impulseCoefficient_pos
plain-language theorem explainer
The per-cycle impulse coefficient is strictly positive in the asteroid trajectory model. Engineers modeling phantom-cavity drives on near-Earth objects cite it to guarantee that cumulative deflection grows positively with lead time. The proof is a one-line wrapper that reduces directly to the positivity of the carrier frequency after the coefficient is defined as equal to that frequency.
Claim. The per-cycle impulse coefficient satisfies $0 <$ impulseCoefficient, where impulseCoefficient is defined to equal the carrier frequency.
background
The Asteroid Trajectory Shaping module defines impulseCoefficient as the dimensionless analogue of per-cycle impulse, set equal to carrier_frequency. The upstream theorem carrier_frequency_pos establishes 0 < carrier_frequency by unfolding the definition and applying mul_pos to a positive numerical factor together with phi_pos. Cumulative deflection is then introduced as the function δ(t) = (impulseCoefficient · t²) / 2.
proof idea
The proof is a one-line wrapper that applies carrier_frequency_pos after the definition impulseCoefficient := carrier_frequency.
why it matters
This result supplies the impulse_pos field required by asteroidTrajectoryShapingCert and is invoked by the downstream theorems deflection_nonneg and deflection_pos_of_ne_zero. It anchors the first step of the module's derivation that deflection scales quadratically with lead time under a phantom-cavity drive at carrier frequency 5φ. The module's falsifier is an observed deflection inconsistent with δ ∝ t² to within 3σ over a 12-month tracking window.
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