Math article pipeline
Collect the articles automatically generated by AI.
Update Log
Mar 18, 2026. Updated one article
GenAI’s ability in mathematics research is incredible. Instead of generating boring articles, I required AI to do research on finding new geometric mechanism, and it did. This is the article. Because the theorem is not very new (I prompted it to focus on new mechanism, not new results), the article fails to be top-tier one.
Mar 16 & 17, 2026. Updated three articles
I prompted AI to find ambitious but applicable problems ,divide the proof , and prove step by step. This article is a great attempt.
Mar 15, 2026. Updated one article.
Beyond the five articles on Mar 13, I tried to generate more articles on Mar 14, but the novelty can hardly beat Sub-static splitting obstruction and Split-prime localization. In these experiments, I have narrowed the research field on Differential Geometry, with more targeted prompts. A possible explanation is too much restriction may limit model’s evaluation on topic selection.
With another prompting methodology, there is finally a satisfactory result. Instead of searching for ambitious projects, I ask AI to extend current results, just like most PhD students’ research path. This is the first publishable result generated by the project.
Mar 13, 2026. Generated five articles.
Here is the comparison of the rankings and evaluations for the five articles across the three AI models:
Comparative Ranking of Articles by AI Models
| Rank | Opus 4.6 | Gemini 3.1 Pro | ChatGPT 5.4 Thinking |
|---|---|---|---|
| 1 | Sub-static splitting obstruction | Sub-static splitting obstruction | Split-prime localization |
| 2 | Split-prime localization | Split-prime localization | Sub-static splitting obstruction |
| 3 | Weighted mode-stability | Weighted mode-stability | Weighted mode-stability |
| 4 | Weighted wall shear stress | Weighted wall shear stress | Weighted wall shear stress |
| 5 | Holomorph description of \(H^1\) | Holomorph description of \(H^1\) | Holomorph description of \(H^1\) |
Model Summaries and Key Comments
1. A Positivity Obstruction to Nontrivial Line Dependence in Sub-static Splittings
- Opus 4.6: Highlights it as the standout paper for identifying a new quantity \(Q_h(\beta)\) and proving a novel rigidity mechanism that attacks a gap in Wang’s 2024 preprint.
- Gemini 3.1 Pro: Notes that it targets and resolves a specific bottleneck using an original geometric observation rather than just generalizing work.
- ChatGPT 5.4 Thinking: Considers it the strongest of the geometric-analysis notes, introducing a meaningful quantity from a tensor trace identity.
2. Split-prime localization and lattice realizations for minus ray class groups
- Opus 4.6: Describes it as a non-trivial algebraic synthesis bridging the Coykendall–Kettinger and Greither–Kataoka formalisms.
- Gemini 3.1 Pro: Appreciates the “constructive realization theorem” that provides concrete arithmetic representatives for abstract classes.
- ChatGPT 5.4 Thinking: Ranks this as the strongest overall novelty, citing the combination of localization, Chebotarev input, and lattice formalism.
3. A weighted mode-stability theorem for Hermitian ALF gravitational instantons
- Opus 4.6: Recognizes the sharpening of the decay threshold to \(\gamma > 1/2\) and the analytic clarification of the inverse Weyl asymptotic.
- Gemini 3.1 Pro: Views it as a highly focused technical “corrigendum” that optimizes a decay threshold despite being thin on new overarching concepts.
- ChatGPT 5.4 Thinking: Calls it a legitimate and useful refinement that identifies a natural decay cutoff while working within an existing proof architecture.
4. A weighted wall shear stress criterion for Serrin-type problems
- Opus 4.6: Identifies it as a routine “mechanical substitution” of a 2025 criterion into the Bakry–Émery setting.
- Gemini 3.1 Pro: Describes it as a “standard, albeit perfectly correct, exercise” achieved by “turning the crank” on known proofs.
- ChatGPT 5.4 Thinking: Notes the shift from \(2/n\) to \(2/m\) is meaningful but represents a “mostly expected weighted transplant”.
5. A holomorph description of \(H^1\) for finite local systems on connected schemes
- Opus 4.6: Labels the core equivalences as standard torsor theory repackaged and likely “known” to experts.
- Gemini 3.1 Pro: Ranks this lowest for having the least novel mathematical substance, serving as a formal dictionary of a known result.
- ChatGPT 5.4 Thinking: Agrees it is formally clean but primarily a scheme-theoretic repackaging of standard material.