry, complex‑rank extensions, and the geometry of the SC parameter space, including the LP curve that organises spectral behaviour within the Symmetric Core. The étage relationship between the SC and higher cores is made explicit, establishing how the SC embeds into the broader hyperoperation programme without requiring modification of its internal structure. The purpose of this monograph is to document the advanced constructions, comparisons, and structural consequences of the Symmetric Core, explicitly dependent on M13a, and to establish their conceptual priority within the hyperoperation theory series. M13b 04.20...e Advanced | PDF