IndisputableMonolith.Physics.Hadrons
Defines simple hadrons as quark-pair composites and places their masses on the RS phi-ladder via a composite rung and the Anchor gap. Supplies Regge mass-squared, a PDG slope certificate, and basic linearity/nonnegativity facts. Anyone matching meson/baryon spectra or Regge trajectories in RS units would cite it. The module is mostly definitions plus short algebraic lemmas over the Anchor mass formula.
claimA hadron is a quark-pair composite. Its composite rung and mass are built from Anchor fermion data and the gap $F(Z)=\ln(1+Z/\varphi)/\ln\varphi$, so $m = m_\star\,\varphi^{r_{\mathrm{comp}}-8+F(Z)}$. Regge mass-squared $m^2(J)$ is linear in angular momentum with a certified PDG slope; equal-$Z$ hadrons are mass-degenerate.
background
Recognition Science puts particle masses on a discrete $\varphi$-ladder. The Anchor bridge supplies the twelve SM fermions, the charge index $Z_i=\tilde q^2+\tilde q^4$ (plus 4 for quarks), the gap $F(Z)=\ln(1+Z/\varphi)/\ln\varphi$, and the anchor-scale mass. Constants fix the RS tick and related units.
This module treats the simplest hadrons as quark pairs (e.g. a meson as up with anti-down). Composite rung and hadron mass lift the single-fermion Anchor formula to that pair. Regge mass-squared and a slope certificate connect the ladder picture to the familiar linear $m^2$ vs spin trajectories used in hadron phenomenology.
proof idea
Definition-heavy module: Hadron, composite rung, hadron mass, and Regge mass-squared are introduced from Anchor fermion/Z/gap data. Short lemmas then record equal-$Z$ mass degeneracy, nonnegativity of Regge $m^2$, and linearity in the Regge quantum number. The PDG Regge-slope certificate packages a numerical slope check; there is no deep forcing argument here, only algebraic consequences of the Anchor mass formula.
why it matters in Recognition Science
Closes the step from Anchor fermions to composite hadron masses inside the Physics domain, so meson/baryon spectra and Regge trajectories can be stated in RS-native units (phi-ladder, gap $F(Z)$, yardstick mass). Sibling exports (hadron mass, Regge slope certificate, linearity) are the natural hooks for spectrum matching and trajectory fits. No downstream modules are wired yet in the graph; the module stands as the hadron layer above RSBridge.Anchor rather than a link in the T0–T8 forcing chain.
scope and limits
- Does not derive QCD confinement or dynamical chiral symmetry breaking.
- Does not treat multi-quark exotics, glueballs, or full baryon three-quark wavefunctions beyond the pair model.
- Does not prove the numerical PDG slope from first principles; it certifies a stated value.
- Does not connect to electroweak precision or running couplings.
- Does not claim completeness of the hadron spectrum or decay widths.