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HFEPX · Eval paper review

Sharp Degree Bounds for Putinar Certificates in Terms of the Positivity Margin via Analytic Sums of Squares

Yuxiang Zhao, Ting Gan

Published

Oct 18, 2026

Citations

0

Trust level

Low

Usefulness score

0/100 (Low)

Extraction confidence

15% (Low)

Derived from extracted protocol signals and abstract evidence.

Rater population

Not reported

Signals refreshed

Oct 22, 2026

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Should you rely on this paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

Use if you need

Background context only.

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Human feedback signal
Not explicit
Not explicit in abstract metadata
Evaluation signal
Weak or implicit
Validate from full paper
Usefulness for eval research
0/100
Adjacent candidate

Treat as adjacent context, not a core eval-method reference.

If you are doing eval pipeline work, start here

Human Eval Papers LLM-as-Judge Papers Pairwise Preference Papers Tool-Use Evaluation Search

Abstract

We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$. For any fixed Archimedean quadratic module with prescribed generators and any fixed degree bound on the objective, normalized polynomial objectives admit a uniform certificate-degree upper bound of $O(δ^{-1/2}\log^2(2/δ))$. The bound is sharp: we construct a matching lower-bound example in three variables. We further show that the number of inequality generators affects the optimal degree bound. For quadratic modules with at most two inequality generators, the bound improves to $O(δ^{-1/2}\log(2/δ))$, which is also sharp. This improvement is obtained by directly converting two-generator Stengle refutations into certificates for the original quadratic module. We also establish sharp degree bounds for trigonometric SOS certificates on tori. In particular, for the full torus without additional constraints, the optimal worst-case order improves to $δ^{-1/4}$, whereas additional equality constraints can lead the order to $δ^{-1/2}\log(2/δ)$. These results also yield sharp worst-case convergence rates for the Lasserre hierarchy.

What we could verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$."

Quality Controls

missing

Not reported

No explicit QC controls found.

"We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$."

Benchmarks and datasets

No benchmark or dataset names were extracted from the available abstract.

Reported metrics

No metric terms were extracted from the available abstract.

Human feedback details
Uses human feedback
No
Feedback types
None
Rater population
Not reported
Expertise required
General
Evaluation details
Evaluation modes
None
Agentic eval
None
Quality controls
Not reported
Evidence quality
Low
Use this page as
Background context only

Research brief

Metadata summary

We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key takeaways

  • We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$.
  • For any fixed Archimedean quadratic module with prescribed generators and any fixed degree bound on the objective, normalized polynomial objectives admit a uniform certificate-degree upper bound of $O(δ^{-1/2}\log^2(2/δ))$.
  • The bound is sharp: we construct a matching lower-bound example in three variables.

Researcher actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended queries

Contribution summary

  • We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin δ.
  • For any fixed Archimedean quadratic module with prescribed generators and any fixed degree bound on the objective, normalized polynomial objectives admit a uniform certificate-degree upper bound of O(δ^{-1/2}\log^2(2/δ)).
  • The bound is sharp: we construct a matching lower-bound example in three variables.

Why it matters for eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher checklist

  • Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Metric reporting is present

    No metric terms extracted.