Core-Cusp Problem (5-Sigma)

The core-cusp problem arises because pure cold dark matter simulations consistently predict that gravitationally bound halos should develop steep central density cusps scaling as ρ ∝ r⁻¹ or steeper, while observed dwarf galaxies and low-surface-brightness galaxies almost universally exhibit flat central density cores. In ΛCDM this discrepancy reaches five-sigma significance and has resisted resolution for decades, with proposed baryonic feedback remedies requiring supernova energy inputs that strain credibility at the low masses where the problem is sharpest. Successive Collision Theory dissolves this tension without invoking feedback or modifying gravity by replacing the dark matter cusp entirely with two physically distinct contributions: inherited angular momentum and gravitational superposition from nested comoving frames.

When the two spacetime pockets collided, the impact parameter deposited a specific angular momentum budget into every debris element, conserved exactly by Noether's theorem as structures assembled. This angular momentum sets a centrifugal barrier at the center of every collapsing structure: infalling matter cannot penetrate below the radius where centrifugal support balances gravity, naturally producing a flat-density core rather than a diverging cusp. Simultaneously, the gravitational superposition of overlapping nested comoving frames adds effective gravitational influence in proportion to the local depth within the frame hierarchy, and this superposition contribution is distributed smoothly rather than concentrated toward a singular center, further flattening the central profile. Together these two mechanisms — angular momentum inheritance and coherent frame superposition — replace the cusp with a core as the generic prediction of SCT for all virialized structures, resolving the five-sigma discrepancy without dark matter particles, modified gravity, or baryonic feedback.

The same angular momentum scaling law J ∝ M^(5/3) that flattens rotation curves at galactic scales applies equally to dwarf galaxies and ultra-faint satellites: each inherits specific angular momentum proportional to its mass and formation radius within the collision debris field. Smaller structures that formed in less angular-momentum-rich regions of the debris develop shallower central gradients, naturally explaining the observed diversity of core sizes and the correlation between core radius and total mass that observations reveal but standard CDM cannot predict without tuning feedback prescriptions on a case-by-case basis.