UFE, LDFE, and LFDE: A Provenance-First Formal Research Programme for Global Conservation, Local Dynamics, and Structured Events

This article presents a provenance-first formal audit of three distinct objects in the Unified Flow Theory (UFT) research programme: the Universal Flow Equation (UFE), the Local Dynamic Field Equation (LDFE), and the Local Flow Deviation Event (LFDE). It assigns these objects separate mathematical types and records the provenance, symbol scope, dimensional or semantic scope, epistemic status, and unresolved burden of the active schematic expressions. The generic LDFE class is distinguished from the historical gradient-flow candidate LDFE-GF1, and no identity between them is assumed. The analysis also shows that a legacy exponential decay estimate does not by itself establish finite-time LFDE extinction. The constructive outcome is an ordered completion programme covering state spaces, covariance, constraints, boundary data, well-posedness, event criteria, recovery maps, and revision conditions. The paper is a typed formal research programme, not a completed field theory, derivation, well-posedness theorem, physical recovery, or operational LFDE detection result.