carrier_frequency
The carrier frequency is defined as five times the golden ratio phi, giving the drive frequency for phantom-cavity asteroid shaping. Engineers cite this constant when computing recoil impulses and t-squared deflection scaling. The declaration is a direct real-number assignment with no lemmas or reduction steps.
claimThe carrier frequency is defined by $5φ$ Hz, where $φ$ is the golden ratio.
background
The Asteroid Trajectory Shaping module models a phantom-cavity drive that produces per-cycle impulse Δp = m · v_recoil, with v_recoil proportional to carrier frequency ω_carrier. The module fixes ω_carrier = 5φ Hz so that the frequency lies inside (8.05, 8.10) Hz. Phi enters from the Recognition Science forcing chain as the self-similar fixed point (T6) that satisfies the J-cost functional equation.
proof idea
The declaration is a direct definition that assigns the literal expression 5 * phi to carrier_frequency. No lemmas are invoked and no tactics are applied.
why it matters in Recognition Science
This definition supplies the concrete frequency value that feeds asteroid_one_statement and the AsteroidTrajectoryShapingCert structure. It instantiates the engineering derivation in which deflection scales as t² and doubling lead time quadruples deflection. The value 5φ is chosen to place the carrier inside the band verified by carrier_frequency_band, linking the model to the phi fixed point forced at T6 of the unified forcing chain.
scope and limits
- Does not derive the numerical bounds on phi itself.
- Does not prove that 5φ lies inside (8.05, 8.10) Hz; that is shown in a separate theorem.
- Does not define the impulse coefficient; that is introduced as a separate definition equal to this frequency.
- Does not address the overall falsifier condition for the asteroid model.
Lean usage
⟨carrier_frequency_band.1, carrier_frequency_band.2, deflection_double, deflection_zero⟩formal statement (Lean)
39def carrier_frequency : ℝ := 5 * phi
proof body
Definition body.
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