value
plain-language theorem explainer
The value definition extracts the real spin number from the Spin structure by halving its twice integer field. Researchers deriving spin-statistics relations from the eight-tick cycle would reference this extractor when converting between integer and real representations. The definition is a direct field projection with no additional computation.
Claim. Let $s$ be a spin quantum number encoded as a non-negative integer $t = 2s$. Then the real-valued spin is $v(s) = t / 2$.
background
The Spin structure encodes half-integer quantum numbers via an integer twice field together with a nonnegativity guard. The QFT.SpinStatistics module derives the spin-statistics theorem from Recognition Science's 8-tick phase cycle: a $2π$ rotation traverses one full cycle, so half-integer spins require two cycles (phase $-1$, fermions) while integer spins require one (phase $+1$, bosons). Upstream half supplies the canonical spin-$1/2$ instance via halfInt 1.
proof idea
One-line definition that projects the twice field of the Spin structure and divides by 2.
why it matters
This extractor supplies the real spin value consumed by forty downstream declarations, including geodesic_minimizes_via_convexity in Action.FunctionalConvexity and defectDist_nonneg in Algebra.CostAlgebra. It directly supports the QFT-001 target of obtaining spin-statistics from the eight-tick octave (T7) and the phase rule exp(2πi s). No open scaffolding is attached.
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