Chronotensor V7 Supplement

This supplement to Chronotensor Gravity Version 7 develops the mathematical and conceptual foundations underlying the main text. It formalizes the chronon field as a carrier of temporal memory, introduces non-Markovian kernel dynamics governing temporal evolution, and clarifies the hierarchy between microscopic resonance-level memory kernels and their infrared effective limits. The supplement further presents the internal phase geometry of matter using quaternionic and octonionic structures, including a composition rule for composite systems, and shows how standard quantum mechanics, Newtonian gravity, and the Einstein–Hilbert action emerge as effective descriptions after temporal renormalization. Singularities and entanglement are reinterpreted as regimes of chronon saturation and temporal coherence rather than geometric pathology or nonlocal signaling. Together, these results establish Chronotensor V7 as a self-consistent framework in which time, rather than spacetime geometry, is the primary dynamical entity.