B05: BRISM and Dark Matter Phenomenology: Resolving the NFW Cusp–Core Problem in IC 2574 with the Structural Projection Constant ε = 1/π²

*** For an updated discussion of the NFW profile as a fold caustic and its physical regularization, please see: *** *** https://doi.org/10.5281/zenodo.22764277 ****** B26: NFW Profiles as Fold Caustics: Physical Regularization and the Finite-Core Case of IC 2574 ****** as of 2026/09/23 ***------------------------------------------------------------------------------------------------------------------------------------------------- *** Superseded Notice as of 2026/09/23 *** This manuscript is retained for transparency and historical documentation but has been superseded by later work. A subsequent methodological review showed that quantities extracted from the analyses of Oh et al. and de Blok et al. were not transformed into fully equivalent and directly comparable numerical representations. As a consequence, the comparison framework used in this manuscript did not provide a sufficiently robust basis for the reported point-by-point correspondence between the observational reconstruction and the proposed fixed-regularized profile. The apparent agreement obtained through a fixed regularization scale (ε ≈ 0.1, including the previously discussed ε = 1/π² case) did not remain methodologically stable under deeper re-analysis and should therefore not be interpreted as evidence for a preferred or universal regularization parameter. The manuscript is retained as part of the historical development of the project. Subsequent work reformulates the problem in a more general framework that treats halo regularization, cusp-core structure, and possible geometric interpretations independently of the original IC2574 comparison. *** For the current consolidated overview of the BRISM framework, readers are referred to: *** *** BRISM after Ten Months: Status, Claims, Tests, and Future Directions. ****** https://doi.org/10.5281/zenodo.23495535 ****** This article represents the most up-to-date overview of the BRISM research program and serves as the primary review and status paper of the series. ****** Further BRISM articles and preprints can be accessed through the author’s ORCID profile: ****** https://orcid.org/0009-0008-7503-6012 ***