SpiralArray
plain-language theorem explainer
SpiralArray builds a list of Coil records by sampling a logarithmic spiral at equal angular intervals for a virtual rotor. Engineers modeling phased-array field propulsion in Recognition Science cite this for discrete phi-spiral geometry. The definition enumerates indices 0 to n_coils-1, computes each angle as a uniform circle division, pulls radius from the logSpiral lemma, and sets phase offset as index modulo 8.
Claim. For natural number $n$, real $r_0$, and integer $k$, the construction yields a list of $n$ coils where the $i$-th coil has angle $2$π$i$/$n$, radius from the logarithmic spiral evaluated at $r_0$, angle, and $k$, and phase offset $i$ mod $8$.
background
The module formalizes a solid-state metric engine: a ring of stationary coils pulsed in sequence to produce a rotating magnetic field that mimics a physical phi-spiral rotor. A Coil is the structure holding an identifier, polar angle, radius, and phase offset restricted to 0..7 to align with the eight-tick cycle. Upstream results supply the logSpiral function from geometry lemmas and the period definition as phi raised to integer power from pulsar emission regimes.
proof idea
The definition applies List.range to n_coils then maps each index i to a Coil record. It computes theta directly as (i : real) times 2 pi over n_coils, obtains radius by calling Geometry.SpiralLemmas.logSpiral with r0, theta, and kappa record, sets phase as i modulo 8, and assembles the four fields.
why it matters
This supplies the geometric sampling step for the virtual rotor hypothesis in the Flight domain. It discretizes the phi-spiral to support field-velocity calculations approaching c at high pulse rates, consistent with the eight-tick octave landmark. No downstream uses are recorded, leaving open its linkage to full metric-engine theorems or relativistic field effects.
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