N_sec
plain-language theorem explainer
N_sec defines the number of fermion sectors as two raised to the power of (D minus one). Researchers deriving lepton masses from cube geometry in Recognition Science cite it to fix the multiplicity at four once D equals three. The definition is a direct arithmetic expression with no lemmas or reductions required.
Claim. The number of fermion sectors is given by $N_ {sec} := 2^{D-1}$, where $D$ is the number of spatial dimensions.
background
Recognition Science fixes D at three via the forcing chain T8. The ElectronMass.Defs module isolates core constants to break import cycles while deriving lepton sector values from cube geometry: twelve total edges, one active per tick, eleven passive edges, and seventeen wallpaper groups. N_sec multiplies the wallpaper count in the R0 offset formula after subtracting the octave-period adjustment from the electron baseline rung of two.
proof idea
One-line definition that directly applies the exponentiation operator to (D minus one) with D instantiated to three.
why it matters
N_sec supplies the sector multiplicity required by downstream definitions electron_baseline_rung and lepton_R0 together with the theorem lepton_sector_is_derived. Those results close the derivation chain showing lepton constants are forced by D equals three, passive-edge count eleven, and the eight-tick octave rather than free parameters. It anchors the T9 electron-mass step that links cube geometry to the phi-ladder mass formula.
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