IndisputableMonolith.Engineering.AsteroidTrajectoryShaping
The AsteroidTrajectoryShaping module supplies definitions for carrier frequency, impulse coefficients, and deflection parameters tailored to asteroid trajectory shaping in Recognition Science. Engineers applying Recognition Science to planetary defense would cite the 5φ Hz drive frequency. The module consists of definitions accompanied by positivity and non-negativity lemmas.
claimThe drive carrier frequency is $5\phi$ Hz, with impulseCoefficient and deflection functions satisfying non-negativity and positivity conditions.
background
The module operates in the engineering domain of Recognition Science. It imports the fundamental time quantum $\tau_0 = 1$ tick from Constants and cost structures from Cost.
Definitions cover carrier_frequency set to $5\phi$ Hz, impulseCoefficient, and deflection, each with lemmas for non-negativity and positivity. The setting applies phi-based constants to frequency selection in deflection systems.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module extends the Recognition framework into engineering applications for asteroid trajectory shaping. It has no listed parent theorems but provides parameters that could support future uses of the phi fixed point from T6. The carrier frequency directly instantiates the self-similar fixed point in a practical frequency choice.
scope and limits
- Does not simulate actual asteroid trajectories or orbital dynamics.
- Does not derive the factor of 5 from upstream forcing chain steps.
- Does not incorporate gravitational constants or mass formulas.
- Does not address multi-body interactions or energy budgets.
depends on (2)
declarations in this module (13)
-
def
carrier_frequency -
theorem
carrier_frequency_pos -
theorem
carrier_frequency_band -
def
impulseCoefficient -
theorem
impulseCoefficient_pos -
def
deflection -
theorem
deflection_zero -
theorem
deflection_nonneg -
theorem
deflection_double -
theorem
deflection_pos_of_ne_zero -
structure
AsteroidTrajectoryShapingCert -
def
asteroidTrajectoryShapingCert -
theorem
asteroid_one_statement