Microscopic Closure of Collective Aether-Cell Recruitment in Neutron-Star Matter:Singular Phase Response and Conductance--Flux Equilibrium

This paper completes the microscopic recruitment mechanism developed in the Aether Metric Coordinates (AMC) series for dense neutron matter. The preceding collective construction established a pair-preserving hierarchy of coherent Aether cells, $M=2K$, but left two questions unresolved: why a saturated fixed-M branch must recruit an additional two-seat cell, and why the enlarged branch enters at the specific coherence qentry required to preserve the matter--space boundary. The local QMU boundary is expressed through the reciprocal conductance and magnetic-flux identities cond=chrg/angm,=1/cond. The collective phase state is described by the maximum-entropy relation q=I₁(κ)/I₀(κ), with exact susceptibility χq=dq/dκ=1-q²-q/κ. As a fixed-M branch approaches full coherence, q→1, the required coupling satisfies κ→∞ while χq→0. In particular, κ(1-q)→1/2. Because the collective deformation $D(M,q)$ retains a finite nonzero slope at $q=1$, this phase-response singularity propagates directly into the conductance boundary and neutron-density coordinates. Exact saturation therefore represents an infinitely stiff fixed-branch limit rather than a regular state attainable at finite coupling. Opening the next pair-preserving branch, M→ M+2, provides the regular continuation. Once the enlarged branch is admitted, its entry state is selected by minimizing reciprocal QMU conductance--magnetic-flux mismatch. Defining r(q)=D(M+2,q)/D(M,1), a class of positive reciprocal boundary actions has the common stable equilibrium $r=1$. The resulting condition is D(M+2,qentry)=D(M,1). Thus the continuity relation used geometrically in AMC II acquires an independent variational interpretation: the newly recruited branch enters at the unique coherence that preserves both the conductance boundary state and its reciprocal magnetic-flux state. The invariant physical result is the matched boundary equilibrium rather than the choice of a particular algebraic mismatch action. The resulting recruitment sequence is reconstructed without using stored entry coherences, density thresholds, or equation-of-state data. The first transitions remain nₙ=0.722972969267\ fm⁻³(M=2→4), and nₙ=1.104423378641\ fm⁻³(M=4→6). The SLY4 endpoint remains within the regularized $M=4$ branch at finite coherence and finite coupling. Equation-of-state information enters only after construction of the recruitment hierarchy and therefore serves as an external validation layer rather than an input to the microscopic mechanism. A logical-independence audit verifies the complete ordering $$QMU reciprocity-seat collective geometry-M response singularity opening boundary matchingentryentryentry.$$ The paper therefore closes the principal microscopic questions left by the first two AMC papers: fixed-branch saturation supplies the recruitment trigger, while reciprocal conductance--magnetic-flux equilibrium selects the entry coherence of the enlarged branch. The resulting mechanism is parameter-free and preserves the pair structure and continuous matter--space boundary of the preceding collective construction. Beyond dense-matter applications, the derived conductance--magnetic-flux--coherence chain identifies a prospective constitutive route for testing whether a local Aether deformation state can be manipulated experimentally. This provides a bridge from compact-object physics toward future investigations of controlled Aether boundary states and space-engineering applications.