Complementary Continuous-Discrete Time, Chronon Layering and Temporal Folding

Within the framework of a discrete-time chronon model, we consider a dual description of physical time. In this description, macroscopic time is a continuous parameter, while a microscopic integer chronon index labels elementary updates of the system. On this basis, a hierarchy of temporal layers ChN (Chronon) is introduced. The simple layers Ch2, Ch3 and Ch4 are analysed, and it is shown that they naturally support U(1) (Unitary group), SU(3) (Special Unitary group) and a pair-locked SU(2) (Special Unitary group) symmetry, respectively. Special attention is paid to the twelve-slot layer Ch12. This layer is the minimal one which simultaneously separates partitions into four triads and three quartets. For Ch12, we demonstrate that the intersection of the corresponding commutants in C3⊗C4 reproduces the Standard Model gauge algebra SU(3)C×SU(2)L×U(1)Y and the pattern of hypercharges and anomaly cancellation. The appearance of three fermion generations is interpreted in terms of three inequivalent embeddings of a triad into the dodecad which preserve the quartet structure. Possible connections of the chronon dynamics with the hierarchy of masses (via Floquet-type quasi-energies), with dark sectors associated with misaligned layers, and with a temporal interpretation of entanglement are briefly discussed on a qualitative level. These questions are formulated as open problems for further study.