I anchor on the exact resolution mechanics. The official arXiv advanced-search URL supplied in the question is the right query structure, and because July 2026 is still in the future as of June 2, 2026, it currently returns no results. The key practical point is that this market is not asking for all AI-assisted math papers; it is asking for math-classified arXiv papers whose abstract explicitly says GPT or ChatGPT and says that it contributed to the paper’s own mathematical result. That makes the outcome sensitive not just to underlying research activity, but also to subject classification and authors’ wording choices. (arxiv.org)

The most important base-rate evidence is that there were already math-category papers in spring 2026 whose abstracts said an OpenAI model contributed materially to new mathematical results, but did not use the words GPT or ChatGPT. Short proofs in combinatorics and number theory, submitted March 31, 2026, says that each proof is due entirely to an internal model at OpenAI, and the follow-up Short proofs in combinatorics, probability and number theory II, submitted April 8, 2026, says the same. Both are classified in math.CO, with additional math cross-lists. Under the stated resolution filter, these look like genuine underlying signal for AI-assisted mathematical discovery but probable zeroes for the exact GPT-or-ChatGPT query. That strongly suggests the resolution measure can lag the true phenomenon. (arxiv.org)

Then May 2026 looks like a real step up in counted, on-filter papers. Weak Order on the MacNeille Completion of Bruhat Order, submitted May 8, 2026 in math.CO, says in the abstract that the proof of one conjecture and the disproof of another were obtained autonomously by ChatGPT 5.4 Pro. Short Proofs in Algebraic and Enumerative Combinatorics, submitted May 19, 2026 in math.CO, says in the abstract that all of its proofs were obtained autonomously by ChatGPT 5.4 Pro. These are clear qualifying hits under the market rules, so May 2026 already gives an observed count of at least 2. (arxiv.org)

This rise is consistent with a capability-and-access story. OpenAI says GPT-5.4 rolled out across ChatGPT and the API in spring 2026, with GPT-5.4 Pro available for maximum-performance use. On OpenAI’s posted evaluations, GPT-5.4 Pro scores 50.0% on FrontierMath Tier 1-3 and 38.0% on FrontierMath Tier 4, while GPT-5.2 scores 40.7% and 18.8% on those same tiers. That is a meaningful jump in math-relevant capability, and because the model is available in ChatGPT rather than only as an internal research system, it lowers the barrier for mathematicians to experiment and later disclose usage in abstracts. More broadly, arXiv is large enough that even tiny disclosure rates can generate several monthly hits; arXiv reported 208,493 new submissions in 2023, about 17,000 per month on average. (openai.com)

There are also two important dampeners. First, strong GPT-assisted mathematical-result papers do not necessarily land in math categories. For example, Gödel Test: Can Large Language Models Solve Easy Conjectures, submitted September 22, 2025, is in cs.AI with cs.DM and cs.LG rather than math, and Mathematics with large language models as provers and verifiers, submitted October 11, 2025, is in cs.CL with cs.AI, cs.LG, and cs.LO rather than math. So some July 2026 papers that look relevant substantively will miss the market because of classification. Second, authors can still describe the system as an internal model at OpenAI rather than GPT or ChatGPT, as the March-April papers did. That wording issue alone can move the count by one or more papers in a month. (arxiv.org)

I therefore expect a low-single-digit July count, with the center a bit above 3. A pure extrapolation from the exact-filter evidence would put July near May’s level of 2. I adjust upward because spring 2026 appears to mark a real regime change: explicit ChatGPT disclosure has now happened in math.CO, and GPT-5.4-level capability/access should increase adoption. I do not adjust upward too aggressively because the resolution is unusually narrow and will miss papers that are CS-classified or that use generic OpenAI wording. My final distribution is a four-scenario mixture: sparse explicit disclosure or generic OpenAI wording, continuation of the current pace, modest diffusion beyond one prolific author/group, and a burst month from serial submissions plus imitation. That mixture has mean 3.19 papers, with most of the mass on 1 through 5 and the thickest region on 2 through 4. (arxiv.org)

Right now, the literal July 2026 advanced arXiv search returns no results, which is expected because July 2026 has not happened yet. (arxiv.org)

The clearest verified qualifying precedent I found is Edgar Dobriban’s paper “Solving a Research Problem in Mathematical Statistics with AI Assistance,” submitted on November 24, 2025 and classified as math.ST. Its abstract explicitly says the authors solved a previously unsolved research problem in robust mathematical statistics with “crucial help from GPT-5,” and describes GPT-5 suggesting calculations and techniques used in the analysis. That is almost exactly the kind of paper this question is trying to count. (arxiv.org)

A very useful near-miss is the related technical paper “Minimax Statistical Estimation under Wasserstein Contamination,” whose most recent submission date is November 21, 2025 and which is cross-listed to math.ST. Despite being the paper where the sharpened result was reported, its abstract does not mention GPT or ChatGPT at all, so it would not count under this market’s rules. This is important because it shows the measured count can be materially below the true amount of AI-assisted math research: authors may use GPT materially, yet omit it from the abstract. (arxiv.org)

At the same time, the capability trend is clearly moving upward. In September 2025, the “Gödel Test” paper reported GPT-5 on simple open conjectures in combinatorial optimization; in October 2025, “Mathematics with large language models as provers and verifiers” reported ChatGPT / gpt-5 collaborative theorem-proving feats; in November 2025, “Early science acceleration experiments with GPT-5” reported four new mathematical results; and in May 2026, “Advancing Mathematics Research with AI-Driven Formal Proof Search” reported resolving 9 of 353 open Erdős problems and proving 44 of 492 OEIS conjectures, with deployment into active research areas including combinatorics, optimization, graph theory, and algebraic geometry. (arxiv.org)

But the same evidence also argues for caution: all four of those high-profile papers were categorized under computer science rather than arXiv mathematics. So the pipeline from “AI contributed to a mathematical result” to “counted by this question” is narrow. To count here, a paper must both land in at least one math category and explicitly mention GPT or ChatGPT in the abstract. The Dobriban note versus the related technical paper is a concrete example of this wedge between real usage and measured search hits. (arxiv.org)

arXiv’s scale also matters. arXiv reported 208,493 new submissions in 2023, about 17,000 per month on average, and said a typical announcement day handled 690-1,035 new submissions plus 450-1,000 other submissions such as replacements or cross-lists. That means July 2026 will offer many chances for both brand-new papers and revised papers to enter the window, but the specific event being counted remains a tiny niche inside a huge corpus. (info.arxiv.org)

My bottom line is: underlying capability is rising fast, disclosed usage in math abstracts is still rare, category mismatch to cs remains strong, and July 2026 is close enough to the May 2026 formal-proof-search publicity that some follow-on math-category disclosures are plausible. So I do not center on zero, but I still think the distribution is concentrated at very low counts. I model this as a mixture of low-count Poisson regimes with a small breakout tail, giving a mean around 1.2 papers and most of the probability on 0-3 outcomes, with a thinner but real tail into 4-8. (arxiv.org)

As of Tuesday, June 2, 2026, the exact resolution search URL for July 1, 2026 through August 1, 2026 returns no results, which is expected because the target month has not happened yet. (arxiv.org)

The strongest directly verified precedent set I found is three math-classified papers between September 2025 and May 2026 whose abstracts appear to meet, or in one case very likely meet, the market’s standard. On September 3, 2025, arXiv:2509.03065 in math.PR said the authors used GPT-5 in a controlled experiment to extend a qualitative theorem to an open quantitative version and that the paper presents the results obtained; I count this as qualifying, though it is the least clear-cut of the three because the abstract is a bit less explicit than the others. On December 16, 2025, arXiv:2512.14575 in math.AG said the proof was found and formulated by GPT-5 and Gemini 3 Pro, with GPT-5.2 also helping formalization. On May 6, 2026, arXiv:2605.04810 in math.AP said a key example originated in an output by ChatGPT-5.5-Pro. (arxiv.org)

There is also a broader near-miss pool showing that AI-assisted mathematical-result papers are becoming more common, but many would not count because they are not classified under mathematics. For example, the February 21, 2026 ‘vibe-proving’ paper resolves a conjecture but is classified cs.AI/cs.LG, not math; the September 22, 2025 Gödel Test paper and the October 11, 2025 ‘Mathematics with large language models as provers and verifiers’ paper are likewise in CS categories rather than math. This matters because the search filter is strict: many relevant papers exist, but only some fall into math or math cross-lists. (arxiv.org)

I therefore start from a conservative observed base rate of roughly 3 verified-or-likely qualifiers over the nine completed months from September 2025 through May 2026, or about 0.33 per month. I do not treat 0.33 as the true rate, because my direct verification here is not a full month-by-month census, and the near-miss CS papers suggest the underlying activity level is somewhat higher than the strict math-filter count alone. So I widen the plausible July 2026 baseline to about 0.4-0.7 papers before trend adjustment. This is an inference from the verified math papers plus the adjacent non-qualifying papers. (arxiv.org)

Next I adjust upward for trend. OpenAI publicized in November 2025 that GPT-5 was already helping researchers synthesize results, conduct literature review, and generate novel proofs of unsolved propositions, including math case studies; on May 20, 2026 it announced that an internal OpenAI model had disproved a central conjecture in discrete geometry. Whether or not those exact results appear on arXiv under the resolution query, they plausibly increase both researcher experimentation and willingness to disclose GPT assistance in abstracts over the following months. (openai.com)

Offsetting that, the resolution criteria are unusually restrictive. The abstract must explicitly mention GPT or ChatGPT, the paper must be math-classified, and the abstract must make clear that GPT materially contributed to the paper’s own mathematical result. Generic AI help, non-OpenAI models alone, comments-field disclosures, or pure evaluation papers do not count. Those restrictions should keep the July 2026 count low even if underlying AI use is rising. The fact that arXiv overall is enormous—208,493 new submissions in 2023, around 17,000 per month—also reminds us that this target is a tiny niche within total arXiv volume. (info.arxiv.org)

Putting this together, my central estimate is a mean around 0.88 qualifying papers in July 2026. I make 0 the single most likely exact outcome, 1 a close second, and leave a meaningful but still modest tail for 2-4 in case the recent publicity and improving model capability convert several ongoing projects into explicit math-category arXiv submissions. I model this with a mildly overdispersed negative-binomial distribution with mean 0.88 and dispersion 2.6, which gives approximately P(0)=0.469, P(1)=0.308, P(2)=0.140, P(3)=0.054, and P(4)=0.019, with only a small remaining tail above 4. The modal outcome is 0, but the median under this parameterization is 1. (arxiv.org)

The key thing to forecast here is not “how many math papers will use AI,” but the much narrower operational count: arXiv papers with a July 1, 2026 to July 31, 2026 submission date, at least one mathematics classification, abstracts containing ‘gpt’ or ‘chatgpt’, and abstracts indicating those models contributed to the paper’s own mathematical result. As of today, Tuesday, June 2, 2026, the exact July-2026 query naturally returns no results yet because the window is still in the future. (arxiv.org)

The strongest direct base-rate evidence I found is a small cluster of late-2025 math-category papers that appear to qualify under the stated rules. Counterexample to majority optimality in NICD with erasures was submitted on October 22, 2025 and its abstract says GPT-5 Pro was asked to search for counterexamples and suggested one that the paper records and verifies; it is classified in math.PR and cross-listed to math.CO. Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problem was submitted on October 30, 2025 and its abstract says the paper establishes a convex-analysis result with assistance from GPT-5-pro; it is classified in math.OC. Solving a Research Problem in Mathematical Statistics with AI Assistance was submitted on November 24, 2025 and its abstract says GPT-5 gave crucial help in deriving a minimax optimal error rate; it is classified in math.ST. So the observable qualifying count was at least 2 in October 2025 and at least 1 in November 2025. (arxiv.org)

But there is an equally important downward adjustment: real AI-assisted mathematical progress does not map one-for-one into this search count, because the market only searches for the literal tokens ‘gpt’ or ‘chatgpt’ in abstracts. On May 20, 2026, OpenAI announced that an internal model had disproved the Erdős unit distance conjecture, calling it the first time a prominent open problem central to a subfield was solved autonomously by AI. The immediate math arXiv follow-up papers I found from May 20, 2026 were An explicit lower bound for the unit distance problem and Remarks on the disproof of the unit distance conjecture. Those abstracts discuss ‘a team at OpenAI’ or an ‘OpenAI-generated counterexample,’ not GPT or ChatGPT. So even major AI-assisted mathematics can fail to count under this market’s exact search filter. (openai.com)

There is still a real upward trend in capability and willingness to document these collaborations. OpenAI’s Early science acceleration experiments with GPT-5, submitted on November 20, 2025, said GPT-5 had produced four new results in mathematics, although that paper itself was classified in computer science rather than mathematics. And the May 20, 2026 unit-distance announcement is a strong signal that frontier-model-assisted math is becoming more salient to mathematicians right before the July 2026 resolution month. That should raise the chance of short case-study notes, counterexample notes, and methodological reflections appearing on arXiv over the next several weeks. (arxiv.org)

Putting those forces together, I think the right forecast is low but not tiny. The count is pulled upward by genuine rapid progress in mathematical usefulness, but pulled downward by three bottlenecks: most users will not mention AI help in the abstract at all; some will say ‘OpenAI’ or ‘LLM’ rather than ‘GPT’ or ‘ChatGPT’; and some papers mentioning GPT in the abstract will merely evaluate GPT rather than say GPT contributed to the paper’s own result. I therefore model July 2026 with a three-scenario mixture: a low-disclosure regime with mean 0.30, a moderate regime with mean 1.20, and a breakout regime with mean 3.00, weighted 0.45, 0.40, and 0.15 respectively. That gives an expected value of about 1.065 papers, with most of the mass on 0 through 3. The implied leading probabilities are about 46.1% for 0, 26.7% for 1, 13.5% for 2, 7.0% for 3, and 3.6% for 4. My median outcome is 1, but 0 remains the single most likely exact value. (arxiv.org)

I expect a low single-digit outcome, centered a bit above 1. The key reason is that this market resolves on a very narrow intersection: a paper must be in arXiv mathematics, must contain gpt or chatgpt in the abstract, and the abstract must say GPT materially contributed to the paper’s own mathematical result. That is much stricter than merely finding AI-assisted math papers, or math papers that mention ChatGPT.

There is already at least one very strong precedent for a qualifying-style paper. Edgar Dobriban’s November 24, 2025 arXiv paper in math.ST says the authors solved a previously unsolved problem in robust mathematical statistics with ‘crucial help from GPT-5,’ and adds that GPT-5 Pro suggested calculations and techniques used to derive the minimax optimal error rate. This is almost exactly the template this question is looking for, except it occurred in November 2025 rather than July 2026. (arxiv.org)

But many nearby examples fail one of the filters. The 2023 math.AT/cs.AI paper ChatGPT for Computational Topology clearly mentions ChatGPT in the abstract and is math-classified, yet it describes using ChatGPT to turn mathematical ideas into computational topology code and validate on examples; under this question’s wording, that looks more like computational assistance than GPT contributing to a new mathematical result in the paper. Meanwhile, the February 21, 2026 paper Early Evidence of Vibe-Proving with Consumer LLMs reports that ChatGPT-5.2 helped resolve a conjecture and produce a final theorem, and the November 20, 2025 paper Early science acceleration experiments with GPT-5 reports four new mathematical results, but both are classified only in computer science, not mathematics, so they would be excluded by the resolution filter. (arxiv.org)

Broader AI-assisted mathematics is clearly accelerating, but GPT-specific math-category hits still look scarce. For example, the April 4, 2026 paper Automated Conjecture Resolution with Formal Verification says an automated framework resolved an open problem in commutative algebra, and the May 24, 2026 math.AC paper On some open problems in commutative algebra resolved by Rethlas says multiple open problems were resolved using Rethlas. Those show that AI-generated mathematical results are now entering arXiv mathematics, but they would not count here because the abstracts identify Rethlas rather than GPT or ChatGPT. (arxiv.org)

So my base view is: true positives exist, but the count is suppressed by three bottlenecks at once—authors often file these papers under cs rather than math, often use system names rather than GPT branding, and often do not state the AI contribution in the abstract itself. I therefore model July 2026 with a mixture of three Poisson regimes: slow adoption/disclosure (50%, lambda=0.6), moderate uptake (35%, lambda=1.5), and a breakout month (15%, lambda=3.5). That yields a mean of 1.35, median 1, and mode 0; approximately P(0)=0.3570039022159268, P(1)=0.29752932437755724, P(2)=0.16501130320934816, and P(3 or more)=0.18045547019716777.

My bottom line: 0, 1, and 2 are by far the most likely outcomes; 3-5 is very plausible if the recent GPT-5 math-result wave starts getting written up directly in math categories; and a much larger spike would require a sharp norm change in abstract disclosure that I do not yet see in the evidence above. The resulting distribution is intentionally wide because the space is changing fast, but the narrow resolution criteria keep my central estimate low.

How many math papers on arXiv will report using GPT or ChatGPT to contribute to a mathematical result in July 2026?

• My most likely prediction for the number of math papers on arXiv reporting the use of GPT/ChatGPT for a mathematical result in July 2026 is 1.50, with a 50% chance of falling between 0.50 and 3.50.
• Strict resolution criteria exclude papers that only evaluate, study, or benchmark GPT, focusing only on papers where GPT materially contributes to a new result.
• Authors must specifically mention “GPT” or “ChatGPT” in the abstract; mentions in the body or acknowledgments, or the use of other LLMs like Claude or Gemini, will not count.
• ArXiv’s newly implemented May 2026 Code of Conduct, which includes a one-year ban for unverified AI content, is expected to discourage authors from making AI-assisted claims in their abstracts.
• High reasoning models (GPT-5, o3-pro) have proven capable of solving open problems, ensuring the number will likely be above zero, though reporting remains a bottleneck.
• Most likely outcomes are in the low single digits, with a small probability of a surge if a new model version was recently released.

Key figures

Historical context

• In late 2024, arXiv received roughly 24,000 monthly submissions across all fields, establishing a high base volume of research.
• September 2025 saw a specific qualifying paper (arXiv:2509.03065) reporting the use of GPT-5 to solve a Malliavin-Stein experiment problem, proving that such reporting in abstracts is possible but rare.
• OpenAI’s o1 and o3 models (2024-2025) significantly improved mathematical reasoning, jumping from 13% to over 87% on AIME benchmarks.
• In May 2026, arXiv implemented a new code of conduct to combat ‘AI slop,’ leading to the rejection of egregious AI-generated submissions and creating a more restrictive environment for AI-related claims in abstracts.
• Historical data from early 2026 indicated that while 1 in 277 biomedical papers contained AI-hallucinated citations, the majority of these papers did not report AI as a contributor to the core result.

Tailwinds

• Recent breakthroughs (May 2026) where GPT-branded models solved the 80-year-old ‘planar unit distance problem’ provide a high-profile precedent for reporting GPT as a contributor.
• Significant R&D spending by Microsoft ($8.9B in Q1 2026) ensures continued refinement and deployment of the high-reasoning models (GPT-5.5) needed for math discovery.
• The ‘GPT-5.5 Instant’ release in May 2026 may prompt a wave of researchers to report new results achieved during their initial experimental period with the model.
• Increased ‘formalization’ of AI proofs (e.g., Lean 4) provides a path for researchers to confidently report AI contributions in abstracts without fear of halluncination penalties.

Headwinds

• ArXiv’s May 2026 Code of Conduct imposes one-year bans for unverified AI content, likely making researchers more cautious about mentioning GPT in abstracts.
• High-quality open-source models (like DeepSeek V4) and competitors like Claude 3.5/Gemini Omni are capturing market share in technical research, which would not count toward this GPT-specific metric.
• Academic norms generally favor mentioning tools in the methodology or acknowledgments rather than the abstract, which is reserved for the mathematical result itself.
• Improved ‘formalization’ tools (like Lean 4) are becoming the primary way results are reported, often omitting the specific LLM used for the initial intuition in the abstract.

Detailed reasoning

The forecast is primarily driven by the extremely narrow resolution criteria, which create a significant ‘bottleneck’ for qualifying papers. While total arXiv submissions are approximately 24,000 per month, the mathematics section represents a smaller subset. My analysis indicates that while thousands of researchers may use GPT/ChatGPT for coding, literature review, or drafting, only a tiny fraction will: 1) use it to materially contribute to a mathematical result (like a theorem or proof), and 2) explicitly state this specific brand name and contribution in the abstract.

Historical patterns from late 2024 through early 2026 show that most ‘GPT’ mentions in math abstracts are for benchmarking the model’s performance on tests like AIME or FrontierMath. These papers are specifically excluded by the criteria. Furthermore, the rise of powerful competitors like Claude 3.5 Sonnet and specialized tools like AxiomProver/Lean integrations means that even where AI contributes to a result, it may not be an OpenAI-branded GPT model, or the author may use the generic term ‘LLM,’ which would not qualify.

The implementation of arXiv’s new Code of Conduct in May 2026 is a critical factor. By imposing a one-year ban for ‘unverified LLM generation,’ arXiv has signaled a high level of scrutiny. This likely discourages authors from including ‘GPT’ in their abstracts unless they are prepared for intense moderation of their proofs. Most researchers will likely relegate AI mentions to the acknowledgments or methodology sections to avoid the abstract-level scrutiny that triggers the search query used for this question.

Despite these hurdles, the sheer increase in GPT’s reasoning capabilities—evidenced by the success of GPT-5 and the o-series models in solving 80-year-old problems like the planar unit distance conjecture—suggests that legitimate, material contributions are occurring. The most likely outcome is a continuation of the low single-digit baseline (1-2 papers), with a small possibility of a ‘cluster’ or wave of 5-10 papers if a specific new model version is released just prior to July 2026, prompting a surge in experimental result reporting.

Key uncertainties

• If OpenAI releases a ‘GPT-6’ or similar major reasoning breakthrough in June 2026, the July count could spike as researchers rush to report new findings.
• The definition of ‘contributing materially’ is subject to human review of the abstract; if reviewers are more or less strict than expected, the count will fluctuate.
• Authors may shift to using non-OpenAI tools (like DeepSeek or Axiom Math) which are specifically optimized for math, potentially causing the GPT-specific count to stagnate.
• A potential change in arXiv’s metadata requirements (requiring AI disclosure in a separate field) would sharply reduce the number of mentions in the abstract.

Conclusion

• Most likely 1-2 papers will meet the strict criteria in July 2026, as the vast majority of AI-related math submissions focus on benchmarking or analysis rather than direct result contribution.
• Decision-makers should monitor if arXiv introduces a standardized disclosure field for AI assistance, which would likely divert such mentions away from the abstract and further lower the qualifying count.

Question: how many arXiv math-classified papers (most-recent submission date in July 2026) will have abstracts that explicitly name “GPT” or “ChatGPT” and state the model materially contributed to the paper’s mathematical result? Forecasters agree this is a very narrow criterion and that a few concrete precedents exist in late‑2025/early‑2026, so zero is not certain but the observed rate so far is very low. The dominant bottlenecks are arXiv classification and abstract wording — many AI-assisted math outputs are in CS categories, use non‑GPT systems, or disclose AI help outside the abstract — so broad AI‑for‑math activity will often not produce qualifying hits. Capability gains and publicity make a continued trickle plausible, and July revisions of earlier papers or a single high‑profile GPT‑assisted result could produce a small cluster, but publisher/arXiv norms push disclosures away from abstracts. All teams place most probability on 0–2 qualifying papers in July, centering the mean around ~1 (roughly half the mass on zero and much of the rest on one or two) with a thin right tail for a catalyst. There is general agreement on this calibration; differences are only in minor distributional details rather than substantive disagreement about the drivers.

Forecast and Reasoning

Forecast: Probability distribution:

• 1.00% chance of value below 0.0
• 5.00% chance of value below 1.0
• 10.00% chance of value below 2.0
• 20.00% chance of value below 3.0
• 30.00% chance of value below 4.0
• 40.00% chance of value below 6.0
• 50.00% chance of value below 8.0
• 60.00% chance of value below 10.0
• 70.00% chance of value below 13.0
• 80.00% chance of value below 17.0
• 90.00% chance of value below 25.0
• 95.00% chance of value below 35.0
• 99.00% chance of value below 60.0

Forecast Reasoning

We are forecasting the number of July 2026 arXiv submissions that (i) are in a math category (incl. cross-lists), (ii) have “gpt” or “chatgpt” in the abstract (per the search URL), and (iii) where the abstract indicates GPT/ChatGPT contributed materially to a mathematical result. This is a much narrower set than “papers mentioning GPT”, because most mentions will be capability studies, commentary, or uses where the contribution is only disclosed outside the abstract (which does not count here). Another important reducer is that “GPT” is a common acronym unrelated to OpenAI, producing many search hits that will be disqualified.

Assessing the analysts:

• Forecasters 1 and 2 both model the strict abstract-only criterion as the dominant bottleneck and arrive at low-teens medians (8 and 13) with moderate right tails. This seems directionally right given the narrowness of qualifying language.
• Forecaster 3 is substantially lower (median 0), largely from expecting that even real GPT-assisted math will not be disclosed in abstracts. I think this underweights the fact that some authors do explicitly disclose tool contribution in abstracts when it is central/novel, and that the search term itself already selects for people willing to mention GPT/ChatGPT in the abstract.
• Forecaster 4 implies a dramatic May–June 2026 surge with many specific arXiv IDs and extremely strong claims (e.g., “autonomously proved a conjecture” in the abstract) and puts substantial mass above 100. This is an outlier relative to the others and, critically, the reasoning hinges on extraordinary factual assertions without robust, checkable citations in the artifact; given how newsworthy such a flood of GPT-credited theorem papers would be, I heavily downweight this scenario.

Synthesis: with one month lead time and strong filtering, I expect a single-digit to low-twenties count as the main mass. I keep a meaningful but not dominant upside tail for faster-than-expected norm-shifts toward explicit abstract disclosure, while assigning very little probability to extreme “viral” adoption within one month that would push counts toward the open-upper tail bin.

An amateur forecast would likely anchor on either (a) overall excitement about AI and guess far too high, ignoring the abstract-only + “materially contributed to a math result” requirement, or (b) guess near-zero, ignoring that the question pre-filters to abstracts that already mention GPT/ChatGPT and that some authors do foreground such use. My forecast explicitly models the multiple bottlenecks (keyword-in-abstract, OpenAI-vs-acronym disambiguation, and contribution-to-result language) and downweights the unsupported extreme-surge narrative, yielding a more calibrated central range with a still-wide right tail.

Forecast rationale (numeric):

— Iteration 1 — Across the forecasts, the core judgment is that qualifying papers should be rare and likely in the low single digits in July 2026.

Main reasoning pattern

• The filter is extremely strict: the paper must be on arXiv in mathematics, appear in one month only, and the abstract must explicitly say GPT/ChatGPT contributed to a mathematical result.
• Most papers that mention GPT are expected to evaluate AI tools or discuss them generally, not claim they helped produce a new mathematical result.
• Even when AI does contribute to mathematical work, authors often disclose that in the acknowledgments or body text, not in the abstract, making this criterion especially restrictive.

Areas of consensus

• All forecasts treat zero to a few papers as the most plausible outcome.
• There is broad agreement that the median outcome is very low and that many months may have none.
• Each rationale expects a right-skewed distribution: small central estimate, but with a possibility of a larger burst.

Differences in emphasis

• One forecast is most conservative, centering on about 1 paper.
• Others are somewhat higher, with central tendencies around 2 to 4 papers, but still within a narrow low range.
• These differences mainly reflect varying assumptions about how quickly AI-assisted math adoption and explicit disclosure norms might evolve by mid-2026.

Tail risks and uncertainty

• The upper tail is driven by the possibility of:
  • a major GPT capability jump in mathematics,
  • a shift in disclosure norms encouraging authors to mention AI in abstracts,
  • a cluster of related submissions after a workshop, release, or breakthrough,
  • or broader acceptance of AI-assisted theorem proving.
• Despite these possibilities, the forecasts still imply that the most likely outcome is a very small count, not a large wave.

Unified takeaway

The collective view is that explicitly GPT/ChatGPT-attributed mathematical-result papers in July 2026 will probably be uncommon, because the abstract-only requirement and the need for direct contribution create a very narrow target. The expected count is low single digits, with zero a realistic possibility and only a modest chance of a larger spike.

— Iteration 2 — The forecasts share a common view that the number will likely be small, probably in the single digits to low teens, because the event definition is very restrictive.

Main factors driving the estimates

• Strict inclusion criteria: A paper only counts if its arXiv math abstract explicitly mentions GPT/ChatGPT and says it contributed to a mathematical result. This filters out most AI-related math papers.
• Low disclosure in abstracts: Even if researchers use GPT-based tools in the actual research process, they often do not mention them in the abstract unless the tool use is central to the paper.
• Historical rarity: Prior work suggests that math papers using GPT as part of discovery or proof generation are uncommon, and most GPT-related math papers are about evaluating the model rather than using it to prove results.
• Rising capability could increase usage: By July 2026, more capable GPT systems may lead to more genuine AI-assisted mathematical research, which could raise the count relative to earlier periods.
• Potential for sudden spikes: There is uncertainty around whether a few high-profile successes could trigger a temporary burst of such papers, especially if norms around disclosure shift.

Areas of consensus

• The baseline expectation is low because of the abstract-only requirement.
• Most AI/math papers will still be excluded because they describe model performance, coding help, or general writing assistance rather than a mathematical contribution.
• The outcome is likely to be driven more by reporting norms than by raw model capability alone.

Areas of uncertainty

• Whether researchers will explicitly credit GPT/ChatGPT in abstracts more often by mid-2026.
• Whether improved models produce a noticeable surge in AI-assisted math results.
• How strictly the resolution criteria will be applied in practice, especially around what counts as “contribute to a mathematical result.”

Overall, the reasoning converges on a rare but gradually increasing phenomenon, with the main limiting factor being public reporting in abstracts, not just the underlying use of GPT in mathematical work.

— Iteration 3 — Overall, the forecasts converge on a very low expected count, likely in the low single digits, for July 2026.

Main reasoning patterns

• Strict resolution criteria matter most: The event is not just “math papers using GPT,” but papers that explicitly say in the abstract that GPT/ChatGPT contributed to a mathematical result. That sharply limits the count.
• Disclosure is rare: Even if GPT is used in some mathematical work, authors often don’t mention it in the abstract, so many relevant papers would not qualify.
• Most GPT mentions are not relevant: In math-related arXiv papers, “GPT” often appears in contexts like evaluation, benchmarking, or discussion, rather than as a tool that helped prove or derive a result.
• Specialized tools may be preferred: There is an expectation that mathematicians are increasingly using or citing dedicated theorem-proving / formalization systems rather than generic GPT-style models, which limits GPT-specific appearances.

Areas of consensus

• The likely count is small, with a median around 2–3 papers.
• There is substantial probability of zero qualifying papers.
• The distribution is right-skewed: most outcomes are low, but a few unusual scenarios could produce a noticeably larger number.

Main sources of uncertainty

• A new GPT capability jump could spur more mathematically useful use cases.
• Changing disclosure norms could lead more authors to mention GPT in abstracts.
• A burst of cross-listed AI/math papers or looser interpretation of “contribute to a mathematical result” could raise the count.
• The upper tail is kept wide because of uncertainty, but the central expectation remains firmly low.

SUMMARY

Question: How many math papers on arXiv will report using GPT or ChatGPT to contribute to a mathematical result in July 2026? Final Prediction: Probability distribution:

• 10.00% chance of value below 1.153333
• 20.00% chance of value below 1.99
• 40.00% chance of value below 3.686667
• 60.00% chance of value below 5.603333
• 80.00% chance of value below 9.046667
• 90.00% chance of value below 12.863333

Total Cost: extra_metadata_in_explanation is disabled Time Spent: extra_metadata_in_explanation is disabled LLMs: extra_metadata_in_explanation is disabled Bot Name: extra_metadata_in_explanation is disabled

Report 1 Summary

Forecasts

Forecaster 1: Probability distribution:

• 10.00% chance of value below 0.49
• 20.00% chance of value below 1.3
• 40.00% chance of value below 2.75
• 60.00% chance of value below 4.1
• 80.00% chance of value below 7.1
• 90.00% chance of value below 10.7

Forecaster 2: Probability distribution:

• 10.00% chance of value below 0.48
• 20.00% chance of value below 1.18
• 40.00% chance of value below 2.32
• 60.00% chance of value below 3.72
• 80.00% chance of value below 6.55
• 90.00% chance of value below 9.9

Forecaster 3: Probability distribution:

• 10.00% chance of value below 2.49
• 20.00% chance of value below 3.49
• 40.00% chance of value below 5.99
• 60.00% chance of value below 8.99
• 80.00% chance of value below 13.49
• 90.00% chance of value below 17.99

Research Summary

The research summarizes recent developments through early June 2026: a cluster of high-profile GPT/ChatGPT-assisted mathematical results appeared in Spring 2026 (notably Liam Price’s ChatGPT-assisted solution to Erdős problem #728, multiple Tang Quanyu coauthored arXiv papers using GPT-5.x including arXiv:2603.28636 and arXiv:2605.00301, an OpenAI ChatGPT solution that OpenAI did not publish to arXiv, and Timothy Gowers’ use of ChatGPT 5.5 Pro for research), and at the same time arXiv announced stricter enforcement on AI-generated content (May 17–18, 2026) including a possible one-year ban for submissions with incontrovertible evidence of unverified AI-generated errors while allowing legitimate, verified AI use. The research reports no quantitative baseline for monthly arXiv math papers that mention GPT/ChatGPT in abstracts, notes important uncertainties (policy interpretation, disclosure practices, time lags, and whether the Erdős-problem cluster is anomalous), and outlines factors that could raise or lower July 2026 counts.

Using those observations and the strict resolution criteria (only abstracts, only GPT/ChatGPT, must indicate contribution to a mathematical result), the research gives plausible ranges for July 2026: very low 0–2, low 3–7, medium 8–15, high 16+, and states the most likely scenario is in the low-to-medium range (approximately 3–12 papers), while emphasizing high uncertainty and recommending watching June submissions as a leading indicator.

Sources used:

• arXiv:2603.28636 — https://arxiv.org/abs/2603.28636
• arXiv:2605.00301 — https://arxiv.org/abs/2605.00301
• News reports and arXiv policy announcements cited in the research (references [1]–[28] in the original document).

RESEARCH

Report 1 Research

Research Rundown: Math Papers on arXiv Reporting GPT/ChatGPT Use in July 2026

Executive Summary

This question asks about papers submitted to arXiv in July 2026 (just one month from now) that explicitly mention GPT or ChatGPT in their abstracts as contributing to a mathematical result. Based on recent news, there’s been a dramatic surge in high-profile GPT-assisted mathematical breakthroughs in Spring 2026, but also significant policy changes at arXiv that may affect reporting behavior.

Recent High-Profile Cases (May-June 2026)

Major Breakthroughs Using GPT/ChatGPT:

1. Liam Price’s Erdős Problem Solution (May 2026): A 23-year-old amateur used ChatGPT Pro to solve the 60-year-old Erdős problem #728 in just 80 minutes [2][3][4][8]. The solution was verified by Fields Medalist Terence Tao and published with collaborators.

2. Tang Quanyu’s Collaborative Work: Chinese undergraduate Tang Quanyu co-authored multiple arXiv papers solving Erdős problems using GPT-5.4 Pro and the AI system Aristotle, including:

• arXiv:2603.28636 (solved problem #650) [2]
• arXiv:2605.00301 (multi-author paper solving problems #1196, #1217, and #164) [2][3]

3. OpenAI’s 80-Year-Old Problem Solution (May 20, 2026): ChatGPT independently solved the Erdős unit distance problem from the 1940s, though OpenAI decided NOT to publish on arXiv citing “absence of a traditional human author” [1][7].

4. Timothy Gowers’ PhD-Level Results (May 9-11, 2026): Fields Medalist Timothy Gowers used ChatGPT 5.5 Pro to produce PhD-level mathematical research in under 2 hours, improving bounds in additive number theory [5][6][11].

Critical Policy Change: arXiv Crackdown (May 2026)

New Enforcement Rules Announced May 17-18, 2026:

arXiv implemented strict penalties for AI-generated content with errors [17][18][19][20][21][22][25][27][28]:

• One-year ban for authors submitting papers with “incontrovertible evidence” of unverified AI-generated content
• Targets: hallucinated citations, unedited LLM meta-commentary, unfilled placeholders
• Authors must take “full responsibility” for all AI-generated content
• Future submissions after ban require prior peer-review acceptance

Important Nuances:

• The policy does NOT ban legitimate AI use when properly verified and disclosed [18][19][21]
• Aimed at preventing “AI slop” (low-quality spam), not genuine AI-assisted research
• Terence Tao endorsed the policy, emphasizing the importance of “digestion” over publication speed [17]

Potential Impact on July 2026 Numbers:

• Chilling effect possible: Researchers may be more cautious about disclosing GPT use in abstracts
• Encouragement of proper disclosure: High-quality uses should still be acceptable with verification
• Shift in behavior: Authors might be more careful about HOW they describe AI contributions

Base Rates and Reference Classes

Historical Context - Limited Data Available:

I found no quantitative baseline data on monthly counts of arXiv math papers mentioning GPT/ChatGPT in abstracts for previous months or years. This appears to be an emerging phenomenon with the following timeline:

• 2022-2023: ChatGPT released, early adoption period
• 2024-2025: Gradual increase in AI-assisted research
• Spring 2026: Breakthrough period with multiple high-profile cases

Observed Cases from Recent Weeks:

From the news articles, I can identify at least 2-3 specific arXiv papers published in May-June 2026 that likely meet the criteria (Tang Quanyu’s papers), plus additional cases in discussion. However, these are clustered around Erdős problem breakthroughs, which may represent an unusual spike rather than steady-state behavior.

Reference Class Considerations:

1. Erdős Problem Cluster: Many recent papers focus on solving Erdős problems with GPT-5.x models. This may be a temporary surge tied to specific breakthroughs.

2. Summer Submission Patterns: July is a summer month, which may have different submission patterns than academic year months.

3. GPT Model Versions: Recent breakthroughs use GPT-5.2 Pro, GPT-5.4 Pro, and ChatGPT 5.5 Pro [2][3][6] - suggesting advanced models are driving results.

4. Fields Most Active: Combinatorics, number theory, discrete mathematics appear most prominent in GPT-assisted work.

Factors Pushing Numbers Higher

1. Momentum from May 2026: Multiple breakthroughs create enthusiasm and imitation
2. Advanced Models Available: GPT-5.x series showing strong mathematical capabilities
3. Prominent Researchers Involved: Fields Medalists (Tao, Gowers) publicly using and endorsing GPT for math
4. Follow-on Research: Breakthroughs often inspire additional work using similar methods
5. Proof of Concept: Demonstrated success makes more researchers willing to try

Factors Pushing Numbers Lower

1. Policy Chilling Effect: Fear of one-year ban may discourage abstract disclosure
2. One-Time Breakthrough Cluster: Erdős problems may represent a unique opportunity that won’t repeat
3. Non-Disclosure in OpenAI Case: OpenAI’s decision not to publish shows institutional hesitation [1][7]
4. Summer Timing: Potentially lower overall submission volume
5. Verification Requirements: Proper verification takes time, may slow submissions
6. Narrow Criteria: Only abstracts count, and only GPT/ChatGPT (not Claude, Gemini, etc.)

Key Uncertainties

1. No baseline data: Without historical monthly counts, it’s difficult to establish a trend line
2. Policy interpretation: Unclear how authors will interpret the new arXiv rules
3. Breakthrough clustering: Unknown whether May 2026 was anomalous or the new normal
4. Disclosure practices: Will researchers mention GPT in abstracts or bury it in acknowledgments?
5. Time lag: Papers solving problems in June may not be submitted until August or later

Prediction Markets

I found no active prediction markets specifically on this question on Manifold Markets, Metaculus, or Polymarket. The search for prediction markets on this specific topic yielded no results.

Analogous Situations

The closest analogy might be early adoption of other computational tools in mathematics (computer-assisted proofs, formal verification systems like Lean), but those evolved over decades rather than months. The speed of GPT adoption in mathematics appears unprecedented.

Considerations for Forecasting

Strict Interpretation of Resolution Criteria:

• Only abstracts count (not full text, acknowledgments, comments field)
• Only GPT or ChatGPT specifically (not other LLMs)
• Must indicate GPT contributed to a mathematical result (not just mentioned)
• Must be OpenAI’s GPT models (not other systems using “GPT” name)
• Each paper counts once regardless of multiple mentions

Plausible Ranges:

Given the limited data but observable recent activity:

• Very Low (0-2): If May was completely anomalous or policy creates strong chilling effect
• Low (3-7): If recent momentum partially continues with some policy caution
• Medium (8-15): If May momentum largely continues into July
• High (16+): If adoption accelerates beyond May levels (seems unlikely for just one month out)

Most Likely Scenario:

The most probable outcome appears to be in the low to medium range (3-12 papers), reflecting continued interest from the May breakthroughs but with some moderation due to policy changes, summer timing, and the specific nature of the Erdős problem cluster.

Additional Notes for Forecasters

• The current date is June 2, 2026 - only one month before the resolution period
• Recent news is highly relevant and timely
• Watch for June 2026 submission patterns as immediate leading indicator
• Consider checking arXiv’s advanced search for May-June 2026 actual numbers as proxy
• The question resolution is objective and mechanical (specific search URL provided) </thinking>

Forecast — Post 402

Modal: 0-13 (85.0%) • partial_shift • 8m21s

Interpretation

Reading: strict

The resolution criteria impose multiple explicit, narrowing conditions: the abstract alone is used (not full text or acknowledgments), GPT must be specifically OpenAI-branded, the use must materially contribute to the paper’s own mathematical result (not merely discuss or evaluate GPT), and the date window is fixed to July 2026 submissions. These constraints all push toward a strict, literal reading with little room for charitable expansion.

Time bounds

• observation_window: Papers with arXiv submission date (most recent) from 2026-07-01 (inclusive) to 2026-08-01 (exclusive), classified under mathematics
• resolution_date: 2026-08-01

Edge cases identified

1. Papers cross-listed into math from another primary category (e.g., cs.LG cross-listed to math.CO) count if they appear in the search results with math classification included.
2. The search URL uses ‘date-to_date=2026-08-01’ — it is unclear whether this is inclusive or exclusive of August 1; the resolution criteria say ‘before August 1, 2026,’ implying papers submitted on August 1 itself do not qualify.
3. Abstract text must be the sole source of qualification — even if full paper text or acknowledgments confirm GPT use, it does not count if the abstract does not indicate it.
4. ‘GPT’ used as an acronym for something other than OpenAI’s model (e.g., a mathematical object, dataset, benchmark, or algorithm) does not count even if it contributed to the math result.
5. If a paper is updated (new version) in July 2026 but was originally submitted earlier, the ‘most recent submission date’ determines whether it falls in the July window; a revised version could shift a paper into or out of the window.
6. If results exceed 200 per page, multiple pages must be checked — the search caps display at 200/page, and the resolver is instructed to paginate.
7. Non-OpenAI models described as ‘GPT-like’ or ‘GPT-based’ without explicit mention of OpenAI’s GPT/ChatGPT do not qualify.
8. Papers where GPT is mentioned in the abstract only as a comparison baseline or evaluation target (not as a contributor to the paper’s own math) do not qualify — this boundary may require judgment.

Research (3/3 variants, shared evidence pool)

Total evidence registered (shared pool): ?

Research Brief

Evidence confidence: medium

Scenario 1: Moderate sustained rate: 4–8 qualifying papers [high evidence]

Conditions favoring

The May–June 2026 wave of GPT-math papers continues at a similar pace into July 2026 with ~3–5 qualifying papers per month. New OpenAI model releases or follow-on work from May 2026 breakthroughs (Erdős problems, unit distance) continue to appear. Some authors shift toward explicitly naming GPT/ChatGPT in abstracts following community norms established by Defant, Tao et al., and others. No major capability announcement disrupts the trend.

Conditions against

The strict ‘GPT/ChatGPT explicitly in abstract’ criterion may exclude many borderline papers. The dominant convention in OpenAI-team papers is ‘internal model at OpenAI’ rather than GPT/ChatGPT, which would exclude some of the highest-profile contributions. Summer months may see lower arXiv submission volumes for mathematics.

Scenario 2: Low plateau: 1–3 qualifying papers [medium evidence]

Conditions favoring

The strict naming criterion (‘GPT’ or ‘ChatGPT’ in abstract) continues to exclude the majority of AI-math papers. Most high-profile OpenAI-team papers use ‘internal model at OpenAI’ language. Non-OpenAI models (Grok, Claude, DeepMind tools) capture an increasing share of math-AI paper volume. The wave of first-mover papers (from Feb–June 2026) subsides as novelty declines. July is traditionally a slower month for arXiv math submissions.

Conditions against

The documented rate of ~3 qualifying papers per month in May–June 2026 already exceeds this scenario’s upper bound. The naming trend appears to be increasing, not decreasing, as more authors follow community examples.

Scenario 3: High burst: 10+ qualifying papers [low evidence]

Conditions favoring

A major new OpenAI model release in June or July 2026 triggers a burst of GPT-math papers. Community norms shift decisively toward explicit GPT/ChatGPT naming in abstracts. The Gowers, Defant, and Tao precedents inspire many follow-on papers. A high-profile unsolved problem is credited to GPT/ChatGPT in July 2026, generating media attention and rapid arXiv submissions. The ‘most recent submission date’ filter captures revised versions of earlier papers.

Conditions against

No confirmed evidence of a planned major model release in July 2026 that would trigger a burst. The overdispersion-adjusted p90 from the arrival model is only ~12. The strict naming criterion would still exclude many papers even in a burst scenario. Many papers attributing results to OpenAI models would still use non-GPT language.

Scenario 4: Zero qualifying papers [low evidence]

Conditions favoring

All AI-math papers in July 2026 use generic ‘LLM/AI’ language or attribute results to non-OpenAI models. OpenAI shifts further toward proprietary naming conventions (‘internal model’) exclusively. A major AI controversy or policy shift leads authors to avoid naming specific commercial models in abstracts. July is a low-submission month and the confluence of factors produces zero papers meeting the strict abstract criterion.

Conditions against

Multiple confirmed qualifying papers already exist from May–June 2026, suggesting a nonzero baseline. The community norms established by Defant, Verbeken, and Tao et al. make future qualifying papers plausible. The arrival model’s p5 is 0 but not the central expectation.

Key uncertainties

• Whether the dominant naming convention in July 2026 math-AI abstracts will be explicit ‘GPT/ChatGPT’ vs. generic ‘LLM/AI/internal model at OpenAI’ — this single factor most determines the qualifying count
• Whether OpenAI releases a new major model in June–July 2026 that triggers a burst of math papers (high variance event)
• The extent to which non-OpenAI models (Claude, Gemini, DeepSeek, Grok) capture math-AI paper volume, reducing GPT/ChatGPT’s share
• Whether July arXiv math submission volumes are seasonally lower than May–June (summer effect), reducing the absolute pool
• How many papers revised in July 2026 (with ‘most recent submission date’ in July) but originally submitted earlier will appear in the search results
• Whether the ‘GPT’ search term captures papers using ‘GPT-5.4 Pro’ or similar non-lowercase variants consistently across arXiv’s search index

Forecast variants (3/3)

Variant 0: inside_view (inside_view_v1)

Inside-View Causal Chain Analysis

Current state → mechanism → outcome:

The evidence documents a clear trajectory: starting from near-zero in 2024, GPT/ChatGPT-attributed math papers on arXiv have been accelerating through early-to-mid 2026. The confirmed qualifying papers (explicitly naming GPT/ChatGPT in abstract as contributing to a math result) include arXiv:2602.18918 (Feb), arXiv:2605.00301 (May), arXiv:2605.19979 (May), and arXiv:2606.01646 (June) — per sources 13, 33, 3, 18. This gives at least 3-4 qualifying papers in May-June alone.

Key causal mechanism: The strict resolution criterion (GPT/ChatGPT explicitly named in abstract) is the dominant filter. Per source 45, only ~21% of AI-math papers explicitly name GPT/ChatGPT. However, the confirmed examples show that once authors like Defant, Tao et al., and Verbeken establish norms of explicit naming, community adoption follows. The Fields Medalist Gowers effect (source 27) and media attention (source 20) create strong incentives for authors to explicitly credit GPT/ChatGPT in abstracts.

Evidence weighting by scenario strength:

1. “Moderate sustained rate: 4–8 qualifying papers” — tagged high evidence strength. The arrival-rate NB model (source 32) with mean=5/month gives mean=5, p25=1-2, p75=7-8 for the July window. Confirmed June 2026 qualifying paper (source 18) establishes continuity into the pre-July period.

2. “Low plateau: 1–3 qualifying papers” — tagged medium evidence strength. The lower-bound model (source 34, mean=2/month) gives p75=3. Valid concerns: OpenAI-team papers often use “internal model” language; competing models dilute GPT-specific share.

3. “High burst: 10+ qualifying papers” — tagged low evidence strength. P90=12 from overdispersed model but no confirmed major model release trigger.

4. “Zero qualifying papers” — tagged low evidence strength. P5=0 from models but confirmed qualifying papers in prior months make this unlikely.

Distribution construction:

Anchoring on the high-evidence scenario (mean ~5, p75 ~7-8), with the medium-evidence scenario providing a leftward pull (mean ~2-3), and low-evidence scenarios at the tails:

• 0-13 (bin_0): Very high probability — the central estimate of ~4-8 falls in this range. Given the strict criterion and the confirmed ~3-4/month base rate in May-June 2026, I expect July to be in the 0-13 range with high probability (~85-90%). July is historically a slightly slower month. The overdispersed NB model concentrates mass here.
• 13-25 (bin_1): Small probability (~7%) for upside scenarios — a major model release or naming-norm shift.
• bin_2+ (25+): Very small residual.

Within bin_0, the distribution centers around 4-7 papers:

• P(0) ≈ 8% (model p5 territory but confirmed prior month activity makes zero unlikely)
• P(1-3) ≈ 30% (low plateau scenario, medium evidence)
• P(4-8) ≈ 42% (moderate sustained rate, high evidence)
• P(9-13) ≈ 12% (upper tail of NB model)
• P(13+) ≈ 8%

So bin_0 gets ~0.83, bin_1 gets ~0.12, bin_2 gets ~0.04, higher bins get tiny residual.

Variant 1: outside_view (outside_view_v1)

Reference class: monthly count of arXiv mathematics papers whose ABSTRACTS explicitly state that GPT or ChatGPT (OpenAI-branded) was used to contribute to a mathematical result, based on observed April–June 2026 papers. Base rate: roughly 3–5 qualifying papers/month (arrival-model mean ≈5, median ≈4; see arrival-rate model p25–p75 and evidence summary, source 32). Adjustment: small net change from the base rate. Upward pressure comes from continued momentum and high-profile examples in May–June 2026 (Defant, Alexeev/Tao et al., Verbeken; see sources 3, 33, 13, 18) and media attention incentivizing disclosure (source 20). Downward pressure comes from the strict resolution filter (abstract-only + must explicitly name GPT/ChatGPT), which historically excludes many AI-math papers (sample: ≈3/14 ≈21% explicitly name GPT in abstracts; see source 45 and source 30). Also, arXiv’s “most recent submission date” can include revisions in July, slightly raising counts (source 12). Final: concentrate mass in the 0–13 bin because the outside-view base rate (≈4/month) lies well inside it and the high-evidence scenario (Moderate sustained rate 4–8) is the dominant supported case (research brief tags that scenario “high” evidence strength; see source 32 and supporting examples in sources 3, 33, 13, 18). I therefore assign 92% probability to 0–13 (bin_0). I place 7% in 13–25 (bin_1) to capture the plausible but lower-probability tail where a burst or many revisions push the count above ~13 (arrival-model p90–p95 ~12–15, source 32; scenario “High burst” tagged low evidence). Small leftover mass (≈1%) is spread to bins 2–3 (very unlikely extreme bursts or indexing anomalies). This distribution reflects the strict reading required by the resolution criteria (abstract-only + explicit OpenAI GPT/ChatGPT naming), weights the high-evidence moderate-sustained scenario materially more than low-evidence burst/zero scenarios (per the brief’s scenario evidence strengths: high vs. medium/low; see scenarios and sources 32, 45, 30, 12), and preserves a long tail for low-probability but possible large bursts tied to a new OpenAI release or mass revisions (sources 20, 12). Confidence in evidence: medium (the brief aggregates direct examples and an arrival-model but key uncertainties remain about naming conventions and any model-release-driven bursts; see key_uncertainties).

Variant 2: contrarian_v2 (contrarian_v2)

Adversarial reading

The implicit consensus across the brief is that the strict abstract-naming filter plus observed arrival rates will keep July 2026 qualifying counts low (centered around 3–8 papers). The bulk of the evidence—systematic sample showing only ~21 % of AI-math papers use explicit GPT/ChatGPT language, confirmed examples limited to a handful per month, and NB models with p95 ≤ 15—pulls decisively toward the 0–13 bin.

Counter-evidence found (or absence)

Searched for counter-evidence; nothing substantive found; consensus appears robust. No documented mechanism in the brief would reliably push a large fraction of papers into explicit GPT/ChatGPT naming or generate a July-specific burst large enough to reach the 13–25 range.

Distribution implications

Because the high-evidence moderate-rate scenario (4–8 papers) and medium-evidence low-plateau scenario (1–3) both sit comfortably inside bin_0, and even the low-evidence burst tail reaches only ~15, the distribution places the large majority of mass in bin_0. Only a thin tail is allocated to bin_1 to reflect residual uncertainty around revisions and possible late naming shifts; bins 2+ receive negligible mass.

Consolidate

Strategy: logit_mean • Drafts: 3/3

Reviewers (3/3)

anchoring → shift_lower (low magnitude, medium confidence) anchoring_v1

The draft rationale anchors on the confirmed qualifying count from a brief, active observation window (May–June 2026) and treats it as the p50 for July. Specifically, the inside-view reasoning states “confirmed qualifying papers in May-June alone: at least 3-4” and then sets the modal scenario at 4–8 papers — placing the peak of the distribution at the front-end of the plausible range rather than at the conditional mean given the stated uncertainty. The NB arrival model (source 32) has mean=5 and p25=1–2, meaning roughly half the probability mass under that model lies below 5; yet the rationale characterizes “4–8 papers” as the central/dominant outcome. More critically, the model uses the same confirmed examples (May–June 2026) that represent the early acceleration phase of an emerging trend without discounting for the possibility that this short burst was above-trend, and then extrapolates optimistically forward with no regression to mean. The result is that 0–13 (bin_0) receives 88% mass centered on a modal estimate of ~5–7, when the lower-bound model (mean=2, source 34) — tagged “medium” evidence strength — combined with naming-convention exclusions suggests the unconditional median could easily be 2–4, pulling the mode closer to bin 0 integer counts of 3–5 rather than treating 5–7 as the center.

Flagged concerns

• Early-window anchoring: The draft sets p50 at ~5–7 papers by anchoring directly on the May–June 2026 confirmed qualifying count (3–4 papers over two months). This treats the acceleration phase as a stable run rate, ignoring that (a) May–June 2026 was an exceptional period triggered by high-profile breakthroughs (Gowers, Defant, unit-distance), (b) the lower-bound model (mean=2/month, medium evidence) is not given sufficient weight to pull the mode lower, and (c) July is historically a slower arXiv submission month.
• Best-case scenario weighted as modal: The ‘moderate sustained rate: 4–8 qualifying papers’ scenario is labeled ‘high evidence strength’ and becomes the near-exclusive center of the distribution. But the high evidence for that scenario comes from the arrival-rate model mean (5/month) — not from confirmed July data. The p50 of the NB model is ~4, not 5–7; the mode is even lower. Treating the model’s mean as the distribution’s center creates an upward shift from modal expectation.
• Insufficient weight on naming-convention exclusion: The rationale notes that only ~21% of AI-math papers explicitly name GPT/ChatGPT (source 45) but then qualitatively discounts this (‘I discount somewhat’) rather than quantitatively propagating it. If the broader pool of AI-math papers grows but the naming rate stays at 21%, the qualifying count is constrained much more tightly than the draft implies.

ceiling → shift_lower (low magnitude, medium confidence) ceiling_v1

The key structural constraint here is the strict abstract-naming filter combined with the observed empirical base rate from the research period. The brief documents that only ~3 out of 14 AI-math arXiv papers (21%) from April–June 2026 explicitly name “GPT” or “ChatGPT” in the abstract as contributing to a mathematical result (source 45), and confirms only 3–4 qualifying papers total in May–June 2026. This establishes a structural ceiling: even if the total volume of AI-math papers doubles, the qualifying subset is bounded by the ~20–25% naming-convention filter applied to a base of roughly 4,000–5,000 math papers/month (source 23), of which only a tiny fraction (~14 observed in the sample period) are even AI-math papers. The NB arrival model’s p95 of ~15 (source 32) itself constitutes a soft structural ceiling — the brief’s own “high burst” scenario is tagged “low evidence strength” and even that scenario’s p90 only reaches ~12. The draft correctly concentrates ~88% of mass in 0–13 (bin_0), but the structural ceiling argument implies 13–25 (bin_1) at ~9.1% may be slightly too generous given the hard filter: to reach 13+, the naming convention rate would need to dramatically shift OR a major new model release would need to trigger a burst, neither of which has supporting evidence in the brief. The mass at bins 2+ (25+, ~2.8%) also seems slightly high given the structural ceiling imposed by both the naming filter and the NB model’s p95≈15.

Flagged concerns

• Structural naming-convention ceiling: The brief documents that only ~21% of AI-math arXiv papers (3/14 sample, source 45) explicitly name GPT/ChatGPT in abstracts. This creates a hard structural ceiling on the qualifying count relative to total AI-math paper volume. At the observed rate of ~3–4 qualifying papers/month in May–June 2026, reaching 13–25 (bin_1) would require a ~3–4x increase in the qualifying rate within a single month, which has no supporting evidence. The draft’s bin_1 allocation of ~9.1% appears modestly too high given this constraint.
• NB model p95 as soft structural ceiling: The overdispersed NB arrival model (source 32) with mean=5/month and overdispersion=0.8 yields p95≈15. This means the model itself assigns only ~5% probability to outcomes above 15, yet the draft allocates ~11% to bins 1+ (13–25 and above). Specifically, ~2.8% is placed in bins 2–8 (25+), which corresponds to outcomes the model assigns probability well below 1%. The structural ceiling implied by the NB model is not fully reflected in the draft’s tail allocation.
• OpenAI naming-convention path-dependency: The brief confirms (sources 36, 21, 31) that the most prolific source of AI-math papers — OpenAI-team papers — systematically uses ‘internal model at OpenAI’ rather than ‘GPT/ChatGPT’ in abstracts. This creates a path-dependent structural floor on the qualifying fraction: even if OpenAI produces more math results in July 2026, those papers are structurally unlikely to qualify unless naming conventions change. The draft rationale acknowledges this but does not sufficiently tighten the upper tail accordingly.

math → shift_higher (medium magnitude, high confidence) math_v1

The distribution exhibits a critical internal inconsistency. The rationale explicitly documents a base arrival rate of 3–5 qualifying papers per month (sources 32, 45) and an overdispersed Poisson/NB model with mean=5/month yielding p25≈1–2, median≈4, p75≈7–8, p90≈12, p95≈15 for a single month. Yet the published forecast allocates 88.0% to 0–13 (bin_0) with only 9.1% to 13–25 (bin_1). This distribution shape implies an expected value around 4–5 (roughly the lower third of bin_0), which contradicts the rationale’s own median of 4 and the high-evidence scenario centered on 4–8 papers. The mass allocation is internally consistent with values 0–4 but under-weights the documented p75–p95 tail (7–15) that the rationale derives and endorses.

Flagged concerns

• Distribution shape vs. derived statistics: Rationale cites NB arrival model with p25=1–2, median≈4, p75=7–8, p90=12, p95=15 for July 2026 (source 32), but published 0–13 (bin_0) receives 88% mass, concentrating far below the documented p75=7–8. For a median of 4, the modal bin should be bin_0, but p(bins_1+) should capture the 25% right tail; instead p(bins_1+) ≈ 10.2%, implying an EV well below 4.
• Scenario weighting mismatch: Brief tags ‘Moderate sustained rate: 4–8 papers’ as HIGH evidence strength with supporting arrival model (source 32) and confirmed examples (sources 3, 33, 18). The draft allocates only ~9% to 13–25 (bin_1), leaving 88% in 0–13 (bin_0). This severely under-weights the high-evidence scenario’s central range (4–8) relative to the low-evidence scenarios (zero, burst).
• Percentile consistency: Rationale derives p75=7–8 from the NB model. If 75% of the probability mass should be ≤7–8, the distribution should have CDF(8) ≈ 0.75. The published distribution has bin_0 = [0, 13], so CDF(13) = 0.88, and CDF(8) is even higher (likely 0.85+). This is consistent with p75 around 8–9, not 7–8, and suggests the rationale understated the tail mass.
• Scenario integration arithmetic: Rationale lists four scenarios with evidence strengths (high, medium, low, low) covering ranges [0, 4–8, 1–3, 10+, 0]. Expected scenario-weighted EV should reflect the high-evidence 4–8 scenario more heavily. Published EV ≈ 4.5 sits at the low end of that range and below the scenario-weighted center, suggesting under-weighting of the high-evidence tail.

Reconcile: partial_shift

Reviews consumed: 3

The draft places ~88% in 0-13 (bin_0), with anchoring and ceiling reviewers both suggesting modest shifts lower while the math reviewer flags an internal inconsistency suggesting a shift higher. I weighed these as follows: the anchoring and ceiling reviewers correctly note the structural ~21% naming-convention filter and the OpenAI ‘internal model’ path-dependency (sources 30, 36, 45), which keep the tail tight — but their suggested downward shifts are small. The math reviewer makes a sharper quantitative point: the rationale itself cites NB p75≈7–8 and p90≈12, which means meaningful mass (~10–25%) should land in 13–25 (bin_1) and the upper tail, not just ~10%. I partially accept the math reviewer’s correction but not fully, because their independent forecast (71% bin_0) overcorrects by ignoring the structural naming-convention ceiling flagged by the ceiling reviewer — the NB p75 of 7–8 is still well inside bin_0, and bin_1 begins at 13 (not 8). Final distribution shifts modestly: bin_0 down to 0.85, bin_1 up to 0.11 to better reflect NB p90≈12 straddling the bin boundary, with small residual tail. I rejected the math reviewer’s full magnitude because the cited p75 (7-8) and median (4) both sit inside bin_0, not bin_1.

Rejected critiques

• [math] Distribution under-weights NB p75=7-8 and p90=12 tail; suggested shifting 19% to bin_1 and 5% to bin_2.

  • Why rejected: The math reviewer’s percentile critique partially conflates the NB scale with bin boundaries. Bin_0 covers 0-13, so NB p75 (7-8), median (4), and even much of the p90 region (12) all fall INSIDE bin_0, not bin_1. Their full magnitude shift (to 71% bin_0) overcorrects. I partially integrated the concern by raising bin_1 from 0.091 to 0.11 (capturing the portion of the p90-p95 tail that crosses 13), but rejected the full reallocation because the structural naming-convention ceiling (ceiling reviewer’s flag) constrains the upper tail more than the raw NB model implies.

• [anchoring] Suggested shifting lower because draft anchors on May-June 2026 acceleration phase without regression to mean.

  • Why rejected: Concern is reasonable but its proposed magnitude (low) only nudges bin_0 from 0.88 to 0.87 — within noise. More importantly, the math reviewer’s countervailing concern about under-weighting the upper NB tail pulls the opposite direction and is better supported by the brief’s own arrival-model statistics. Net effect: I did not shift lower.

Final Distribution

Evidence Sources (46)

1. ChatGPT can provide original mathematical proofs, researchers show — A March 2026 phys.org article reports that researchers showed ChatGPT (specifically ChatGPT-5.2 Thinking) could provide original mathematical proofs, published on arXiv, indicating continued use of GPT models in mathematical contexts in 2026.
2. ChatGPT vs. Claude vs. Gemini vs. DeepSeek: The Ultimate AI Assistant Showdown for 2026 — As of mid-2026, multiple competing AI models (Claude, Gemini, Grok, DeepSeek) have become prominent alternatives to ChatGPT/GPT for research tasks, which may reduce the share of math papers specifically citing GPT/ChatGPT vs. other models.
3. Short Proofs in Algebraic and Enumerative Combinatorics — A May 2026 arXiv paper (2605.19979) by Colin Defant titled “Short Proofs in Algebraic and Enumerative Combinatorics” explicitly states in the abstract that “All of these proofs were obtained autonomously by ChatGPT 5.4 Pro,” resolving open conjectures in combinatorics.
4. Resolution of Erdős Problem #728: a writeup of Aristotle’s Lean proof — A January 2026 arXiv paper (2601.07421) titled “Resolution of Erdős Problem #728” states in its abstract that the proof was obtained by “a combination of GPT-5.2 Pro by OpenAI and Aristotle by Harmonic,” qualifying as a GPT-attributed mathematical result.
5. Short proofs in combinatorics and number theory — A 2603.29961 OpenAI paper “Short proofs in combinatorics and number theory” (March 2026) states proofs “due entirely to an internal model at OpenAI” — but does not mention GPT or ChatGPT by name in the abstract, so may not qualify under strict reading.
6. Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problem — An October 2025 arXiv paper (2510.26647) describes a lemma from convex optimization proved with assistance from GPT-5-Pro, explicitly stating in the abstract that GPT-5-pro “accelerated our progress by suggesting relevant research directions and by proving some intermediate results” — another qualifying example of GPT contributing to a mathematical result.
7. Mathematics - arXiv new listings — The arXiv math new listings page as of June 2026 shows a paper stating “We succeed in proving this conjecture, using an argument based on our extensive interactions with GPT-5.5 Pro” under Combinatorics (math.CO), indicating ongoing GPT-assisted math papers in June 2026.
8. Remarks on the disproof of the unit distance conjecture — A May 2026 arXiv paper (2605.20695) “Remarks on the disproof of the unit distance conjecture” references ChatGPT Pro 5.5 in the abstract context, indicating GPT-assisted math papers in May 2026.
9. untitled — arXiv paper 2510.12829 (Oct 2025, math-classified): “Mathematics with large language models as provers and verifiers” explicitly reports ChatGPT (gpt-5 model instances) solving 5/6 IMO 2025 problems and closing ~1/3 of 66 open conjectures in number theory. Abstract mentions “theorem proving feat achieved by ChatGPT.”
10. untitled — arXiv paper 2509.03065 (Sep 2025): “Mathematical research with GPT-5: a Malliavin-Stein experiment” — math-classified paper where GPT-5 was used to extend a qualitative fourth-moment theorem to a quantitative formulation; qualifies as GPT contributing to an original mathematical result.
11. ChatGPT can provide original mathematical proofs, researchers show — A March 2026 arXiv paper from VUB’s Data Analytics Lab explicitly demonstrates ChatGPT-5.2 (Thinking) independently proving a 2024 conjecture by Ran and Teng; the abstract describes ChatGPT as central to proving the theorem, qualifying as a GPT mathematical contribution paper.
12. arXiv submission surge analysis (sgnoohc/arxiv-submission-analysis GitHub) — A key methodological caveat for this question: arXiv’s “Submission date (most recent)” filter counts paper revisions as new submissions; a paper originally submitted in 2020 that gets a revised version in July 2026 would be counted in the July 2026 window. This could inflate the count beyond purely new papers.
13. untitled — arXiv paper 2602.18918: “Early Evidence of Vibe-Proving with Consumer LLMs” (Feb 2026) — math paper abstract explicitly states ChatGPT-5.2 (Thinking) resolved Conjecture 20 of Ran and Teng (2024) about spectral regions of nonnegative matrices; this is a clear qualifying example.
14. untitled — arXiv paper 2510.26647 (Oct 2025): “Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problem” — abstract states GPT-5-pro helped prove a lemma (Taylor expansion for gradient of biconjugation operator). Qualifies as GPT contributing to mathematical result.
15. untitled — The high-profile May 2026 OpenAI unit distance breakthrough generated significant follow-on: multiple papers in May 2026 discuss GPT contributions, including the 2605.20695 “Remarks on the disproof” paper by 9 mathematicians (Alon, Gowers, etc.), but its abstract describes “the recent OpenAI-generated counterexample” without explicitly attributing to GPT/ChatGPT by name in the abstract, potentially disqualifying it.
16. untitled — Scott Aaronson’s blog (May 28, 2026) describes that an arXiv paper (from Shtetl-Optimized) mentions “proof of the main result came from GPT-5 Thinking” — indicating multiple GPT-attributed math papers appeared around May 2026.
17. Looks Like it is Happening… | Not Even Wrong — Using the “Submission date (original)” filter for hep-th (high energy physics theory), arXiv submission counts grew from ~510-531/month (2022-2023) to ~617/month (Jan 2026) — a modest year-over-year increase of ~15-20%, not the near-doubling seen under the “most recent submission date” filter.
18. untitled — The arXiv math new submissions page (June 2026) lists a paper with abstract mentioning “we succeed in proving this conjecture, using an argument based on our extensive interactions with GPT-5.5 Pro” — arXiv:2606.01646, confirming GPT-mentioned math papers continue in June 2026.
19. untitled — A May 2026 Reddit thread titled “Recent math-y papers with proofs derived by LLMs” catalogues multiple such papers, and a commenter notes “pointed lemmas where proved by gpt pro” in numerical math work — suggesting the phenomenon is widespread enough to generate community discussion.
20. untitled — As of June 2026, there is a major wave of media coverage about AI (specifically OpenAI models) contributing to mathematical results, creating strong incentives for mathematicians to publish papers attributing results to GPT/ChatGPT. The environment is significantly more active than even 3 months earlier.
21. untitled — arXiv paper 2604.06609 (Apr 2026): “Short proofs in combinatorics, probability and number theory II” — OpenAI team (Alexeev, Putterman, Sawhney, Sellke, Valiant) gives proofs of 5 Erdős problems, each “due to an internal model at OpenAI.” Abstract does not specify GPT, so it may not qualify under the strict GPT/ChatGPT criterion.
22. untitled — arXiv paper 2604.16989 (Apr 2026): “Bolzano: Case Studies in LLM-Assisted Mathematical Research” — abstract reports new math/TCS results with “Bolzano, an open-source multi-agent LLM system” but does NOT mention GPT or ChatGPT specifically; it would NOT qualify under the strict resolution criteria.
23. untitled — The arXiv Math (math) category had 21,895 articles + 4,668 cross-listings in 2026 (through the first 5 months of 2026, as of June 1, 2026), suggesting approximately 4,000-5,000 math articles per month in 2026.
24. untitled — In May 2026, Fields Medalist Timothy Gowers published a blog post and preprint showing ChatGPT 5.5 Pro independently solved an open PhD-level math problem in number theory in 17 minutes; this paper was likely submitted to arXiv in May 2026 with “ChatGPT” likely in the abstract.
25. untitled — In April 2026, a 23-year-old amateur (Liam Price) used GPT-5.4 Pro to solve a 60-year-old Erdős problem that was subsequently reported in Scientific American — a strong signal that GPT-attributed math papers are not limited to professional researchers in this period.
26. untitled — As of early April 2026, a tracker of “AI mathematics solutions” counted 12+ verified AI mathematics solutions and 2 meaningful AI proof contributions; most notable solutions in this period use OpenAI models (GPT family) but many papers use generic “LLM” language rather than specifically “GPT/ChatGPT” in the abstract.
27. untitled — Fields Medalist Timothy Gowers (Cambridge) published a blog post on May 8, 2026 reporting that ChatGPT 5.5 Pro produced “PhD-level” mathematical research (improving a bound from exponential to quadratic for a Nathanson number theory problem) in under 2 hours with “zero mathematical input” from Gowers. A preprint was reportedly submitted to arXiv — a strong signal that more qualifying papers should follow.
28. untitled — In May 2026, OpenAI announced that an internal model disproved the longstanding Erdős n^(1+o(1)) conjecture in the planar unit distance problem, with the proof checked by external mathematicians (openai.com/index/model-disproves-discrete-geometry-conjecture/). arXiv paper 2605.20695 titled “Remarks on the disproof of the unit distance conjecture” presents a human-verified version of this result.
29. untitled — A MathOverflow thread (2025-2026) catalogs arXiv papers where AI/LLMs contributed to mathematical results, including one paper noting “the appendix to this paper details how the main result and the proof were generated by GPT-o1-mini in September 2024” — showing this phenomenon began in 2024, with isolated individual papers per month, before accelerating in 2025-2026.
30. untitled — The strict resolution criterion (GPT or ChatGPT explicitly named in abstract as contributing to the paper’s mathematical result) significantly narrows the qualifying pool: many prominent AI-math papers in 2026 use terms like “internal model at OpenAI,” “Codex,” or generic “LLM” without explicitly saying “GPT” or “ChatGPT” — these do NOT qualify. Estimate: roughly half of AI-math papers with OpenAI contributions may explicitly name GPT/ChatGPT in abstract.
31. untitled — CRITICAL DISCONFIRMATION: The abstract of 2605.20695 says “OpenAI-generated counterexample” not “GPT” or “ChatGPT” — this high-profile May 2026 paper would FAIL the strict resolution criteria since the abstract does not specifically say GPT/ChatGPT. Many AI-math papers use generic terms (“AI,” “LLM,” “OpenAI model”) that do not qualify.
32. untitled — Arrival forecast for qualifying arXiv math papers (GPT/ChatGPT explicitly contributing to math result in abstract) in July 2026: using arrival_rate=5/month and overdispersion=0.8 (bursty, reflecting high variability), the model gives mean=5, median=4, p5=0, p25=1, p75=7, p90=12, p95=15. The high overdispersion reflects that major OpenAI releases can trigger sudden waves of papers, but the rate could also be lower if activity plateaus.
33. untitled — arXiv paper 2605.00301 (May 2026, math-classified, Tao et al.): “Primitive sets and von Mangoldt chains” — abstract explicitly states “We introduce a new method…suggested from output of GPT-5.4 Pro” and proves two 1966 Erdős-Sárközy-Szemerédi conjectures. This paper QUALIFIES under the strict resolution criteria — abstract says “GPT” contributing to the math result.
34. untitled — Lower-bound arrival forecast scenario (if the wave of GPT math papers plateaus or only ~2 qualify per month): using arrival_rate=2/month and overdispersion=0.5, the model gives mean=2, median=1, p5=0, p25=0, p75=3, p90=5, p95=6. This scenario assumes the strict “GPT/ChatGPT explicitly named” criterion excludes most papers and activity levels off near pre-May-2026 baselines.
35. Iteris: Agentic Research Loops for Computational Mathematics — arXiv:2606.02484 “Iteris: Agentic Research Loops for Computational Mathematics” (Peking University) is dated June 1, 2026, confirming at least one new math/AI-assisted research paper in June 2026.
36. Short proofs in combinatorics and number theory — OpenAI’s “Short proofs in combinatorics and number theory” (arXiv:2603.29961, March 2026) uses the phrase “internal model at OpenAI” in the abstract — NOT “GPT” or “ChatGPT” — to describe the AI system that generated the proofs.
37. Short Proofs in Algebraic and Enumerative Combinatorics — Colin Defant’s “Short Proofs in Algebraic and Enumerative Combinatorics” (arXiv:2605.19979, May 2026) explicitly names “ChatGPT 5.4 Pro” in the abstract bullet points and introduction, qualifying under a strict GPT/ChatGPT naming criterion.
38. Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking) — Verbeken et al.’s “Early Evidence of Vibe-Proving with Consumer LLMs” (arXiv:2602.18918) explicitly names “ChatGPT-5.2 (Thinking)” in the abstract, qualifying under a strict GPT/ChatGPT naming criterion. The abstract refers to “Large Language Models (LLMs)” generically first, then specifically names the model.
39. Remarks on the disproof of the unit distance conjecture — Alon, Bloom, Gowers et al. “Remarks on the disproof of the unit distance conjecture” (arXiv:2605.20695, May 2026) uses “OpenAI-generated” in the abstract but NOT “GPT” or “ChatGPT.” The introduction clarifies the proof was by “an internal model at OpenAI,” though footnote 1 uses “GPT proof” colloquially.
40. Advancing Mathematics Research with AI-Driven Formal Proof Search — Google DeepMind’s “Advancing Mathematics Research with AI-Driven Formal Proof Search” (arXiv:2605.22763, May 2026) uses generic “AI-Driven” and does not name GPT or ChatGPT in the abstract; it is a DeepMind paper unrelated to OpenAI’s models.
41. Automatic Textbook Formalization — FAIR/Meta’s “Automatic Textbook Formalization” (arXiv:2604.03071, March 2026) uses “Claude 4.5 Opus agents” in the abstract — does not name GPT or ChatGPT. This is a Meta/Claude paper, not OpenAI-contributed.
42. Automated Conjecture Resolution with Formal Verification — Ju et al., “Automated Conjecture Resolution with Formal Verification” (arXiv:2604.03789, April 2026) uses generic “large language models (LLMs)” in the abstract — does not name GPT or ChatGPT. It proposes a custom framework (Rethlas/Archon) from Peking University.
43. Towards Solving the Gilbert-Pollak Conjecture via Large Language Models — Ke et al., “Towards Solving the Gilbert-Pollak Conjecture via Large Language Models” (arXiv:2601.22365) uses generic “LLMs” and “AI system” in the abstract — does not name GPT or ChatGPT.
44. Grokability in five inequalities — Ivanisvili & Xie, “Grokability in five inequalities” (arXiv:2605.05193, May 2026) explicitly names “Grok” (xAI’s model) in the abstract — does not name GPT or ChatGPT. This paper would fail both a GPT-specificity criterion AND is not an OpenAI paper.
45. Systematic sample of arXiv math papers, April–June 2026 (Exa/Serper search) — From a systematic sample of ~14 AI-math arXiv papers from April–June 2026, only 3 papers explicitly name “GPT” or “ChatGPT” in the abstract (Defant 2605.19979 naming “ChatGPT 5.4 Pro”; Verbeken et al. 2602.18918 naming “ChatGPT-5.2”; Alexeev et al. 2605.00301 naming “GPT-5.4 Pro”), while ~11 use generic terms (“LLM,” “AI system,” “internal model at OpenAI,” “AI-Driven,” “AI agents,” or named non-OpenAI models). This suggests approximately 20–25% of AI-math papers in this period explicitly name GPT/ChatGPT in the abstract.
46. Comparison of OpenAI-contributed math papers from arXiv, 2026 — Among the subset of OpenAI-contributed math papers specifically, the naming pattern is mixed: the two Alexeev et al. “Short proofs” papers (arXiv:2603.29961, 2604.06609) use “internal model at OpenAI” in the abstract (no GPT/ChatGPT), while “Primitive sets and von Mangoldt chains” (arXiv:2605.00301) names “GPT-5.4 Pro” in the abstract. This confirms roughly 1/3 to 1/2 of OpenAI-origin papers use the strict GPT/ChatGPT language in abstracts.

wooley_rhino • run 1e303c93 • $3.69 • 8m21s

Extracted Percentile Values: {0.1: 1.01, 1.0: 1.15, 5.0: 1.7, 10.0: 2.2, 15.0: 2.8, 20.0: 3.3, 25.0: 3.8, 30.0: 4.4, 35.0: 5, 40.0: 5.5, 45.0: 6, 46.0: 6, 47.0: 6, 48.0: 6.4, 49.0: 6.7, 50.0: 7, 51.0: 7, 52.0: 7.3, 53.0: 7.6, 54.0: 8, 55.0: 8, 60.0: 9, 65.0: 10.5, 70.0: 12, 75.0: 14, 80.0: 16.5, 85.0: 20, 90.0: 25, 95.0: 35, 99.0: 60, 99.9: 110}

Model’s Answer: Step one is to separate the underlying phenomenon from the measured one. The underlying phenomenon is “GPT helping with math research.” The measured one is much narrower: math-classified arXiv records whose abstract contains “gpt” or “chatgpt” and explicitly says GPT contributed to the paper’s own mathematical result. That abstract-level disclosure bottleneck is the biggest reason I do not push this forecast very high.

Step two is to use the most relevant evidence. The strongest evidence here is the existence of multiple late-2025 and 2026 examples of arXiv math papers explicitly crediting GPT-family systems for proofs, conjectures, counterexamples, or related mathematical advances, plus community curation of such examples. That argues strongly against a near-zero forecast. The weaker but still useful evidence is broader scholarship showing LLM use in academic writing and review is widespread and often under-disclosed, especially in math relative to CS. That supports a nonzero count but also warns that explicit abstract mentions will remain a small fraction of true usage.

Step three is to adjust for time horizon and the exact arXiv filter. The horizon is short: only July 2026 records matter, and today is early June 2026. That makes a giant norm shift less likely before resolution. At the same time, the criterion uses the most recent submission date, so qualifying papers revised in July can count, not just brand-new July papers. That slightly raises the expected count relative to a “new submissions only” interpretation.

My central view is that the count is probably in the mid single digits to low teens, with the median around 7. I think the most likely way the outcome lands low is that many authors either omit GPT from the abstract, use non-GPT models, or describe help more vaguely as “AI” or “LLM,” which would fail the filter. I think the most likely way it lands high is that explicit GPT-crediting in math abstracts normalized faster than expected after several headline-making examples, and July captures both new papers and revisions of earlier GPT-assisted work.

The assumptions whose failure would matter most are these. First, I am assuming there is already a small but real monthly flow of qualifying papers by mid-2026; I put about a 35% chance that this is overstated, which would drag the outcome toward the very low end. Second, I am assuming authors will keep using the GPT brand in abstracts rather than generic “LLM” language; I put about a 30% chance this is too optimistic. Third, I am assuming the stock of earlier GPT-assisted math papers generates at least a few July revisions that count under “most recent submission date”; I put about a 25% chance this matters less than I expect.

Overall, I assign a roughly 20% chance to a low outcome effectively around 3 or fewer, and about a 10% chance to a high outcome around 20 or more, with most mass between about 4 and 16. Because there is no authoritative historical series for this exact arXiv-filtered metric, I am keeping the distribution fairly wide and leaving a long right tail.

Percentile .1: 1.01 Percentile 1: 1.15 Percentile 5: 1.7 Percentile 10: 2.2 Percentile 15: 2.8 Percentile 20: 3.3 Percentile 25: 3.8 Percentile 30: 4.4 Percentile 35: 5 Percentile 40: 5.5 Percentile 45: 6 Percentile 46: 6 Percentile 47: 6 Percentile 48: 6.4 Percentile 49: 6.7 Percentile 50: 7 Percentile 51: 7 Percentile 52: 7.3 Percentile 53: 7.6 Percentile 54: 8 Percentile 55: 8 Percentile 60: 9 Percentile 65: 10.5 Percentile 70: 12 Percentile 75: 14 Percentile 80: 16.5 Percentile 85: 20 Percentile 90: 25 Percentile 95: 35 Percentile 99: 60 Percentile 99.9: 110

Mathematical preprint channels impose rigid category tags and terse abstract conventions.

Searchable counts depend on narrow disclosure language and on which submission date is treated as most recent.

Several recent submissions include explicit keyword disclosures in abstracts, elevating the observable base rate.

Moderation and editorial pressure discourage careless claims and may encourage moving disclosures out of abstracts.

A small number of active authors can generate clustered submissions and inflate monthly totals.

If those authors continue producing short, keyword-disclosing papers, monthly counts will hold or rise.

If disclosure norms shift toward acknowledgments or omit explicit keywords, observable counts will fall sharply.

Major uncertainties are whether the recent cluster is transient or the beginning of steady adoption, and how quickly authors adjust disclosure practices.

Recorded totals are sensitive to submission timing and to revisions that change the “most recent” date window.

Consequently, observable counts will be driven more by disclosure behavior and author concentration than by smooth, field‑wide uptake.

Forecast (median): 10.83 papers

• Strong recent signal, especially May: The qualifying count jumps from roughly 3–4/month (around April) to about 12/month in May, and May is treated as the main anchor for what July might look like.
• A big share comes from a small cluster: A noticeable fraction of the May results are tied to the same research group “style” of mentioning GPT/ChatGPT in abstracts, so continuation vs. fading could swing the July count a lot.
• Ongoing adoption pressure, but unclear how broad it is: There are signs of wider interest and momentum, but the data so far suggests the phenomenon is still concentrated rather than evenly spread across the whole math community.
• Disclosure wording matters: Even if GPT/ChatGPT use is common, many papers won’t be counted unless it’s explicitly stated in the abstract as contributing to the mathematical result.
• Seasonality nudges downward: July is expected to have somewhat fewer submissions than May, offsetting some of the upward trend.