Canonical Primitive PDE System of SDEF

Canonical Primitive PDE System of SDEF consolidates the minimal closed continuum architecture of the Scalar Drag Emerence Framework (SDEF), a coherence-first nonlinear transport framework derived from the GPLA primitive ontology. The framework begins from four primitive organizational roles: Gradient Density (G) Fatigue/Persistence (P) Loop Integrity/Coherence (L) Ancestry Compression (A) From these, two primitive continuum fields are constructed: phi (x, t) = coherence fieldM (x, t) = ancestry-memory field The canonical recursive transport generator is: d2phi/dt2 = div (g grad (phi) ) - lambda phi³dM/dt = (|grad (phi) | - M) /taug = M |grad (phi) | / (1 + phi²) The system forms a closed recursive transport loop: phi-> |grad (phi) |-> M-> g-> div (g grad (phi) ) -> d2phi/dt2-> phi From this primitive closure emerge: packet reconstruction, corridor dynamics, timestamp-echo Riccati behavior, regime transitions, emergent transport geometry, and asymptotic weak-field inverse-square sectors. The framework interprets geometry, packets, and force-like behavior as emergent organizational consequences of recursive transport persistence rather than as primitive ontological entities. The paper introduces: recursive transport-memory closure, regime-order parameters, emergent transport geometry, nonlinear asymptotic sectors, weak-field Poisson-like reduction, and diagnostic mesoscopic quantities including MRI, ACG, LGV, PCG, CPO, and ARF. The weak-field asymptotic sector admits: phi (r) ~ 1/r|grad (phi) | ~ 1/r² providing the organizational bridge to inverse-square-like far-field behavior while preserving the fundamentally nonlinear transport ontology. The present formulation is intentionally minimal and represents: the canonical PDE freeze of SDEF, the first continuum closure of the GPLA ontology, and the mathematical foundation for future numerical, chemical, biological, and cosmological extensions. This release is intended as: a canonical archival reference, a transport-theoretic ontology freeze, and a foundation for future asymptotic, numerical, and phenomenological development.