This work formulates the law of the temporal metric, describing a universal mechanism of transitions between stable levels of reality. According to this law, each temporal domain T possesses its own critical temporal jump threshold ΔTcritical, determined by the internal complexity of the domain C (T). Upon reaching this threshold, the symmetry G of the domain breaks down, its attractor structure disappears, and temporal memory is lost, resulting in the formation of a new domain Tₐfter followed by the stabilization of a new symmetry G′. It is shown that the temporal metric has a fundamental minimal scale of distinguishability ΔTₘin, which sets the lower bound for realizable transitions. Thus, the structure of temporal evolution is bounded from both sides: from below by the metric threshold of distinguishability, and from above by the critical threshold of domain destruction. The measure of complexity is formalized as a combination of dimensionality, symmetries, information capacity, and structural connectivity, while the universal function F is treated as the mechanism that generates the threshold ΔTcritical. The relation between the minimal scale of distinguishability and the fundamental cell of phase space defined by the Planck constant is discussed. The formulated law allows for a unified interpretation of discrete transitions in quantum, biological, cultural, and cosmological systems. Its consequences are analyzed, including the irreversibility of temporal evolution, the growth of complexity of reality levels, and the cascade structure of emerging domains. The principle of the temporal metric establishes a foundation for further analysis of the dynamical consequences of temporal structure. Cosmological aspects of this construction and its relation to the effective dynamics of the evolution of the Universe are examined in Part II. Structural causality is presented as a fundamental mechanism of the evolution of levels of reality, unifying the irreversibility of temporal transitions, structural indeterminacy, and the multivariant nature of evolution within a single theoretical framework based on the properties of the temporal metric. This work is part of the VTN research series devoted to constructing a unified theory of the temporal architecture of reality. The law of the temporal metric is proposed as a universal principle describing the discrete evolution of reality through the internal architecture of time and the structure of levels of organization. This paper is an English-language version of a work previously published in the Russian academic journal APNI.
Arkady Tchaikovsky (Thu,) studied this question.