half
plain-language theorem explainer
The definition introduces the spin-1/2 quantum number for fermions such as electrons and quarks. Researchers deriving the spin-statistics theorem from the 8-tick phase cycle in Recognition Science would cite this object as the base fermion spin. It is constructed by applying the half-integer spin constructor to the natural number 1, which sets the twice field to 1 and discharges nonnegativity by omega.
Claim. Let Spin be the structure whose field twice is an integer satisfying twice ≥ 0. The object half is the element of Spin with twice equal to 1.
background
The QFT.SpinStatistics module derives the spin-statistics theorem from Recognition Science's 8-tick phase structure. A 2π rotation traverses one 8-tick cycle; half-integer spins require two cycles to return to identity, producing phase factor -1 for fermions and +1 for bosons. The Spin structure encodes the quantum number via the twice field to keep arithmetic integer-valued, with a nonnegativity constraint. The halfInt constructor creates an instance by pairing a natural number n with the omega proof of nonnegativity. This declaration depends on halfInt from the same module together with anchor maps W and Z from the Masses and Physics modules that supply integer labels for lepton and quark sectors.
proof idea
This is a one-line definition that applies the halfInt constructor to the natural number 1. The constructor builds the Spin structure with twice set to 1 and invokes the omega tactic to confirm nonnegativity.
why it matters
The definition supplies the canonical spin-1/2 object required by the spin-statistics theorem in the QFT-001 module, which links directly to the eight-tick octave (T7) and the emergence of three spatial dimensions (T8) in the forcing chain. It is referenced in downstream results on pleasure symmetry, kinship cohomology, style succession, and planetary formation, showing its role in carrying J-cost structure across domains. The module doc-comment flags its potential for first-principles spintronic device design.
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