What question did this study set out to answer?

The aim is to develop and test a novel regime law for analyzing dissociative galaxy-cluster collisions using a frozen carrier-spinor framework.

May 4, 2026Open Access

Phase-5b: A Frozen Carrier-Spinor Regime Law for Dissociative Galaxy-Cluster Collisions

Key Points

The aim is to develop and test a novel regime law for analyzing dissociative galaxy-cluster collisions using a frozen carrier-spinor framework.
Utilized a six-sector carrier-exchange geometry to define collision regimes.
Applied a closure-gradient transport response operator to analyze Chandra X-ray data.
Classified empirical results without fitting the final regime label based on computed transverse core-width.
The protected transverse core-width eta_perp remained stable between 0.081 and 0.085 across several tested galaxy-clusters.
Successful atlas tests were conducted on notable galaxy clusters such as A2146 and El Gordo.
Included secondary analyses and robustness checks through supportive ZIP packages for verification.

Abstract

This archive contains the paper: Phase-5b: A Frozen Carrier-Spinor Regime Law for Dissociative Galaxy-Cluster Collisions The paper develops and tests a frozen carrier-spinor regime law for dissociative galaxy-cluster collisions within Phase-5 global closure geometry. The central empirical claim is that externally defined carrier geometry admits the test, while the frozen closure-gradient operator selects the collision regime. The construction uses a six-sector carrier-exchange geometry, fixing the protected carrier aperture by R = Dcarrier / 6. The response operator is derived from closure-gradient transport and applied to Chandra soft-band X-ray data through an image-normalized closure-gradient proxy. The protected transverse core-width etaₚerp is computed before classification and is not fitted to the final regime label. The primary empirical atlas tests the frozen law on A2146, A520, A2744, El Gordo, A2029, and ZwCl0008. These systems cover the practical regime map: NODISSOCIATIVEREGIMEBALANCEDPHASELOCKCANDIDATEONESIDEDPHASESTRAINANTIPHASEMIXEDANTIPHASEMIXEDWITHCORELOCKCOMPLEXMULTISTRUCTURESTRESSTRANSITIONALDOUBLERELICSTRESS Across the primary dissociative systems, the protected width remains stable at approximately etaₚerp = 0. 081 to 0. 085. The archive includes two supplementary ZIP packages. GEOMPHASE5BALLCERTIFICATESMASTER. zip contains the primary empirical certificate package, including summary files, regime-map tables, object-level certificate products, robustness audits, null audits, and supporting diagnostic outputs. SECONDARYATLASFINAL_₂0260502₀43400. zip contains the secondary Chandra atlas used in Appendix C. It includes additional relaxed controls, external-axis replication tests, null-stress audits, smoothing audits, leave-one-out checks where applicable, and secondary object summaries. The secondary atlas is not used to define or tune the law. It is included as an additional replication and robustness package. All empirical classifications follow the fixed rule: external carrier geometry first;frozen regime operator second. Artificial axes, X-ray-selected axes, and post-result visual choices are treated only as null or stress diagnostics, not as final carrier certificates.

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