PhaseEntry
plain-language theorem explainer
PhaseEntry is a record pairing a complex phase with an elapsed tick count to track accumulation during the eight-tick cycle. Researchers formalizing the spin-statistics theorem from discrete time would cite this record when modeling the sign change under 2π rotation for half-integer versus integer spin. The declaration is a direct structure definition with no computational content or proof obligations.
Claim. A structure consisting of a complex number representing accumulated phase and a natural number counting elapsed ticks.
background
Recognition Science derives the spin-statistics theorem from phase accumulation over the eight-tick cycle. A full 2π rotation corresponds to one cycle of eight ticks. Half-integer spins require two cycles to return to identity, yielding a minus sign under exchange, while integer spins return after one cycle. The tick is the fundamental time quantum set to 1 in RS-native units. The phase function from the EightTick module supplies the discrete phases kπ/4 for k in 0 to 7. PhaseEntry aggregates these increments into a running total for a given spin.
proof idea
The declaration is a direct structure definition introducing fields for the complex phase and the natural number tick count.
why it matters
This structure supports the derivation of the spin-statistics connection in the QFT module. It implements the phase mechanism described in the module documentation, where exp(2π i s) determines fermion or boson character. It connects to the eight-tick octave (T7) in the forcing chain and prepares the ground for the full spin-statistics theorem.
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