Carrasco's Conjecture on the O'Shea-Zames-Falb Test

Precise statement

Is the O'Shea-Zames-Falb multiplier test necessary for robust stability of Lur'e systems with slope-restricted nonlinearities, as conjectured by Carrasco? No: there is a stable Lur'e interconnection, certified by a full-block multiplier, that admits no OZF multiplier.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT 5.5

A finite-horizon counterexample provided by ChatGPT 5.5 motivated the construction; the author built and certified the full interconnection.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Single-author arXiv note; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-26

   arXiv:2607.23599 - Existence of stable Lur'e systems for which the O'Shea-Zames-Falb stability test fails

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.