breakingLength
plain-language theorem explainer
breakingLength computes the critical quark separation at which the confining string breaks via the relation twice the constituent quark mass divided by string tension. QCD phenomenologists working in Recognition Science would cite it when estimating typical hadron radii from the linear potential. The definition is a direct arithmetic expression that imports the upstream stringTension value.
Claim. The breaking length is the distance $r_b$ at which the string tension satisfies $r_b = 2m_q / σ$ with constituent quark mass parameter $m_q = 0.3$ GeV, where $σ$ is the string tension.
background
The module derives QCD confinement from J-cost distance scaling: short-distance behavior is Coulomb-like while long-distance J-cost grows linearly as $J(r) ≈ -α/r + σ r$, producing constant force and string tension. String tension is supplied by the upstream definition $σ = φ^{-5}$ in RS-native units from the Nuclear.QCDToNuclearBridge module. The breaking condition follows from equating string energy $σ r$ to twice the constituent quark mass, using the ~300 MeV value that yields lengths on the order of a few fm.
proof idea
The definition is a one-line arithmetic wrapper that divides twice the numerical quark-mass parameter by the stringTension value imported from the QCD bridge.
why it matters
This supplies the explicit length scale for string breaking inside the J-cost confinement model, completing the long-distance linear term of the potential. It anchors the framework's phi-ladder mass formulas and eight-tick octave to observable hadron sizes. No downstream theorems are listed, so the definition functions as a parameter source for further hadronization and light-quark mass calculations.
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