What was already known
Yun, Sra and Jadbabaie proposed both near-identity inequalities in 2021. General positive-semidefinite RS–GD was already false for n≥5.
AI involvement
Peng says GPT-5.5 Pro supplied the complete proof idea after his prompt. Peng verified and edited the proof; Claude Code assembled the prose.
The paper expressly credits the complete proof idea to GPT-5.5 Pro, with Peng prompting and checking. The human prompt and editorial role prevent an unsupported AI-autonomous label.
Importance
The paper refutes one half of the proposed chain and proves the other under an explicit conditioning bound.
Limitations
The counterexample does not refute RS–GD under the stated near-identity condition. The symbolic script checks the counterexample identities, while Peng reports checking both proofs by hand.
Technical verification
Peng reports verifying the proof of both the counterexample and RS–GD theorem. Appendix A also reports exact symbolic verification of Section 3's matrix polynomial identities only, not the Section 4 positive inequality. The checks are source-reported.
Formal checking
Human verification of the model-origin proof
- Checker
- Binghui Peng, author-reviewer
- Scope
- Theorem 2 SS–RS counterexample and Theorem 3 conditional RS–GD inequality
- Basis
- Reported by the linked checker
Exact symbolic polynomial identities and sum-of-squares certificates
- Checker
- Peng's SymPy script
- Scope
- Section 3 counterexample's matrix eigenvalue and gap polynomial identities
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Peng verifies and polishes the argument and presents an explicit mechanism for both the counterexample and positive near-identity inequality; no unexplained central step is reported.
Correction and publication history
The paper refutes one half of the proposed chain and proves the other under an explicit conditioning bound.
Read this published revision