weakIsospin
plain-language theorem explainer
Weak isospin is defined as the rational number 1/2 to label the doublet representations of left-handed fermions under the emergent SU(2)_L. Researchers deriving the weak force from Recognition Science ledger geometry cite this value when constructing chiral couplings and boson counts. The definition is a direct constant assignment with no lemmas or computation.
Claim. The weak isospin quantum number $I$ for left-handed fermion doublets is $I = 1/2$.
background
The Weak Force Emergence module (P-019) derives the weak nuclear force from the 3D ledger geometry of Recognition Science. This produces an SU(2)_L gauge structure with three generators, chiral coupling to left-handed fermions via the 8-tick cycle orientation, and massive mediators whose masses arise from J-cost minima at phi. The module lists predictions including weak isospin doublets such as (ν_e, e^-) and (u, d), parity violation, and the Fermi constant scale.
proof idea
Direct definition that assigns the rational constant 1/2. No lemmas or tactics are invoked.
why it matters
The definition supplies the isospin value required for doublet constructions and parity-violation statements in the same module. It fills the I = 1/2 slot in the SU(2)_L emergence from 3D geometry (T8) and the eight-tick octave that enforces left-handed coupling. No downstream uses are recorded yet.
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