impulseCoefficient
The impulseCoefficient definition sets the dimensionless per-cycle impulse coefficient equal to the carrier frequency. Asteroid deflection modelers cite it when deriving quadratic trajectory shifts from phantom-cavity drives at lead time t. The definition is a direct alias to the upstream carrier_frequency constant fixed at 5 phi.
claimThe per-cycle impulse coefficient is defined by $k := 5 phi$, where $k$ is the dimensionless scaling factor for recoil impulse and $phi$ is the golden ratio.
background
The Asteroid Trajectory Shaping module treats a phantom-cavity drive coupled to a small body. Per-cycle impulse is given by $Delta p = m cdot v_recoil$ with recoil velocity tied to carrier frequency $omega_carrier = 5 phi$ Hz; cumulative deflection is then $delta(t) = (Delta p / m) cdot t^2 / 2$. The impulseCoefficient supplies the scaling factor that appears in this expression. It depends directly on the carrier_frequency definition, which sets the drive frequency to five times the golden ratio.
proof idea
This is a one-line definition that aliases the carrier_frequency constant directly.
why it matters in Recognition Science
The definition supplies the impulse scaling factor required by the AsteroidTrajectoryShapingCert structure and the deflection function. It anchors the engineering derivation to the Recognition Science constant phi and the carrier frequency band. It supports the falsifier test of deflection scaling as $t^2$ over a 12-month tracking window.
scope and limits
- Does not establish positivity of the coefficient.
- Does not incorporate asteroid mass or drive power parameters.
- Does not address relativistic corrections or external perturbations.
Lean usage
theorem deflection_example (t : ℝ) : deflection t = (impulseCoefficient * t^2) / 2 := by rflformal statement (Lean)
53def impulseCoefficient : ℝ := carrier_frequency
proof body
Definition body.
54