IndisputableMonolith.Engineering.AsteroidTrajectoryShaping
This module supplies RS-native engineering definitions for asteroid trajectory shaping, with the central object being a drive carrier frequency of 5 phi Hz. Engineers applying Recognition Science to space deflection or propulsion systems would reference it. The module is a collection of definitions and elementary nonnegativity lemmas with no complex proofs.
claimThe drive carrier frequency satisfies $f_c = 5 \phi$ Hz, where $\phi$ denotes the Recognition Science self-similar fixed point; related quantities include impulseCoefficient and deflection with their positivity and zero properties.
background
The module imports the fundamental RS time quantum $\tau_0 = 1$ tick from Constants and the Cost module that supplies the J-cost function. It operates in the engineering domain, extending the phi-ladder and eight-tick octave structures to practical trajectory parameters. Sibling definitions establish carrier_frequency, impulseCoefficient, deflection, and the AsteroidTrajectoryShapingCert certificate.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module provides the carrier frequency and shaping certificate primitives that support downstream engineering applications of Recognition Science. It instantiates the T7 eight-tick octave and phi-based constants for concrete engineering use cases such as asteroid deflection.
scope and limits
- Does not derive the 5 phi frequency from the forcing chain.
- Does not contain dynamical equations for trajectory integration.
- Does not address interaction with external gravitational fields.
- Does not prove optimality of the chosen frequency.
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