FieldVelocity
plain-language theorem explainer
The FieldVelocity definition supplies the tip speed of a virtual rotating magnetic field produced by sequentially pulsing a ring of stationary coils. Researchers modeling solid-state metric engines would cite it to express effective velocity as circumference divided by the aggregate pulse period. The definition is a direct one-line algebraic expression of the distance-over-time relation with no lemmas or reductions required.
Claim. The virtual field velocity is defined by $v = 2π r / (n · τ)$, where $r$ is the coil radius, $n$ the number of coils, and $τ$ the pulse width of each coil.
background
This definition sits inside the Virtual Rotor module, which develops a solid-state metric engine: a ring of stationary coils pulsed in sequence to generate a rotating magnetic field that mimics a physical φ-spiral rotor. The module replaces spinning mass with spinning information density (magnetic flux) and notes that sufficiently short pulse widths (MHz/GHz) allow the field velocity to approach c. The supplied expression follows the standard tip-speed formula with period taken as the product of coil count and individual pulse width.
proof idea
This is a one-line definition that directly encodes the tip-speed formula as circumference divided by the product of coil count and pulse width.
why it matters
The definition supplies the velocity quantity required by the RS Hypothesis for a Virtual Rotor in the Flight domain. It provides the input needed to treat an approaching-c field as a relativistic mass current under the ILG kernel. No downstream theorems are recorded in the used-by graph, so the declaration functions as a foundational quantity for later modeling of information-density propulsion. It aligns with the Recognition Science emphasis on virtual fields and the eight-tick octave structure without invoking the J-cost or phi-ladder explicitly.
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