feat: add /physics-proof live benchmark endpoint

[SarmaHighOnCode]

Description

Adds a /physics-proof GET endpoint that runs live physics engine benchmarks (energy conservation, batch propagation speed, KDTree performance, Tsiolkovsky fuel precision, J2 RAAN regression) and reports pass/fail results. Intended for the dashboard 'Physics Proof' button.

Domain

• API Layer (backend/api/, main.py, schemas.py, Dockerfile)

Changes

• backend/api/physics_proof.py [NEW] — defines /physics-proof route with 6 benchmarks and engine state reporting.

Known Limitations

Warning

The following should be addressed before merging to production:

• No rate limiting — each request runs expensive benchmarks (1K-object propagation, 10K-point KDTree). Could cause load issues if spammed.
• No caching — results are recomputed on every call; consider caching results for a short TTL.
• Hardcoded test count — line 130 returns a static string 1,163 pytest tests (all passing) that is not verified at runtime.
• Owner attribution — docstring says Owner: Dev 1 (Physics Engine); confirm this is correct.

Testing

• Unit tests pass (pytest backend/tests/ -v)
• Docker build succeeds (docker build -t acm-orbital .)
• Manual verification completed

Checklist

• All constants imported from config.py.
• No O(N^2) loops in physics code.
• All physics functions have corresponding tests.

[SarmaHighOnCode]

Closing PR due to severe performance and security concerns. The endpoint lacks rate limiting (introducing a DoS risk) and runs heavy computations synchronously which will block the FastAPI event loop. Additionally, it returns hardcoded/fake test metrics and lacks automated tests.