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

This publication presents an updated structural explanation of the Navarro–Frenk–White (NFW) density profile within the BRISM framework (Brane–Resonance–Interface–State Model). In BRISM, the observable universe is interpreted as the real‑structured projection of unitary bulk states through a phase‑neutral, σ‑additive and positive Naimark–Stinespring interface. Under these constraints, the Born‑quadratic form emerges as the unique stable projection rule determined by probability conservation, Gleason/Busch additivity, and spectral stability of the dilation space. A key result of this version is the identification of a structural projection constant ε = 1/π²,which represents the minimal phase‑neutral surface element of the S²‑averaged interface. This constant is not a tunable parameter: it regularizes the otherwise divergent inner NFW cusp and produces a finite, stable core while preserving the universal r⁻¹ and r⁻³ regimes of the NFW profile. A quantitative comparison with the THINGS dwarf galaxy IC 2574 shows that the BRISM‑derived projection profile reproduces both the amplitude and shape of the observed core region without parameter fitting, whereas the standard NFW prediction overshoots the central density by nearly an order of magnitude. The constant ε = 1/π² therefore provides a purely geometric resolution of the long‑standing cusp–core discrepancy, positioning the NFW form as a projection‑induced attractor rather than a dynamical outcome. This dataset includes analytic expressions, numerical evaluations, and side‑by‑side comparisons with observational anchor ranges for IC 2574. It provides a reproducible foundation for applying the BRISM projection framework to galaxy‑scale mass modelling and for further testing the universality of the structural coherence scale ε across different astrophysical systems.