Quantum Relational Emergence in Strong Gravity II: Constitutive Flow, Horizon Bifurcation, and Local Singularity Avoidance

Quantum Relational Emergence (QRE) separates the loss of a general-relativistic effective description from the loss of spacetime itself. Strong Gravity I formulated this distinction as a closure-first continuation problem and introduced primitive first-loss and general-relativistic extrapolation preemption. Here we ask the next question: whether a QRE branch that has left the general-relativistic rigidity basin can continue through a strong-field regime without developing a local metric singularity. We study a spherically symmetric one-function constitutive sector in which the dimensionless strong-field variable xi=Gml_*^2/r^3 obeys the autonomous flow dxi/ds=3xi-E(xi), with s=-ln r+const. A finite attractive constitutive fixed point produces a de-Sitter-type leading core, finite quadratic curvature invariants, and an exact Weyl-flow identity involving both the constitutive beta function and the constitutive slope. Consequently, an intermediate conformally flat shell and at least two positive Weyl maxima occur between the weak-field endpoint and the regular core. We derive the compactness flow, the zero/degenerate/two-horizon trichotomy, the scaling M_crit~l_*/G, and the square-root saddle-node law for horizon birth. Smooth analytic cores obey constitutive sum rules, whose cubic truncation admits two minimal classes; higher-order deformations show that the regular architecture occupies an open region of constitutive-function space rather than an isolated fine-tuned model. Under stated regularity assumptions the center is locally geodesically extendible. These results establish local singularity avoidance within the spherical constitutive sector, not global singularity resolution; inner-horizon stability and nonlinear backreaction remain separate dynamical questions.