Complementary Continuous-Discrete Time, Chronon Layering and Temporal Folding

Abishev M. Berkimbayev D.Z.
February 2026 Multidisciplinary Digital Publishing Institute (MDPI)

Symmetry
2026 #18 Issue 2

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 (Formula presented.) (Chronon) is introduced. The simple layers (Formula presented.), (Formula presented.) and (Formula presented.) are analysed, and it is shown that they naturally support (Formula presented.) (Unitary group), (Formula presented.) (Special Unitary group) and a pair-locked (Formula presented.) (Special Unitary group) symmetry, respectively. Special attention is paid to the twelve-slot layer (Formula presented.). This layer is the minimal one which simultaneously separates partitions into four triads and three quartets. For (Formula presented.), we demonstrate that the intersection of the corresponding commutants in (Formula presented.) reproduces the Standard Model gauge algebra (Formula presented.) 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.

chronon , discrete time , emergent gravity , entanglement , Floquet dynamics , foundations of time , multimetric gravity

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Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Physics, National University of Singapore, Singapore, 117551, Singapore

Department of Physics and Technology
Department of Physics

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