Collective Phase Transitions: A Phase-Ordering Time Model of Social Resilience and Ethical Stability

Version 2.0 — Revision NotesThis version constitutes a substantive revision of the original publication. The core theoretical contributions — Water/Iron/Mercury phase structure, A_min as a formal ethical constraint, and bipolar locking symmetry — are unchanged. Revisions address terminology consistency, conceptual precision, and integration with the broader IPCSALT series. Key changes: Added Series Position Note locating this paper within the IPCSALT framework and connecting forward to Papers #19, #33, #51, and #52 Corrected Iron phase description throughout: replaced "fragmentation/independence" with "anti-phase locking" for conceptual accuracy Corrected Mercury phase description: replaced "rapid switching" with "reversible adaptive flexibility" Added PLV sign structure clarification (PLV_sgn) in Section 3.1 with notation history note Updated terminology: "stability band" now includes parallel reference to Goldilocks Coherence Band (GCB, Paper #19); CRGZ replaced with GCB throughout Replaced "UPF roadmap" with "IPCSALT research program" Added forward-connection annotations to Papers #19, #21, #33, #51, #52 at relevant sections Added epistemic status notes in Sections 1.4 and 5.3 Relabeled Section 5.3 from "Historical Validation Patterns" to "Illustrative Historical Patterns" Added reference to IPCSALT Core Definitions Document (Zenodo, DOI: 10.5281/zenodo.20102846) Theoretical claims and mathematical structure are identical to v1.0. This paper introduces a phase-transition framework for understanding collective behavior, focusing on the conditions under which social systems remain resilient, ethical, and reversible. Rather than classifying collectives by static states such as cohesion or fragmentation, the model defines collective health by the system’s ability to transition reversibly between coordination regimes. Using a Phase-Ordering Time (POT) approach, the paper formalizes three canonical collective phases—Water (fusion), Iron (polarized fragmentation), and Mercury (adaptive flexibility)—and analyzes the dynamical rules governing transitions among them. A central contribution of the work is the introduction of an ethical stability constraint, expressed as a lower bound on collective awareness Amin⁡A_{\min}Amin. When awareness falls below this threshold, the system enters irreversible collapse attractors, manifesting as totalitarian fusion, extreme polarization, or runaway mob dynamics. Both excessive consensus and excessive conflict are shown to share the same underlying phase-locking structure, differing only in alignment direction. The framework integrates concepts from emotional contagion research, complex systems theory, and social psychology into a unified phase-space representation defined by external pressure, coupling strength (PLV), and awareness. Phase diagrams and early-warning indicators are derived to diagnose collapse risk and loss of reversibility. Beyond theory, the paper outlines practical design principles for organizational governance, democratic resilience, and online platform moderation, emphasizing awareness preservation and reversible coordination as core safeguards. The model provides a conceptual and mathematical bridge to subsequent work on the Cosmic Resonance Goldilocks Zone (CRGZ), extending phase-based stability analysis across cognitive, social, and ethical domains. This work is an exploratory contribution situated within the IPCSALT phase-based meta-framework.