In the first three months of 2026, about 1 in every 435 papers in physics, chemistry, materials science, engineering and computer science cited at least one reference that appears not to exist, according to a Columbia University audit of 500,000 papers. That rate is 23.0 per 10,000 papers, up from about 1 in 1,600 in 2023. The team extrapolates that roughly 8,500 published papers in these fields carry at least one fabricated reference.
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Maxim Topaz of Columbia’s School of Nursing and Data Science Institute led the work, which appears in the Proceedings of the National Academy of Sciences. His summary of why it matters is short: “A reference is a promise to the reader that a source exists.”
An automated check of 21.6 million references
The audit drew on papers published between January 2023 and March 2026 from the OpenAlex database. An automated tool checked 21.6 million references that carried a DOI, and flagged 1,135 whose cited titles could not be found in online databases. Those references sat in 619 papers, according to the Columbia release on the study, which is also indexed under the paper’s PNAS DOI.
A machine flag is not proof, so two independent experts reviewed a random sample of 400 flagged references. They confirmed that 85.8% were fabricated. The team’s 8,500 figure applies each field’s rate to roughly 7 million papers published in the same fields over the same period, so it is an estimate rather than a count. The 85.8% confirmation rate also means roughly one flagged reference in seven in that sample was not confirmed as fabricated, and the audit only examined references that carried a DOI, so papers citing sources without one were outside its reach.
Physics at 25.6 per 10,000, chemistry at 4.3
The rate is far from uniform. Per 10,000 papers, the study found 25.6 in physics, 18.4 in materials science, 11.1 in computer science and artificial intelligence, 10.3 in engineering and 4.3 in chemistry. Across all fields, the share of affected papers rose from 6.3 per 10,000 in 2023 to 15.4 in 2025 and 23.0 in the first quarter of 2026.
Most affected papers contained only one or two bad references. A small group did not. Twenty-seven papers had five or more fabricated references, and together they accounted for more than a third of all the fabricated references the audit found.
Topaz drew a line between those cases. “A paper with one unverifiable reference and a paper with five or more are not the same thing,” he said, arguing that editors should not treat them identically.
Correction has barely begun. When the audit was run, two of the 619 affected papers had been retracted.
Medicine was the first audit, and the numbers there are higher
The same team has been tracking the problem in medicine. A May research letter in The Lancet, described on the Columbia nursing school’s site, found 4,046 fabricated citations across 2,810 of 2.5 million biomedical papers. It reported that the medical rate climbed from about 4 per 10,000 papers in 2023 to about 57 per 10,000 by early 2026, and that 98.4% of the affected papers had received no publisher action. Coverage of that audit appeared from the University of Eastern Finland, where co-author Laura-Maria Peltonen works, and from HealthDay.
Two other pieces of the team’s work, described in the release, point the same way. A July paper in the Journal of Internal Medicine found fabricated references about twice as common in medRxiv preprints as in peer-reviewed articles, at 37.2 versus 16.4 per 10,000. A September arXiv preprint, not yet peer reviewed, found that 26 large language models fabricated 55% of the medical references they were asked to supply, a result that points to one plausible source of invented citations.
The new study asks whether medicine is special. Topaz’s answer in the release is a flat “It is not.” The authors recommend routine automated reference checks at submission, retroactive screening of the published literature, and a separate category in indexing services and integrity databases for fabricated references, distinct from plagiarism or data falsification.
Topaz is optimistic about one point: “The encouraging part is that this is one of the few integrity problems that can be checked automatically.” The team is now screening up to 12 million medical papers published since 2020, with experts grading how much several hundred fabricated references affect the papers that cite them. That work is funded by a $249,999 award from the Department of Health and Human Services, and its first results will show how many of the missing sources were ever load-bearing.
This article was produced with the assistance of AI and reviewed by Morning Overview editors prior to publication.
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