# AC13 atmospheric escape, standalone scientific material

Save all eight public files in one ordinary folder. No SandboxPhysics checkout,
Lab engine, secret or network service is needed for the calculations.

The input is **authored synthetic boundary conditions**, not observed planet
profiles, not a MESA run and not an AIOLOS reproduction. SI units, coordinate
conventions and fixed effective collision cross section are recorded in
escape-input.json and provenance.json. Temperature is independently prescribed;
XUV power does not automatically determine it.

## Basic replay (standard library)

Use Python3.10 or newer. The recorded verification also succeeded with the host's
Python3.9.6. No third-party package is imported by this script.

```sh
python3 -W error replay-wind.py --input escape-input.json --out wind-replay-rerun.json
```

Compare the input hash, five named cases, critical radii, local Knudsen numbers,
mass flow, power ratios, profile arrays and failed-regime explanations with
wind-replay.json. Numerical last digits may depend on the platform. The fixed
hash identifies identical input bytes; it does not establish physical accuracy.

The script brackets the critical radius and independently integrates the regular
log-Mach ODE with RK4 on both sides of the sonic point. It halves the maximum
step at seven radii and records the change. Jeans escape uses Simpson integration
of the **flux-weighted** Maxwellian energy tail; it is not a count of particles
above escape speed. It evaluates the first hydrostatic local-Knudsen exobase
crossing only below the formal critical region. A strong-binding criterion of
six is a declared teaching restriction, not a universal physical transition.

## Optional Lambert-W reference

This separate analytic comparison needs the pinned packages. In a new environment:

```sh
python3 -m venv .venv
source .venv/bin/activate
python3 -m pip install -r requirements-reference.txt
python3 reference-lambert.py --out lambert-reference-rerun.json
```

The numerical ODE script must remain beside reference-lambert.py. The latter loads
that standalone file, and SciPy supplies an independent Lambert-W implementation.
The fixed reference was run with NumPy2.0.2 and SciPy1.13.1. Compare eleven radii
with lambert-reference.json; the exact sonic point is assigned its regular limit.
The wrong principal branch at twice the sonic radius gives Mach0.457695 instead
of the accelerating branch1.674346, even though both satisfy the implicit relation.

## Meaningful experiments and limits

Copy the input before changing it. Doubling base density leaves the velocity
shape fixed, doubles the normalized Parker flow and mechanical power, and halves
the sonic Knudsen number. Doubling only XUV irradiance changes available power
and the energy-limited scale, not the independently prescribed-temperature flow.
Increasing the finite outer radius increases the required mechanical heat.

The lower boundary is a fixed gas reservoir, not a measured rocky surface or
transit radius. The wind requires a subsonic base and a sufficiently collisional
sonic region. A power surplus is only a necessary opportunity; heating, cooling,
chemistry and ionization have not been solved. The fixed effective particle mass
and cross section are deliberately simple. No magnetic field, tides, stellar-wind
confinement, atmosphere depletion or planetary evolution is integrated. Do not
infer an atmosphere lifetime or radius valley from these steady profiles alone.

## Permissions and provenance

The authored scientific scripts are offered under the MIT License; the authored
input, frozen numerical outputs, prose and provenance are offered under CC BY4.0,
with attribution to Sandbox Physics, AC13,2026-10-28. This grant covers this
explicit public scientific package only. Original primary papers retain their
own licenses; they are linked, not redistributed. The protected interactive Lab
engine is not part of the package. No observed astronomical data are included.

MIT permission: Copyright2026 Sandbox Physics. Permission is hereby granted, free
of charge, to any person obtaining a copy of these scientific scripts to use,
copy, modify, merge, publish, distribute, sublicense and/or sell copies, subject
to retaining this copyright and permission notice. THE SOFTWARE IS PROVIDED
"AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.