quarkDoublet
The declaration sets quarkDoublet to the natural number 2, encoding the two-component isospin doublet of up and down quarks in the weak sector. Workers on Recognition Science derivations of electroweak structure reference it when counting left-handed fermion representations that arise from 3D ledger geometry. The entry is introduced by direct constant assignment with no reduction steps or external lemmas.
claimThe quark isospin doublet $(u,d)$ is assigned the dimension $2$.
background
The module derives the weak force from Recognition Science ledger geometry. SU(2)_L symmetry emerges from the three generators of 3D rotations, chiral coupling follows from the orientation of the eight-tick cycle, and massive mediators arise from the J-cost minimum at phi. The module lists weak isospin doublets such as (νe, e−) and (u, d) among its predictions.
proof idea
Direct constant definition that assigns the value 2.
why it matters in Recognition Science
The definition supplies the quark representation count required by the weak-force emergence derivation (P-019). It supports the module's enumeration of left-handed doublets that couple to the SU(2) generators obtained from the 3D ledger. No downstream theorems are recorded, so the entry functions as a fixed input to the overall doublet tally.
scope and limits
- Does not derive the integer 2 from the phi-ladder or J-cost functional.
- Does not list the explicit quark fields or their hypercharges.
- Does not address CKM mixing or intergenerational transitions.
formal statement (Lean)
93def quarkDoublet : ℕ := 2
proof body
Definition body.
94
95/-- Each generation has 2 isospin doublets. -/