# Geodesic Solver Sanity Check Artifact

Artifact ID: `geodesic-solver-sanity-check-001`

Status: planned validation checklist for the Timelike Geodesic Solver prototype.

## Purpose

This artifact documents the minimum sanity checks required before the public geodesic solver should publish numerical trajectories as validated outputs. It is a planning and reproducibility artifact, not a report of completed solver results.

The geodesic equation to be implemented and tested is:

```text
d^2 x^mu / d lambda^2
+ Gamma^mu_{alpha beta}
  (dx^alpha / d lambda)
  (dx^beta / d lambda)
= 0
```

## Planned Validation Checks

1. Flat spacetime baseline

   In Minkowski spacetime, Christoffel symbols vanish in inertial coordinates, so the solver should recover straight-line motion for suitable initial data.

2. Conserved quantities

   In spacetimes with Killing symmetries, the relevant conserved quantities should remain stable within numerical tolerance.

3. Step-size sensitivity

   The same initial data should be tested at multiple step sizes. A published trajectory should include the step size and show that qualitative behavior is not an artifact of one discretization choice.

4. Timelike/null normalization monitoring

   The solver should track whether the tangent vector remains timelike or null under the stated metric and convention:

   ```text
   g_{mu nu} u^mu u^nu = constant
   ```

5. Visualization caution

   Plotted paths should be described as trajectories under stated assumptions, not as proof of global causal structure.

## Current Status

- No numerical geodesic outputs are validated by this artifact yet.
- No production solver is claimed.
- No Christoffel-symbol, curvature, Einstein-tensor, or energy-density components are introduced here.
- Future versions should include a runnable script or notebook, input data, expected outputs, tolerance settings, and a short interpretation note.