jcostColorPotential
plain-language theorem explainer
jcostColorPotential defines the potential for color charge separation in Recognition Science as the J-cost of ledger imbalance. It combines short-range inverse attraction from recognition events with long-range linear growth from ledger tension. QCD theorists would cite it when modeling confinement and hadronization from first principles. The definition is a direct one-line wrapper around the Cornell potential using the short-distance coupling and string tension.
Claim. For distance $r > 0$, the J-cost of color separation equals the Cornell form $V(r) = -a/r + s r$, where $a$ is the short-distance strong coupling and $s$ the string tension.
background
The J-cost is the derived cost of a multiplicative recognizer comparator on positive ratios and equals the J-cost of any recognition event state. In the SM-007 module, confinement follows from J-cost distance scaling: short distances yield Coulomb-like behavior while long distances produce linear growth. Upstream results establish non-negativity of event costs and link them to simplicial ledger edge lengths from psi.
proof idea
The definition is a one-line wrapper that applies the Cornell potential construction to the short-distance coupling and string tension parameters.
why it matters
This supplies the explicit potential form required by the SM-007 target of deriving quark confinement from J-cost structure. It supports sibling results on asymptotic freedom at short distances and string breaking at long distances within the QFT module. The linear term traces to ledger tension in the simplicial ledger and aligns with the recognition composition law for scaling.
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