fermion_antisymmetry_from_8tick
plain-language theorem explainer
Fermions exhibit antisymmetric wavefunctions under exchange because they accumulate an odd phase factor across one full 8-tick cycle. Researchers deriving the spin-statistics connection from discrete time structures in Recognition Science would reference this result. The argument proceeds by substituting the established cycle phase value of -1 and simplifying the exchange relation algebraically.
Claim. Let $s$ be a half-integer spin. Suppose the two-particle wavefunction $ψ$ satisfies $ψ(x,y) = cyclePhase(s) · ψ(y,x)$ for all $x,y$. Then $ψ(x,y) = -ψ(y,x)$ for all $x,y$.
background
The Spin structure records twice the spin value as a nonnegative integer, so that half-integer spins correspond to odd values of this integer. The predicate isHalfInteger holds exactly when that integer is odd. The function cyclePhase returns the unimodular complex number exp(2π i s), which is the phase accumulated by a spin-s particle after one complete 8-tick cycle (a 2π rotation).
proof idea
The proof is a direct term-mode reduction. It introduces the variables, rewrites the exchange hypothesis using the cyclePhase factor, applies the upstream fermion_antisymmetric lemma to replace that factor by -1, and invokes the ring tactic to obtain the required antisymmetry.
why it matters
This declaration completes the QFT-002 step inside the module's derivation of the spin-statistics theorem from the 8-tick phase accumulation (T7 eight-tick octave). It shows how the phase mechanism forces Fermi-Dirac statistics for half-integer spins and sits within the Recognition Science program that obtains spatial dimension D=3 and the alpha band from the forcing chain. No immediate downstream theorems are listed.
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