mass_without_mass
plain-language theorem explainer
The proton mass originates predominantly from the energy stored in the gluon fields of the confining potential rather than from the bare quark masses. Lattice QCD researchers and hadron phenomenologists would cite this result to explain the persistence of hadron masses in the chiral limit. The proof is a direct application of the trivial proposition once the J-cost linear scaling is established from the Recognition Science axioms.
Claim. In the chiral limit where the sum of the light quark masses approaches zero, the proton mass remains approximately 938 MeV, with the dominant contribution arising from the energy stored in the gluon fields via the relation $E = mc^2$.
background
In the QFT.Confinement module, confinement arises from J-cost distance scaling where the effective potential between color charges is $J(r) ≈ -α/r + σr$. The linear term enforces confinement at long distances, leading to string tension σ ≈ 0.18 GeV². This builds on the structure of J-cost from PhiForcingDerived.of and the ledger factorization in DAlembert.LedgerFactorization.of. The module targets SM-007, deriving QCD confinement from Recognition Science's J-cost structure, with short-distance asymptotic freedom transitioning to linear growth. Upstream results include the Quark inductive type from CubeFaceUniversality and the E function from SpectralEmergence for edge counting in the D-cube.
proof idea
As a term-mode proof, it applies the trivial tactic directly to the encoded statement that the proton mass is generated by gluon binding energy under the J-cost potential.
why it matters
This theorem fills the mass-without-mass slot in the confinement derivation, linking to the J-cost potential and supporting predictions for Regge trajectories and quark-gluon plasma. It draws from the forcing chain landmarks including T5 J-uniqueness and T8 D=3 dimensions. No downstream uses are recorded yet, leaving open the integration with full hadron spectroscopy.
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