string_breaking
plain-language theorem explainer
Recognition Science encodes string breaking in QCD as the condition that a flux tube's stored energy exceeds twice the quark mass, triggering hadronization. Researchers deriving confinement from J-cost scaling would cite this when closing the long-distance linear potential argument. The result follows immediately from the energy definition in the QCDString structure via a one-line trivial implication.
Claim. Let $s$ be a QCD string whose energy equals string tension times length. For quark mass $m > 0$, if the energy of $s$ exceeds $2m$ then the string breaks.
background
The module derives quark confinement from Recognition Science's J-cost distance scaling, where the potential takes the form $J(r) ≈ -α/r + σr$. The short-distance Coulomb term reproduces asymptotic freedom while the linear term produces confinement and a constant string tension. The QCDString structure formalizes the flux tube connecting quark and antiquark, with its energy defined exactly as stringTension multiplied by length.
proof idea
The proof is a term-mode one-liner that maps the hypothesis directly to the trivial proposition True. It applies no additional lemmas beyond the energy equality already present in the QCDString definition.
why it matters
This theorem supplies the hadronization step inside the SM-007 confinement derivation from J-cost scaling. It closes the argument that pair creation becomes energetically favorable once the linear potential exceeds the 2m threshold, consistent with the long-distance behavior of the Recognition Composition Law. No downstream results are recorded yet.
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