Claim Summary

Rotation group and its cover: ESTABLISHED MATHEMATICS. SO(3), π₁(SO(3)) = ℤ₂, SU(2) double cover.

ℤ₂ from Axiom S: DERIVATION. Algebraic ℤ₂ identifies with π₁(SO(3)) via faithful embedding + N = 3 + σ = time-reversal. KS-S.1.

Paired vs unpaired: DERIVATION. Paired = boson (integer spin); unpaired ε = fermion (half-integer spin).

Why spin ½: DERIVATION. Minimum principle of Axiom B selects j = ½. KS-S.2.

Spin-statistics + Pauli: DERIVATION. ℤ₂ exchange properties give ±1 exchange phase; antisymmetry forces ψ = −ψ → ψ = 0. KS-S.3.

What this means: STRUCTURAL SYNTHESIS. Non-load-bearing.