Mirror-Inversion Cycle (MIC) v5: Scale-Invariant Hamiltonian Pat- terns in XOR Difference Space

We present a comprehensive theory of Mirror-Inversion Cycles (MIC) as scale-invariant patterns in XOR difference space (Z₂)^n. MIC operates in difference space where Hamming distance equals the weight of XOR differences and patterns are sequences of difference composition. We identify exactly three fundamental difference units (k=1, 2, 3) as generators: all MIC patterns can be constructed from these units. Larger weights appear as composite transitions. MIC exhibits scale invariance because the XOR algebraic structure is dimension-independent. The framework is verified across 13 pattern sizes (2-15 bits). Version 4 provides complete mathematical proof for the 6-bit case; v5 proposes conjectural generalizations based on empirical verification. MIC exhibits structural correspondence with the Binary Distinction Model (BDM), where differences, not entities, are fundamental. Both are formal specifications of structural behavior without ontological or semantic assumptions. 実装と例はhttps://github.com/YuragiMito/minisでご覧いただけます。