Existing multi-agent simulations often suffer from the "Agent-Centric Paradox": rules are hard-coded into individual agents, making complex social dynamics rigid and difficult to align with educational values. This paper presents EDU-MATRIX, a society-centric generative cognitive digital twin architecture that shifts the paradigm from simulating "people" to simulating a "social space with a gravitational field." We introduce three architectural contributions: (1) An Environment Context Injection Engine (ECIE), which acts as a "social microkernel," dynamically injecting institutional rules (Gravity) into agents based on their spatial-temporal coordinates; (2) A Modular Logic Evolution Protocol (MLEP), where knowledge exists as "fluid" capsules that agents synthesize to generate new paradigms, ensuring high dialogue consistency (94.1%); and (3) Endogenous Alignment via Role-Topology, where safety constraints emerge from the agent's position in the social graph rather than external filters. Deployed as a digital twin of a secondary school with 2,400 agents, the system demonstrates how "social gravity" (rules) and "cognitive fluids" (knowledge) interact to produce emergent, value-aligned behaviors (Social Clustering Coefficient: 0.72).