FieldVelocity
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not prove that the field velocity can reach c for any concrete pulse rate.
- Does not incorporate Lorentz factors or relativistic corrections.
- Does not derive the coil count or pulse width from the phi-ladder or Recognition Composition Law.
- Does not address power consumption or material limits of the coil array.
formal statement (Lean)
46def FieldVelocity (r : ℝ) (n_coils : ℕ) (pulse_width : ℝ) : ℝ :=
proof body
Definition body.
47 (2 * Real.pi * r) / (n_coils * pulse_width)
48
49/-- RS Hypothesis: Relativistic Field Effect.
50 If the virtual field velocity approaches c, the ILG kernel treats it
51 as a relativistic mass current, even if no matter is moving. -/