step_down_gen1
plain-language theorem explainer
The down-quark generation step constant is fixed at 6. Researchers constructing fermion mass spectra via the phi-ladder in Recognition Science cite this value when placing down-type quarks on the rung positions. The assignment follows at once from the geometric relation F equals twice the spatial dimension D.
Claim. The first-generation step for down quarks equals 6, satisfying the face count relation $F=2D$ with spatial dimension $D=3$.
background
The module defines Sector-Dependent Generation Torsion (SDGT) for each fermion sector. Down quarks employ the consecutive pair {F=6, V=8} summing to 14, completing the cyclic chain V+F-C=13, E_pass=11, F=6, V=8 that partitions N₃=2D^D+1=55. This replaces the legacy universal torsion {0,11,17} retained only for leptons.
proof idea
The declaration is a direct definition that hard-codes the integer 6, motivated by the relation F=2D with D fixed at 3.
why it matters
It supplies the down-quark entry for tau_sdgt, the canonical cumulative generation torsion across all sectors. This completes the SDGT partition in the masses module and aligns with T8 fixing D=3 from the eight-tick octave. The hypothesis tag flags that the geometric origin of F as twice the dimension remains open.
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