Run the warp-bubble time-integration solver on convergence results to extract strong-field curvature diagnostics, then assemble a timeline summary for visualization.

• Python 3.7+
• NumPy

Note: This project depends on solver.py, which provides the core RK4 integration and curvature computation functionality.

1. run_strong_curvature.py

   • Reads convergence.ndjson.
   • For each entry, runs the full solver and computes:
     • max_R (Ricci scalar)
     • peak_R2 ($R_{μν}R^{μν}$)
     • Constraint-violation series vs. time.
   • Emits:
     • strong_curvature.ndjson
     • strong_curvature.am

2. assemble_visualization.py

   • Reads the curvature diagnostics.
   • Detects events (curvature peaks, constraint breaches).
   • Emits:
     • simulation_summary.ndjson
     • simulation_summary.am

• convergence.ndjson
  JSON lines of:

  {
    "parameters": { "grid": 128, "dr": 0.01, "dt": 0.005 },
    "L2_error": 1e-6,
    "Linf_error": 2e-6,
    "order": 2.0
  }

python run_strong_curvature.py \
  --input convergence.ndjson \
  --output-json strong_curvature.ndjson \
  --output-am   strong_curvature.am

python assemble_visualization.py \
  --input-json strong_curvature.ndjson \
  --input-am   strong_curvature.am \
  --output-json simulation_summary.ndjson \
  --output-am   simulation_summary.am

• strong_curvature.ndjson
  JSON lines, each:

    {
      "parameters": { ... },
      "max_R": 0.123,
      "peak_R2": 0.000456,
      "violations": [ [0.0, 1e-7], [0.1, 2e-7], … ]

• strong_curvature.am
  AsciiMath summary, e.g.:

run: grid=128, dr=0.01, dt=0.005, max_R: 0.123, peak_R2: 0.000456

• simulation_summary.ndjson
  JSON lines of timeline events:

 {
   "event": "constraint_violation",
   "time": 0.1,
   "params": { ... }
 }

• simulation_summary.am
  AsciiMath timeline notes:

  timeline:
  - at t=0.1: constraint_violation for params { … }
  - at t=0.5: peak_R for params { … }

warp-curvature-analysis/
├─ run_strong_curvature.py
├─ assemble_visualization.py
├─ convergence.ndjson
├─ [convergence.am]
├─ strong_curvature.ndjson
├─ strong_curvature.am
├─ simulation_summary.ndjson
├─ simulation_summary.am
└─ README.md