Nested 3–6–9 Cycles as a Helical Time Lattice

This paper presents a compact state-lattice (mixed-radix) model for nested cycles orga-nized by three symbolic roles: 1–2–6 (segmentation), 1–1–7 (gate), and 3–6–9 (motor).A year-like unit is defined as Y (∆) = 364 + 3∆ days, and is lifted by the fixed recursionfactor K = 7292/20 to define a platonic scale and a second-lift universe scale. A helicalembedding is introduced: each shell lift advances along a nesting axis Z while applying a120◦ phase rotation modeled by a 3-cycle permutation.