How the Direct-Projection Version Came Together
Implementation notes on the geometric equivalence, tail-stable probability calculation, benchmark identity, and API cases that shaped the finished component.
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Foster 2D Independent Reproduction
A compact implementation that carries CDM state and covariance through frame conversion, encounter-plane construction, and stable circular Gaussian integration—then tests the result against a fixed NASA CARA reference corpus.
- 53 / 53
- Pinned CARA cases reproduced
- 10⁻¹²
- Benchmark acceptance tolerance
- 10⁻¹⁶⁸
- Tail probabilities kept nonzero
The question
Can the reference result be reproduced without translating its procedure line by line?
The implementation uses the geometry that survives projection: rotate the covariance, form the encounter plane, project the miss vector, and integrate over the hard-body circle.
The explicit linear closest-approach shift disappears in the projected geometry. That equivalence is retained as a test instead of carried as unnecessary production machinery.
Calculation path
One small pipeline, with each boundary made explicit.
- 01Parse CDM semantics
- 02Rotate covariance
- 03Build encounter plane
- 04Integrate collision region
- 05Verify pinned corpus
What it establishes
Agreement is an executable claim, not a screenshot.
The benchmark pins the source commit, workbook digest, case count, exact CDM membership, and benchmark-directory cleanliness. It fails its process status if a case leaves the published tolerance.
Boundary tests separately cover geometry invariance, covariance roundoff, semantic CDM errors, the deep Gaussian tail, and the near-certainty limit.