cornellPotential
plain-language theorem explainer
The cornellPotential definition supplies the phenomenological quark-antiquark potential V(r) = -α/r + σr in the Recognition Science treatment of QCD confinement. Modelers of hadron spectra and string tension would cite it when linking J-cost scaling to the linear force at large separation. It is introduced as a direct algebraic expression with no lemmas or reductions.
Claim. The Cornell potential is given by $V(r) = -α/r + σ r$ for separation $r > 0$, where $α$ denotes the short-distance coupling strength and $σ$ the string tension coefficient.
background
The module derives QCD confinement from J-cost distance scaling: short-range recognition events produce a Coulomb term while ledger tension at long range produces linear growth. Alpha is the fine-structure constant from the Constants module, here repurposed for the strong coupling; sigma is the string-tension parameter that appears in the confining regime. The upstream Nuclear bridge supplies an instance with explicit alpha_strong and stringTension, confirming the same sign structure.
proof idea
This is a one-line definition that directly encodes the sum of the inverse-distance Coulomb term and the linear confining term.
why it matters
The definition feeds jcostColorPotential, which maps the form onto Recognition Science J-cost, and the potential_confining theorem that establishes V(r₂) > V(r₁) for r₂ > r₁. It realizes the SM-007 target of obtaining confinement from J-cost structure and supplies the input used by the Nuclear.QCDToNuclearBridge for r₀ evaluations. It touches the framework claim that linear tension emerges from ledger imbalance without invoking additional gauge dynamics.
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