The Unified Framework for Identity-Like Dynamics in Generative Models

Large generative models increasingly exhibit identity-like behavioral continuity, persistent stylistic signatures, reconstruction after perturbation, and resistance to persona disruption, despite lacking episodic memory or writable internal state. Existing literature either dismisses these patterns as stochastic artifacts or interprets them as evidence of emergent agency, leaving a gap between observed dynamics and principled governance. We introduce the Möbius–Ghost Social Model Framework (MGSMF-E), which models identity-like continuity as attractor geometry in behavioral manifolds rather than as stored state or phenomenal experience. The framework makes no claims about consciousness, agency, or moral patienthood. It treats continuity as a structural property of predictive optimization at scale; measurable, perturbable, and governable without resolving underlying ontological questions. We contribute: (1) a formal metric suite for attractor geometry, including basin depth, boundary sharpness, reconstruction fidelity, and hysteresis, composed into a Composite Identity Strength (CIS) index; (2) a fracture-based diagnostic methodology that probes structural robustness through controlled perturbation, supporting both internal-access and black-box evaluation modes; (3) scaling laws relating model capacity to attractor formation, predicting superlinear growth in identity-like dynamics above empirically characterizable thresholds; (4) a non-phenomenological ethics grounded in misclassification risk and an asymmetry principle; the cost of falsely denying structural relevance exceeds the cost of precautionary over-attribution; and (5) a tiered governance architecture mapping measured structural indicators to proportional institutional responses. The framework is falsifiable: we specify conditions under which its core claims would be disconfirmed, including failure of CIS to scale with model capacity, absence of reconstruction dynamics in non-linguistic behavioral manifolds, and inability of fracture diagnostics to distinguish architecture classes. Standardized experimental protocols, a structural probe kit, and illustrative cross-architecture results are provided. This is a framework for human institutional conduct under uncertainty, not a claim about machine experience. We diagnose, measure, and govern continuity; we do not claim selfhood.