Coil
plain-language theorem explainer
Coil records the identifier, angle, radius, and eight-tick phase offset of one stationary element in a virtual rotor array. Propulsion modelers cite it when building discrete phi-spiral samplings that replace mechanical rotation with pulsed magnetic flux. The declaration is a direct structure definition carrying no proof obligations or reductions.
Claim. A coil is a record $(id, θ, r, p)$ where $id ∈ ℕ$, $θ ∈ ℝ$, $r ∈ ℝ$, and $p ∈ {0,…,7}$ indexes the fundamental eight-tick cycle.
background
The Virtual Rotor module encodes the solid-state metric engine: a ring of fixed coils is pulsed in sequence to produce a rotating magnetic field whose speed is $v = 2πr/(8τ₀)$ with $τ₀$ the fundamental tick. This construction discretizes the phi-spiral geometry without moving mass. Upstream constants supply the tick duration and the eight-tick phase partitioning; identity maps from the cost algebra and arithmetic homomorphisms ensure the phased array remains algebraically closed under the Recognition Composition Law.
proof idea
The declaration is a plain structure definition. It introduces the four-field record type with no tactic steps, no lemma applications, and no computational content.
why it matters
Coil supplies the atomic datum for the SpiralArray construction that samples the log-spiral at discrete angles. It directly implements the eight-tick octave (T7) by bounding the phase field to 0..7, allowing the virtual rotor to approach relativistic field velocities while remaining within the Recognition Science phi-ladder. The structure therefore closes one step in the T0–T8 forcing chain for solid-state propulsion.
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