Abstract
The Bullet Cluster separates hot X-ray plasma, cluster galaxies and the gravitational-lensing record on the sky. We test the observation-field branch of Physical--Observation Dual-Axis (PODA) dynamics using the ordinary initial--boundary-value standard of field theory: the universal equations and the previously fixed intrinsic observation-mode coefficient are held fixed, while the particular cluster is allowed object-specific initial data determined from non-lensing observations or from a declared calibration subset. No external dark-matter halo profile, modified-gravity law, mass--dispersion scaling relation or merger simulation enters the PODA calculation. The source geometry provides the first target. In equal 100-kpc apertures the Bullet plasma position contains \( (2.64\pm0.68)\times10^{12}M_\odot \) more measured baryonic mass than the Bullet BCG position, while the weak-lensing maximum lies on the galaxy side. The fixed PODA mode, \( m=5.6698\times10^{-61}\,\mathrm{kg} \), is coherent on 50--200 kpc scales over 100 Myr. We then construct a disjoint non-lensing phase-space initialization. The published DS+ Bullet component has nine galaxies, projected centre \( (-736,223) \) kpc and line-of-sight dispersion \( 849^{+232}_{-185}\,\mathrm{km\,s^{-1}} \). Mapping that component to the Barrena member table gives the Bullet projected axes \( (109.4,80.8) \) kpc. Removing those nine galaxies leaves 69 main-component members; a robust proje\( (-736,223) \)cted covariance gives axes \( (444.5,156.1) \) kpc, and their rest-frame gapper dispersion is \( 1241\,\mathrm{km\,s^{-1}} \) with a nonparametric 16--84 percentile interval \( 1124 \)--\( 1319\,\mathrm{km\,s^{-1}} \). This disjoint construction removes the earlier risk of using a whole-cluster dispersion as a main-component datum while adding the Bullet subgroup separately. A declared Gaussian moment closure of the PODA Vlasov--Poisson branch converts these measured phase-space data into one low-order Cauchy state. At the independently reported Bullet central dispersion, the common-source moment masses are \( 1.003\times10^{15}M_\odot \) and \( 1.676\times10^{14}M_\odot \) for the main and Bullet components. Their ratio, 5.99, is not identified with an \( M_{200c} \) ratio. The frozen two-dimensional source places its main and Bullet maxima \( 5.53'' \) and \( 3.62'' \) from the later weak-lensing maxima. The strongest test uses the 2026 spectroscopic strong-lensing sample. From the 27 secure background galaxies spanning \( z=0.897 \)--6.64 we retain one predeclared gold multiply-imaged feature per galaxy, giving 79 image positions and preventing multiple knots from one source from dominating the statistic. The physical deflection is computed directly from the frozen PODA surface density; the Fourier normalization was previously verified against the analytic Gaussian deflection to better than \( 0.7\% \). Because the Bullet velocity dispersion is an object-specific initial datum rather than a universal coupling, it is estimated only on training galaxies in a nested five-fold procedure. In each outer fold, an inner leave-one-galaxy-out calculation chooses \( \sigma_{\rm Bullet} \) on a predeclared 650--1100 \( \mathrm{km\,s^{-1}} \) grid and simultaneously fits a nonparametric monotone source-distance efficiency \( 0\le\beta(z)\le1 \). Both are then frozen before the outer galaxies are opened. The five PODA folds select \( \sigma_{\rm Bullet}=800 \)--825 \( \mathrm{km\,s^{-1}} \), close to the independent DS+ value, and give a pooled held-out source-plane angular scatter of \( 1.591'' \). Repeating the identical calibration with the same extra field moved to the X-ray plasma gives \( 4.009'' \); baryons alone give \( 13.836'' \). PODA is better for all 27 outer-held-out galaxies, with median per-galaxy RMS ratios 0.370 relative to the plasma-centred control and 0.103 relative to baryons only. The result establishes a transferable galaxy-side gravitational source within the declared low-order initialization. It does not yet constitute a resolved merger simulation or a full cosmological distance prediction.