A Field-Theoretic Model of Demographic Distribution Based on Node Density, Balance, and Environmental Feedback

This paper presents a Nodes Density Field Theory (NDFT) for modelling demographic distributions as a continuous field derived from discrete interacting agents (nodes). The framework integrates three governing principles drawn from the Four Universal Laws: system integrity (parameterised by η), universal balance (encoded in an environmental potential Φ_E), and a feedback loop mechanism (source–loss terms S₀ and L₀). Together, these yield a unified partial differential equation (PDE) governing population dynamics. The model is calibrated using Philippine regional density data and reproduces observed distributions with a mean absolute percentage error of 5%–15%. Results suggest that population distributions follow structured patterns driven by environmental gradients and system-integrity constraints, and that the NDFT framework captures phenomena absent from classical logistic or gravity models.