Mirror-Inversion Cycle (MIC): A Symmetric Binary Circular Ordering of 64 Six‑Bit States

This document specifies the Mirror-Inversion Cycle (MIC), a circular ordering of all 64 six-bit binary states constructed through symmetry operations. The cycle exhibits half-cycle inversion symmetry: the second half is generated by reversing the first half and applying full bitwise inversion (0↔1). Adjacent states differ by Hamming distance 1, 2, or 4 only—no other difference values occur. MIC is fully determined by binary symmetry and circular closure. No physical, semantic, or interpretive meaning is assumed. The model provides a closed formal structure for binary state ordering.