feat(search): support algebraic-extension SOS coefficients
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Description
Background
The current certificate format and verifier use rational coefficients throughout (CMvPolynomial n ℚ). This is sound and easy to check, but it means goals whose only SOS witnesses use algebraic coefficients, such as coefficients involving √2, are out of scope.
Desired outcome
Investigate and implement a certificate path for algebraic-extension coefficients, or document a principled alternative if this should remain out of scope.
Notes
This likely touches certificate representation, verifier soundness lemmas, search/rounding, and user-facing witness printing. It should remain kernel-checkable and should not make successful proofs depend on trusting CSDP.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by mapping the certificate representation, verifier soundness lemmas, search/rounding, and user-facing witness printing named in the issue. Determine whether an algebraic-extension path can remain kernel-checkable without trusting CSDP. Done means either an implemented certificate path or a principled documented alternative if the feature remains out of scope.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100