threeHalves
plain-language theorem explainer
The threeHalves definition supplies the spin-3/2 quantum number inside the Recognition Science derivation of spin-statistics from the 8-tick cycle. Supersymmetry and gravitino modelers would cite it when listing allowed half-integer spins. It is a direct one-line wrapper around the halfInt constructor applied to 3.
Claim. The half-integer spin value $s = 3/2$, encoded in the Spin structure by setting the twice field to 3 while satisfying the non-negativity constraint.
background
The Spin structure represents the spin quantum number as a half-integer $n/2$ for integer $n$, stored as the twice field (a non-negative integer) together with a non-negativity proof. The halfInt constructor builds a Spin object directly from a natural number $n$ by pairing it with the omega-generated non-negativity witness. This construction lives inside the QFT.SpinStatistics module whose module document states that the spin-statistics connection arises from phase accumulation over the 8-tick cycle: a $2π$ rotation traverses one full period, and half-integer spins accumulate a minus sign after one cycle.
proof idea
This is a one-line wrapper that applies the halfInt constructor to the natural number 3, inheriting the non-negativity obligation already discharged inside the halfInt definition.
why it matters
It populates the explicit list of spins examined by the no_sm_falsifier theorem, which asserts that every listed spin (including this one) obeys the exchange symmetry rule dictated by its half-integer or integer character. The declaration therefore fills the QFT-001 target of obtaining the spin-statistics theorem from the 8-tick phase mechanism. It instantiates the T7 eight-tick octave landmark for the hypothetical gravitino case.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.