Earth's Integrated Local Protective Envelope: A Reproducible Quantitative Model of Magnetosphere–Atmosphere–Gravity Coupling and Its Sensitivity to Field Weakening

Earth's habitability depends on three coupled physical systems that together constitute what we term the Integrated Local Protective Envelope (ILPE): magnetospheric deflection of solar wind plasma, gravitational retention of the atmosphere, and radiative and thermal atmospheric regulation. We present a fully reproducible, open quantitative treatment of this coupling: an adaptive Runge-Kutta (RK4/RK45) integration of the Lorentz force equation of motion for solar wind protons in an idealized terrestrial dipole field, a pressure balance model of the magnetopause standoff distance, a Jeans thermal escape treatment for atomic hydrogen and oxygen, and a Monte Carlo propagation of parametric uncertainty in B0, solar wind speed, and solar wind density. Contrary to a widely repeated but, we find, physically unsupported expectation that a 10 to 20 percent reduction in the geomagnetic dipole moment would raise single particle penetration probability into the 10 to 20 percent range, our particle tracing Monte Carlo, matched against the analytic Larmor gyroradius to a relative accuracy of 1.6 times 10 to the power minus 14, finds the ballistic penetration probability statistically indistinguishable from zero, zero out of 60 test particles, for dipole reductions up to 99 percent, consistent with Störmer geomagnetic cutoff theory. We show this result is expected once the diverging near planet field strength is accounted for, and we use it to reframe, rather than simply restate, the mechanism by which field weakening could plausibly enhance atmospheric loss: not single particle ballistic entry through a weakened but still divergent dipole, but a reduced magnetopause standoff distance and consequent expansion of reconnection accessible regions, such as the cusps and the low latitude boundary layer, which are outside the scope of a vacuum test particle model and require global MHD or kinetic treatment. We quantify the ILPE's comparative advantage over Mars, Venus, and Mercury using published MAVEN, Mars Express, and MESSENGER escape rate determinations, and we provide a fully executable, reproducibility audited Python code base that regenerates every number, table, and figure in this manuscript from the stated assumptions alone.