Complete resultmathematics · analysis and differential equations
ChatGPT suggests a differential-equation counterexample
ChatGPT-5.5 Pro supplied the key oscillatory construction for a smooth non-uniqueness counterexample after five comparison models failed or returned incorrect proofs.
Editorial context
What happened
Brian Street asked whether zero initial data force uniqueness for a difference-quotient differential equation with a positive smooth weight. The successful model response arrived after 43 minutes of reported thinking and proposed the flat, oscillatory construction that became the core of the counterexample. The source is especially valuable because it does not present the successful run in isolation. It dates five comparison attempts, states that they failed or produced incorrect proofs, prints the successful prompt and response, and annotates where human repair was required.
Keep in view
The work is a recent preprint without formal verification or identified peer review. The printed prompt uses a closely related weighted-Laplace formulation rather than the final theorem verbatim.
Chronology
Timeline
Five comparison-model attempts failed or returned incorrect proofsattempt · day date
ChatGPT-5.5 Pro produced the successful constructionattempt · day date
Human-checked counterexample, prompt, and annotated response publishedpreprint · day date
Trust boundaries
Validation
Street repaired skipped steps, supplied missing estimates, and wrote a detailed proof of the counterexample.
Five same-problem model attempts were unsuccessful, although their full raw outputs were not published.
System
AI and tools
- ChatGPT-5.5 Pro
- ChatGPT-5.2 Pro
- ChatGPT-5.4 Pro
- Gemini 3 DeepThink
- Claude Opus 4.6 Extended
People
Human contributors
- Brian Street
Organizations
Affiliations
None recorded.
Primary materials