This work introduces Phase Correction Dynamics (PCD) as a general, testable framework for modeling delayed feedback in time-structured systems. Many real-world systems—ranging from physical oscillators and timing networks to biological regulation and memory processes—exhibit correction behavior that does not occur instantaneously, but instead accumulates and returns over time in structured, often oscillatory ways. PCD formalizes this behavior as a temporal convolution over prior system states, in which present outcomes emerge from a weighted accumulation of past states modulated by a delay kernel. This approach captures nonlinear scaling, phase-dependent interaction, and delayed correction effects that are not fully explained by memoryless or purely stochastic models. The framework is embedded within the Chronos time-field formulation, where time is treated as a dynamical scalar field Θ(x) rather than a passive parameter. Within this context, delayed feedback arises naturally from nonlocal temporal evolution, and PCD represents the observable mechanism through which prior states persist and re-emerge. A central component of the model is the Chronos stability constant χ≈0.551285598, which defines a universal balance condition between collapse (over-damping) and blow-up (runaway amplification). PCD provides the dynamic pathway through which systems evolve toward or away from this stability condition, linking delayed correction directly to stability regulation. The paper develops the full mathematical structure of PCD, establishes its connection to time-field-driven evolution, and provides explicit experimental protocols for validation using oscillator drift, timing correction systems, biological regulation, and memory processes. The framework is fully falsifiable through comparison with baseline models including autoregressive, exponential recovery, and stochastic approaches. If validated, this work provides a unified and testable description of delayed correction phenomena as a fundamental feature of systems evolving within a structured time field, with implications for physics, biology, and complex systems modeling.
Matthew Hall (Sun,) studied this question.