Aether Metric Coordinates: Neutron-Induced Length-Density Strain and Photon-Path Curvature in Compact Objects

This work develops Aether Metric Coordinates (AMC) for compact objects within the Aether Physics Model (APM) and Quantum Measurement Units (QMU), connecting QMU source length density, material-space strain, neutron dense-matter geometry, and photon trajectories. Starting from the QMU identities $$c=\lambda_C F_q$$ and $$m_a={\lambda_C}^3{F_q}^2/G,$$ the maximum Aether length density follows as $$m_a/\lambda_C=c^2/G.$$ This provides the normalized compact-object coordinate $$\vartheta_A=\frac{M/r}{m_a/\lambda_C}=\frac{GM}{rc^2},$$ with the associated strain variable $$\epsilon_A=2\vartheta_A.$$ The resulting dimensionless AMC line element, $$d\sigma_A^2=-d\tau^2+(d\rho+\sqrt{\epsilon_A}\,d\tau)^2+\rho^2d\Omega^2,$$ has exact correspondence with the Painlevé--Gullstrand representation of Schwarzschild geometry. The radial null condition is $$\frac{d\rho}{d\tau}=-\sqrt{\epsilon_A}\pm1.$$ This separates two geometrically distinct thresholds. The null-propagation standoff condition occurs at $$\epsilon_A=1,$$ equivalently $$\vartheta_A=1/2,$$ whereas the proposed maximum Aether length-density state occurs at $$\epsilon_A=2,$$ equivalently $$\vartheta_A=1.$$ The metric remains non-degenerate at both thresholds. For spherical exterior geometry, the AMC shift field reproduces the characteristic extrinsic-curvature eigenvalue ratio $$-1/2:1:1$$ and the quadratic source invariant $$K^2-K_{ij}K^{ij}=16\pi\hat{\rho}_A.$$ The paper distinguishes this established geometric correspondence from the proposed APM interpretation in which the shift and extrinsic curvature describe strain of a discrete material-space substrate. The dense-matter analysis further distinguishes the stellar radial source coordinate from a local neutron equivalent-cell coordinate. For Stage-4 neutron geometry, $$D_{\rm cell}=(n_nV_{n0})^{-1/3}=\frac{r_{\rm WS}}{r_{n0}}$$ is shown to be exactly the neutron Wigner--Seitz equivalent-cell radius normalized to the reference neutron radius. This many-body coordinate is compared with the independently derived single-Aether-unit deformation function $D(\eta)$. NL3, DDME-X, GM1-2D, and GM1-1D maximum-stable configurations fall within the monotonic $0\leq\eta\leq1$ single-unit deformation domain. SLY4 provides a counterexample to universal continuation: its stable-side TOV sequence reaches the $D(1)$ boundary and continues to $$D_{\rm cell}=0.722484044913,$$ below the complete positive-$\eta$ single-unit minimum $$D_{\min}=0.822115465507$.$ Thus the proposed equality $$D(\eta)=D_{\rm cell}$$ is retained as a finite-domain constitutive registration rather than a universal neutron-density law. The SLY4 endpoint requires approximately $12.12\%$ additional radial equivalent-cell compression beyond that represented by the present single-Aether-unit deformation family, quantitatively defining the many-body continuation problem. The compact-object construction is also confronted with photon-propagation observations using NICER/XMM pulse-profile data for PSR J0030+0451 and an X-PSI-based ray-bending test. The real-data high-likelihood profiles return to the undeformed relativistic propagation law, corresponding to $\Gamma=1$. A controlled synthetic injection with $\Gamma_{\rm inj}=0.900$ is recovered near $\hat{\Gamma}=0.911$, demonstrating sensitivity of the analysis pipeline to a nearby nonstandard path law. Because a parameter-free many-body constitutive mapping from neutron dense-matter geometry to photon-path deformation has not yet been derived, $\Gamma$ is treated phenomenologically. The observational result is therefore a null result for the tested path-law family rather than a standalone falsification of AMC. The combined result establishes an exact QMU compactness normalization, an AMC correspondence with Painlevé--Gullstrand geometry, distinct propagation and constitutive thresholds, a neutron-specific radial source coordinate, an exact neutron equivalent-cell coordinate, an empirically constrained finite domain for the single-unit neutron--Aether deformation registration, and a validated observational pathway for testing future parameter-free AMC photon-propagation predictions. Version 1.3 includes the final neutron-cell comparison table, machine-readable EOS/deformation results, figure source data, and NICER/X-PSI validation products required for numerical reproduction.