Collective Aether-Cell Coherence: A Parameter-Free Many-Body Continuation of Neutron-Star Density Geometry

This paper develops the many-body continuation of the Aether Metric Coordinate (AMC) framework introduced in ``Aether Metric Coordinates: Neutron-Induced Length-Density Strain and Photon-Path Curvature in Compact Objects,'' DOI 10.5281/zenodo.22087711. The primary objective is to resolve the neutron-star density gap left by the single-Aether-unit deformation law. The original single-unit phase field reaches a monotonic compression boundary near $D=0.822767$, corresponding to a neutron equivalent-cell density of approximately 0.722973\ fm⁻³. This boundary is insufficient to represent higher-density nucleonic equations of state such as SLY4, whose tabulated endpoint occurs near nₙ=1.067747\ fm⁻³ and Dcell=0.722484. The present work demonstrates that this limitation belongs to the single-unit phase ansatz rather than to the neutron-density geometry itself. The single phase coordinate is generalized to a winding-preserving collective angular phase field. A canonical positive Fejer kernel, FM(x)=|SM(x)|²/M, generates the required harmonic structure without fitting individual harmonic coefficients. Its triangular coefficients arise directly from coherent contributor-pair counts. The original single-unit deformation is recovered exactly as the $M=2$ member of this hierarchy, with the original deformation coordinate identified as the nearest-neighbor coherence coordinate q. Preservation of the elementary two-seat Aether-cell structure restricts the collective hierarchy to $$M=2K,$$ where K is the number of coherently participating Aether cells. Successive branches are joined by the parameter-free continuity condition D(2K,qentry)=D(2K-2,1). This produces a continuous recruitment hierarchy in which saturation of one coherent branch is followed by recruitment of the next intact two-seat Aether cell. The first transition occurs at nₙ=0.722972969267\ fm⁻³, and the second occurs at nₙ=1.104423378641\ fm⁻³. These thresholds are obtained from the collective geometry and neutron reference volume rather than from an equation-of-state fit. The SLY4 endpoint is returned only after construction of the hierarchy. It lies naturally on the $M=4$ branch at $$q=0.909000564377$$ and nₙ=1.067746871408\ fm⁻³, approximately $3.43%$ below the independently derived $M=4$ to $M=6$ recruitment density. Thus the high-density SLY4 state that exceeded the single-unit domain in the first AMC paper is accommodated without modifying the neutron reference geometry, fitting harmonic coefficients, or imposing an EOS-derived transition density. The collective coherence matrix is Cᵢⱼ=q|i-j|. Its inverse is tridiagonal, showing that the collective correlations can be generated by nearest-neighbor local links rather than an all-to-all interaction. The additive local transfer coordinate is s=-ln q, so that longer-range coherence follows from repeated local transfer. The collective geometry is connected to Quantum Measurement Units through the fundamental conductance identity eₑₘₐₓ²=h\, Cd, or equivalently magnetic charge equals angular momentum times conductance. The invariant QMU conductance defines the reference matter-space boundary, while the local boundary state satisfies CA/ Cd=Dcell and the reciprocal magnetic-flux state satisfies mflxA/ mflx=1/Dcell. Conductance and magnetic flux therefore remain continuous through collective recruitment while the internal variables $(M,q)$ reorganize discretely. The full-coherence hierarchy approaches an absolute meridional geometric bound Dabs=π/L(0)=0.596086108674, corresponding to the asymptotic neutron equivalent-cell density nn, abs=1.901192474720\ fm⁻³. A polar boundary-layer analysis of the Fejer kernel derives the leading asymptotic law D(M,1)=Dabs+A/M+o(M⁻¹), with $$A=0.481356924853.$$ Propagation through the neutron equivalent-cell density relation gives nn, abs-nM=B/M+o(M⁻¹), with B=4.605805184191\ fm⁻³. Thus nn, abs is an accumulation density of the pair-preserving collective hierarchy rather than another finite-M recruitment threshold or a prediction of the maximum stable neutron-star density. The resulting parameter-free conditional map is nₙ → Dcell → (M,q) → s together with the corresponding QMU conductance and magnetic-flux boundary states. This closes the neutron-star density problem left by the single-unit AMC construction at the geometric and constitutive level. The remaining problem is microscopic: deriving the conductance-to-link transfer and pair-recruitment dynamics directly from ligamen circulatus, magnetic-charge, angular-momentum, and inter-cell magnetic-flux dynamics.