coreCuspProblem
plain-language theorem explainer
The coreCuspProblem definition states the discrepancy between N-body simulations predicting a central density cusp scaling as 1/r and observations showing a constant-density core. Galaxy formation modelers and dark-matter phenomenologists cite it when evaluating alternatives to standard NFW halos. The entry is a direct string assignment that embeds the Recognition Science claim of ledger interactions suppressing the cusp.
Claim. The core-cusp problem is the mismatch in which Navarro-Frenk-White profiles give central density scaling as $ρ ∝ 1/r$ while observations indicate a constant core $ρ ≈ const$ near galaxy centers; Recognition Science attributes the core to ledger interactions that raise J-cost faster than $1/r^2$ at high density.
background
The module COS-011 models galaxy rotation curves as arising from dark-matter ledger distributions, where dark matter consists of ledger shadows in odd 8-tick phases and flat outer velocities follow from J-cost equilibrium. J-cost is the recognition cost of an event, defined as the derived cost induced by a multiplicative recognizer on positive ratios and satisfying the Recognition Composition Law. Upstream results supply the constant admissible path, the structure of nuclear densities on φ-tiers, and the ledger factorization that calibrates J.
proof idea
This is a one-line definition that directly assigns the descriptive string for the core-cusp discrepancy together with the RS ledger-resolution note.
why it matters
The definition records the RS prediction that high-density ledger entries interact more strongly, driving J-cost above the 1/r² scaling that would produce a cusp and thereby forcing a core. It sits inside the COS-011 target of deriving flat rotation curves from ledger distributions and connects to the eight-tick octave and φ-forcing chain. No downstream theorems depend on it yet; it leaves open whether the ledger mechanism quantitatively matches observed core radii without additional baryonic feedback.
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