eight_tick_interference
plain-language theorem explainer
The sum of eight phase exponentials over a complete cycle vanishes, establishing destructive interference for equal-amplitude configurations in the discrete-time ledger. Researchers connecting Recognition Science ledgers to quantum superpositions would cite this when deriving vacuum fluctuation cancellation from the eight-tick structure. The proof is a direct one-line application of the roots-of-unity summation already proved in the EightTick module.
Claim. $∑_{k=0}^{7} exp(i k π / 4) = 0$, where the terms are the eighth roots of unity.
background
The QuantumLedger module connects ledger entries (each carrying a J-cost) to quantum states viewed as superpositions over ledger configurations, with the Born rule emerging from cost minimization rather than being postulated. The eight-tick octave supplies the fundamental evolution period: one tick is the RS-native time quantum τ₀ = 1, and eight ticks close the cycle. Upstream, phaseExp(k) returns the complex exponential exp(i · phase(k)) for k in Fin 8, while sum_8_phases_eq_zero records that these eight terms are the roots of unity and therefore sum to zero.
proof idea
One-line wrapper that applies the sum_8_phases_eq_zero theorem from the EightTick module.
why it matters
This supplies the interference step required by the downstream quantum_ledger_fundamentals theorem, which lists “8-tick phases enable interference” among its five core properties. It realizes the T7 eight-tick octave from the forcing chain and supplies the discrete mechanism for vacuum fluctuation cancellation in the quantum ledger setting.
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