IndisputableMonolith.Engineering.AsteroidTrajectoryShaping
This module defines the carrier frequency and auxiliary coefficients for asteroid trajectory shaping in Recognition Science units. It fixes the drive frequency at 5φ Hz and certifies basic algebraic properties of impulse and deflection. Engineers applying RS constants to deflection problems would cite these definitions. The module is a collection of direct definitions and elementary positivity proofs built on the imported Constants and Cost modules.
claimThe drive carrier frequency is given by $f_c = 5φ$ Hz, with impulse coefficient $k$ and deflection function $d$ satisfying $k > 0$, $d ≥ 0$, and $d(2x) = 2d(x)$.
background
The module imports the fundamental RS time quantum τ₀ = 1 tick from Constants and cost functions from Cost. It introduces the carrier frequency as 5 · φ Hz, where φ is the self-similar fixed point forced in the T5–T6 steps of the unified forcing chain. Definitions cover impulseCoefficient, deflection, and the AsteroidTrajectoryShapingCert wrapper, together with their non-negativity and doubling lemmas. The local setting is the translation of RS-native constants into engineering parameters on the phi-ladder.
proof idea
This is a definition module. It consists of direct definitions for carrier_frequency, impulseCoefficient, and deflection, followed by one-line wrappers establishing positivity, non-negativity, and the doubling property using the imported constants and basic real-number facts.
why it matters in Recognition Science
The module supplies the engineering interface that applies the phi-ladder and T8 D=3 spatial setting to concrete deflection tasks. It feeds the AsteroidTrajectoryShapingCert and related trajectory calculations, operationalizing the RCL and phi-based constants for practical use. No downstream theorems are recorded in the current graph, but the definitions close the gap between abstract RS units and applied shaping problems.
scope and limits
- Does not derive the 5φ frequency from the forcing chain.
- Does not compute explicit asteroid trajectories or orbits.
- Does not incorporate external gravitational perturbations.
- Does not address relativistic or quantum corrections beyond RS units.
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