Temporal Misalignment and Cross-Regime Coupling in Innovation Systems: A Formal Theory of Transition Dynamics within the Temporal Alignment Framework™ (TAF™)

Working Paper No. 3 of the Temporal Alignment Framework™ (TAF™) research programme. This paper presents the formal theoretical extension of the Temporal Alignment Framework™ (TAF™), developing a mathematical framework for analyzing transition dynamics across temporally heterogeneous innovation regimes. Building upon the structural theory introduced in Paper 2: Temporal Misalignment as the Structural Condition of Innovation Systems, it introduces Cross-Regime Coupling (CRC) as the mechanism governing transition feasibility between scientific, financial, regulatory, industrial, and market regimes. The framework formalizes multidimensional temporal divergence through differences in time horizons, evaluation cycles, and evaluation logics, and derives structural propositions describing how these dimensions influence coupling strength, transition feasibility, and innovation trajectories. A computational instantiation is included to illustrate the structural implications of the formal model. Rather than treating innovation as a problem of coordination within systems, the paper argues that innovation trajectories are fundamentally constrained by the feasibility of transitions across heterogeneous regimes. In doing so, it extends the Temporal Alignment Framework™ from a structural theory of temporal misalignment to a formal theory of cross-regime transition dynamics. This publication represents Working Paper No. 3 in the TAF™ research programme and provides a theoretical foundation for future computational development and empirical validation.