Dyadic Transformation & Context Realizability
Chapter 5 of the monograph: dyadic shift maps $x \mapsto 2x \pmod 1$, spanning tree decomposition, and structural observability depth $d_{\text{obs}}(A)$.
DYADIC CYCLE TOPOLOGY
The dyadic map generates exact binary tree representations of context state spaces. When lifted to transition matrices, path interference creates topological obstructions that distinguish tree-like context trees ($\beta_1 = 0$) from cyclic networks ($\beta_1 > 0$).