hadron_mass
plain-language theorem explainer
hadron_mass defines the mass of a Hadron as the coherent energy scale multiplied by phi raised to the composite rung. Particle physicists modeling Regge trajectories would cite this when connecting quark rung assignments to observed meson and baryon masses. The definition is realized as a direct noncomputable expression that applies the composite rung function to the input structure.
Claim. For a Hadron $h$ formed by fermions $q_1$, $q_2$ and binding integer $b$, the mass is $E_{coh} · ϕ^{r}$ where $r =$ rung($q_1$) − rung($q_2$) + $b$.
background
The Hadron structure represents simple quark pairs such as a meson from an up quark and anti-down quark, with an optional binding integer defaulting to 1. The composite_rung function computes the effective level as the difference of the individual RSBridge rung values plus the binding term. Constants.E_coh and Constants.phi come from the abstract Constants bundle in CPM.LawOfExistence, which bundles projection and energy scales with nonnegativity conditions. Upstream rung assignments from RSBridge and Masses.AnchorPolicy provide the integer tiers for each fermion species. This definition operates in the setting of hadron mass relations derived from phi-tier spacing, as described in the module documentation for Phase 6 scaffolding.
proof idea
This is a definition that directly returns the product of the coherent energy constant and phi to the power of the composite rung of the given Hadron. It applies the composite_rung function from the same module to determine the exponent.
why it matters
The definition provides the mass formula used by the hadron_equal_z_degenerate theorem to show that hadrons with equal composite rungs have identical masses. It fills in the hadron mass relations from the module's derivation of Regge slopes and phi-tier spacing. Within the Recognition Science framework it connects to the phi-ladder and eight-beat binding, though the module marks the entire section as Phase 6 scaffolding outside core Level A completion.
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