quark_hierarchy
plain-language theorem explainer
The quark_hierarchy definition supplies the rung separations for the top-bottom-charm-strange quarter-ladder inside the GenerationStructure record. A physicist embedding quark mass spectra into the Recognition Science phi-ladder would cite it to align the quark sector with the unified generation model. The construction is a direct structure literal that assigns the two delta fields from the deep ladder mapping.
Claim. The quark hierarchy is the record $G = (G_1, G_2)$ where $G_1$ is the top-to-bottom rung step and $G_2$ is the bottom-to-charm rung step, both taken from the quarter-ladder mapping of the deep ladder.
background
GenerationStructure is the record type whose two real fields delta1 and delta2 hold the rung separations between the three fermion generations. These separations are derived from the cubic voxel geometry with parameters $E_p = 11$ and $F = 6$, giving integer gaps of 11 and 6 rungs for leptons and scaled quarter-ladder gaps for quarks. The module unifies discrete ladder positions across fermion sectors to demonstrate structural coherence of the three-generation model; the quark portion adopts quarter-ladder coordinates from MixingGeometry as a hypothesis lane (Gap 6) distinct from the integer-rung core spectra. Upstream, SpectralEmergence.of shows that the Q3 structure forces exactly three generations together with the gauge content SU(3) × SU(2) × U(1). Constants.tick supplies the fundamental time quantum whose octave equals eight ticks.
proof idea
The definition is a one-line structure literal that directly populates the delta1 and delta2 fields of GenerationStructure with the step_top_bottom and step_bottom_charm terms drawn from the deep ladder mapping.
why it matters
This definition supplies the quark-sector input required by the downstream hierarchy_coherence theorem, which establishes that lepton and quark hierarchies are both sub-structures of the same 8-tick recognition cycle. It fills the quarter-ladder component of the unified generation hierarchy, linking to the phi-ladder mass formula and the spectral emergence result that fixes three generations from the cubic voxel. It touches the open Gap 6 question of integer versus quarter-ladder quark coordinates.
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