perf(ldl): replace brute-force four-squares search
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Description
Background
Strict positivity certificates use rational LDL reconstruction plus Lagrange four-square decomposition. The current fourSquaresNat implementation brute-forces with a practical cap, which limits how small an epsilon the strict-positivity path can certify.
Desired outcome
Replace the brute-force four-squares step with a faster algorithm, such as Cornacchia-style or randomized number-theoretic search, while preserving exact certificate reconstruction.
Notes
This is independent from CSDP soundness: the reconstructed certificate must still be checked exactly by the verifier.
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 locating the fourSquaresNat implementation and the strict-positivity certificate reconstruction path. Read how the current brute-force cap is used, then review the exact verifier mentioned in the issue. Done means the four-squares step is faster, supports smaller certified epsilons, and reconstructed certificates still pass exact verification.
Written by the indexing model from the issue text.
Assessment
- Domain
- performance
- Issue type
- Refactor
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Needs clarification
- Newbie friendliness
- 35/100