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 $0.722973\ {\rm fm}^{-3}$. This boundary is insufficient to represent higher-density nucleonic equations of state such as SLY4, whose tabulated endpoint occurs near $n_n=1.067747\ {\rm fm}^{-3}$ and $D_{\rm cell}=0.722484$. 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, $$F_M(x)=|S_M(x)|^2/M,$$ 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 $$D(2K,q_{\rm entry})=D(2K-2,1).$$ 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 $$n_n=0.722972969267\ {\rm fm}^{-3},$$ and the second occurs at $$n_n=1.104423378641\ {\rm fm}^{-3}.$$ 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 $$n_n=1.067746871408\ {\rm fm}^{-3},$$ 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 $$C_{ij}=q^{|i-j|}.$$ 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 $${e_{\rm emax}}^{2}=h\,{\rm Cd},$$ 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 $$C_A/{\rm Cd}=D_{\rm cell}$$ and the reciprocal magnetic-flux state satisfies $${\rm mflx}_A/{\rm mflx}=1/D_{\rm cell}.$$ 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 $$D_{\rm abs}=\pi/L(0)=0.596086108674,$$ corresponding to the asymptotic neutron equivalent-cell density $$n_{n,\rm abs}=1.901192474720\ {\rm fm}^{-3}.$$ A polar boundary-layer analysis of the Fejer kernel derives the leading asymptotic law $$D(M,1)=D_{\rm abs}+A/M+o(M^{-1}),$$ with $$A=0.481356924853.$$ Propagation through the neutron equivalent-cell density relation gives $$n_{n,\rm abs}-n_M=B/M+o(M^{-1}),$$ with $$B=4.605805184191\ {\rm fm}^{-3}.$$ Thus $n_{n,\rm abs}$ 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 $$n_n \rightarrow D_{\rm cell} \rightarrow (M,q) \rightarrow s$$ 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.