cornellPotential
plain-language theorem explainer
The declaration defines the Cornell potential as V(r) = -α_s/r + σ r, substituting the Recognition Science values α_s = 2/17 and σ = φ^{-5}. Nuclear physicists bridging QCD confinement to the semi-empirical mass formula would cite this when evaluating binding energies at nuclear scales. It is a direct definition that inserts the module constants into the standard phenomenological form.
Claim. $V(r) = -{α_s}/r + σ r$ for $r > 0$, where $α_s = 2/17$ is the strong coupling constant and $σ = φ^{-5}$ is the string tension in Recognition Science units.
background
This module bridges the QCD-level strong force, with coupling α_s = 2/17 from wallpaper groups and string tension σ = φ^{-5}, to the coefficients of the semi-empirical mass formula. The Cornell potential supplies the standard phenomenological form for the quark-antiquark interaction. Upstream results define alpha_strong as the RS strong coupling constant (2/17) and stringTension as σ = φ^{-5}; the general form V(r) = -alpha/r + sigma r appears in the Confinement module.
proof idea
This is a direct definition that substitutes the module constants alpha_strong and stringTension into the linear combination of the Coulomb term and the confining linear term.
why it matters
It supplies the potential used by the theorem cornell_at_r0_formula to verify the sign structure at r0 = 1.2 fm. Downstream it supports jcostColorPotential, which interprets the linear term as J-cost of color separation, and potential_confining, which proves the potential grows with r. This implements the bridge from Recognition Science constants (T5 J-uniqueness and T7 eight-tick octave) to nuclear binding energies.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.