Universal Phase Crystallization Theory (UPCT): A Phase Transition Law for Generative Systems under Measurement Optimization

UPCT transforms the long-held intuition that “partial optimization harms the whole” into a formal dynamical law describing the collapse of generative systems under measurement-driven optimization.

This work presents the second major development of the Universal Phase Crystallization Theory (UPCT), extending the framework from its original formulation in quantum measurement theory to a universal dynamical law governing resilience and collapse in complex generative systems.

The initial UPCT study (Ohumi, 2026; DOI: 10.5281/zenodo.18230537) introduced phase crystallization as an information-theoretic effect of temporal sampling, reinterpreting wavefunction collapse, the uncertainty principle, and the quantum Zeno effect as consequences of resolution-dependent observation. That work established the ontological primacy of continuous generative dynamics (“It from Wave”) over discrete measurement outcomes.

The present paper generalizes this mechanism beyond quantum systems. Here, phase crystallization is defined as a dynamical phase transition that occurs when measurable outputs (S) become optimization targets. Feedback from metrics restructures the system’s constraints (G), progressively suppressing the underlying generative dynamics (Φ) that sustain adaptability and resilience. Using a minimal nonlinear model, the study demonstrates analytically that increasing optimization pressure shrinks the basin of attraction of generative equilibria. At a critical threshold, system resilience collapses to zero, leading to irreversible rigidity.

UPCT thus unifies diverse phenomena across domains, including:

• Metric fixation and Goodhart’s law in economic and governance systems
• Mode collapse in AI alignment under excessive optimization
• Over-specialization and loss of adaptability in evolutionary dynamics
• Resilience loss and tipping points in complex networks

Together with the earlier quantum-focused paper, this work establishes UPCT as a two-layer theoretical framework:

1. Epistemic Layer — Observation as phase crystallization via sampling
2. Dynamical Layer — Collapse of generativity under optimization of crystallized states

UPCT reframes systemic collapse not as failure of parameter tuning but as a universal structural consequence of measurement-driven optimization. The theory provides a cross-domain principle for understanding resilience, fragility, and the preservation of generative degrees of freedom in physical, biological, technological, and social systems.

Significance Statement:

Many fields have long observed that optimizing measurable parts of a system often leads to failure of the whole, yet this principle has remained an empirical heuristic rather than a formal law. Universal Phase Crystallization Theory (UPCT) provides a mathematical formulation of this phenomenon by demonstrating that sustained optimization of measurable states (S) systematically reduces the resilience of the underlying generative dynamics (Φ). As optimization pressure approaches a critical threshold, the basin of attraction collapses, leading to a phase transition from adaptive flow to rigid crystallization. This work reframes systemic fragility — in physics, biology, AI, and social systems — as a universal dynamical consequence of measurement-driven optimization, transforming a long-standing intuition into a cross-domain stability law.