Short-Memory Local Reduction of the Licensed Geometric Branch and the Poisson-Type Effective Gravitational Limit

This preprint establishes the strongest currently retained local scalar gravitational derivation in the TRUQC framework. It demonstrates that, within a short-memory and strongly metrically licensed local window, the unique delayed constitutive response channel reduces to a local scalar elliptic closure whose generic linear form is Helmholtz-type and whose further transport-dominated sublimit is Poisson-type. In this reading, effective local gravity is not primitive but emerges as a geometric readout of a deeper delayed constitutive channel. The paper is local, scalar, regime-explicit, and controlled, and it does not yet claim a completed tensorial Einstein-like derivation.