FermionSector
plain-language theorem explainer
The fermion sector type enumerates three cases: leptons, up quarks, and down quarks. Mass ratio derivations cite it to select the base rung on the phi-ladder before adding generation torsion offsets. The definition is a direct inductive enumeration that automatically supplies decidable equality and representation.
Claim. The type of fermion sectors is the inductive type whose constructors are leptons, up-quarks, and down-quarks.
background
In the RSLedger module, masses sit on the phi-ladder with each sector carrying a fixed base rung taken from the charge map Z. Leptons receive base rung 2 while both up and down quarks receive base rung 4; the full rung for a given generation is then base plus the torsion offset 0, 11 or 17. Torsion itself arises from D=3 cube combinatorics: zero for the ground generation, cube edges minus one for the second, and edges plus faces for the third.
proof idea
The declaration is an inductive definition that introduces exactly three constructors. No lemmas or tactics are invoked; the type is supplied directly to downstream functions that pattern-match on sector to retrieve the corresponding base rung.
why it matters
The type supplies the sector argument to the canonical mass-ratio theorems (canonical_massRatio_21, canonical_massRatio_31, canonical_massRatio_32) that establish the ratios phi^11, phi^17 and phi^6 once torsion equals generationTorsion. It therefore realizes the sector-dependent base rungs required by the Recognition Science mass formula and the eight-tick octave structure.
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