The Dual Sequence Principle in the I11 Number Space: Fractal Mirror Symmetry from 12242 and 21224

This publication introduces the Dual Sequence Principle within the quantized I11 number space.

Two cyclic fragment sequences — the internal core pattern 12242 and the external emitter pattern 21224 — share the same total value (11) but differ in ordering. This structural asymmetry acts as an intrinsic mirror operator and generates all outward geometric and spectral phenomena in the I11 framework.

The study shows how the emitter sequence produces the radii 3, 5, 7, and 11, the first geometric Vesica intersections, the high-precision opening angles, and the characteristic 0.5 drift of the I11 mirror structure. The same sequence also reproduces the normalized solar spectrum fractions (2/11, 1/11, 2/11, 2/11, 4/11).

All results emerge directly from the internal arithmetic of the I11 algebra, without external assumptions. The paper establishes a deterministic connection between resonance, geometric projection, spectral quantization, and mirror symmetry — all generated from a single quantized cyclic law.