Fractal Symmetry and Operator Geometry: Redefining the Pauli Matrices in a Quantized Interval Space I11

Description: This work introduces a new geometric framework based on a finite, mirror-symmetric interval from 0 to 11. The space is structured through a recursive fractal partition logic and includes a reflection operator that maps any point x to 11 minus x. Within this setting, the Pauli matrices are reinterpreted not as abstract quantum objects, but as real geometric operators acting on a discrete coordinate space with an additional binary state. This allows the spin structure to be represented as an isometry group instead of a purely algebraic construction. A practical example is provided using a triangulation scenario that mirrors GPS geometry. Two reference points at positions minus 5 and plus 5 with a radius of 5 point 5 create a lens intersection with an opening angle of 49 point 24 degrees. This demonstrates how overlapping operators restrict positional states in the same way quantum spin constraints or classical localization work. The paper also discusses the role of mirror pairs such as 1 point 444 and 9 point 556, as well as the rational factor 0 point 0606 (two over thirty three), which relates to two out of three active axes in projected operator geometry. This publication establishes a mathematically consistent foundation for uniting fractal structure, reflection symmetry and operator theory. It provides a bridge between discrete geometry, spin representations and macroscopic triangulation logic. License: Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0)