PulseCoherence
plain-language theorem explainer
PulseCoherence encodes the eight-tick neutrality requirement for any boolean pulse schedule in the virtual rotor model. Propulsion researchers simulating phased-array magnetic fields would invoke it to certify that a sequence produces zero net bias over the fundamental period. The definition is realized by a direct one-line wrapper that maps the schedule to signed weights and applies the eight-gate sum predicate at offset zero.
Claim. Let $s : ℕ → {true, false}$ be a pulse schedule. Pulse coherence holds precisely when $∑_{k=0}^{7} σ(k) = 0$, where $σ(k) = +1$ if $s(k)$ is true and $σ(k) = -1$ otherwise.
background
The Virtual Rotor module formalizes a solid-state metric engine in which stationary coils are pulsed sequentially to generate a rotating magnetic field that emulates a φ-spiral rotor. Field velocity is expressed as $v = 2πr / (8 τ_pulse)$, so that sufficiently rapid pulsing can approach relativistic speeds. The upstream eightGateNeutral predicate (re-exported from SpiralField into Schedule) states that the sum of any eight consecutive weights equals zero; the Atomicity.Schedule structure supplies the underlying sequential, one-per-tick history.
proof idea
The definition is a one-line wrapper that applies eightGateNeutral to the schedule converted by the map $t ↦$ if schedule $t$ then 1 else -1, evaluated at $t0 = 0$.
why it matters
This definition supplies the RS falsifier for 8-tick coherence inside the virtual-rotor construction. It directly encodes the eight-tick octave constraint (T7) of the forcing chain, guaranteeing that the signed pulse sequence carries no net contribution over the period-8 window. In the Recognition framework the predicate closes the phase-stability requirement for information-density rotation; any violation would destroy the solid character of the virtual object.
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