A continuously maintained, source-linked index of notable claimed and confirmed advances in mathematics and science. Mathematics receives the deepest coverage, with explicit labels for peer review, formal verification, early evidence, disputes and corrections.
Coverage promise: This tracker aims for broad, systematic coverage; it is not a claim of literal completeness. Reporting delays and omissions are possible. A posted manuscript establishes that a result has been claimed, not that the field has accepted it.
New and updated this week
Four records were added and five received material evidence, source or publication updates. All other provisional, disputed, claimed-proof and preprint-only records were rechecked without an evidence-supported status change.
- The Jacobian conjecture is false in dimension 3Announced; exact object independently checked · Mathematics
- Hilbert's tenth problem for rings of integers of number fieldsOne proof published; independent proof forthcoming · Mathematics
- The Friedlander–Iwaniec Gaussian-primes conjectureAccepted by Acta Mathematica; final publication pending · Mathematics
- A claimed proof of Godbersen's mixed-volume conjecturePreprint-only claimed proof; review pending · Mathematics
- Claimed counterexamples to the Duval–Reiner majorization conjecturePreprint counterexamples; verification pending · Mathematics
- A counterexample to Thakur's conjecture on Carlitz–Wieferich primesPreprint counterexample; reported independent check · Mathematics
- Separating QMA from QCMA with a classical oracleVerified/published conference result · Computer Science
- A planetary-mass exosatellite candidate around CD-35 2722 BPeer-reviewed candidate; confirmation pending · Astronomy
- Gene-edited donor islet cells survived and secreted insulin without immunosuppression for 14 months in one patientFirst-in-human proof of concept · Medicine
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19 tracked records
Mathematics breakthroughs
The Jacobian conjecture is false in dimension 3
Evidence tier 1
Peer reviewed: No
AI role: Yes
An explicit polynomial map from C³ to C³ has constant Jacobian determinant −2 but is not injective. The example disproves the unrestricted Jacobian conjecture in dimension 3.
- Problem or result
- Jacobian conjecture
- Authors
- Levent Alpöge; example credited to Claude Fable after a question from Akhil Mathew
- Institutions
- Affiliation not stated in the inspected announcement
- Result date
- Announced July 19, 2026
Why it matters: The conjecture had been open since 1939 and is a central problem in affine algebraic geometry.
Limits: The two-dimensional conjecture remains open. The exact determinant and collision have been checked independently, but no conventional paper or refereed publication by the announcer was located.
Sources and record details
- Primary Levent Alpöge’s original announcement and explicit map
- Independent T. Shaska, Graded Keller maps and the Jacobian Conjecture
- Independent Terence Tao, A digestion of the Jacobian conjecture counterexample
- Independent Wolfram MathWorld, Jacobian Conjecture
- Independent Oliver Knill, exact Mathematica verification
- Independent Independent symbolic check and explainer
- Independent Christopher D. Long, Small Counterexamples to the Gaussian Moments Conjecture
AI involvement: Claude Fable reportedly found the example; humans posed the question, checked the algebra and announced the result.
Change history
- — Added as an announced, directly checkable counterexample with conventional peer review still pending.
- — Added a new independent scholarly preprint analyzing the grading of the announced counterexample; this does not change the entry's peer-review status.
A formally verified proof package for the Cycle Double Cover Conjecture
Evidence tier 1
Peer reviewed: No
AI role: Yes
The proof package establishes that every finite loopless bridgeless undirected multigraph has a multiset of cycles covering every edge exactly twice. A Lean formalization and two independent specialist expositions are public.
- Problem or result
- Cycle Double Cover Conjecture
- Authors
- OpenAI proof system; independent expositions by Jim Geelen and Sang-il Oum
- Institutions
- OpenAI; University of Waterloo; Institute for Basic Science
- Result date
- Announced July 9–10, 2026; expert expositions July 16–17, 2026
Why it matters: The Szekeres–Seymour conjecture is a foundational, decades-old problem in graph theory and a prominent test of AI-generated research mathematics.
Limits: No peer-reviewed journal publication was located. Formal verification checks the encoded theorem and proof, while specialists must still assess exact correspondence with the accepted conjecture and the surrounding mathematical exposition.
Sources and record details
- Primary OpenAI proof PDF
- Primary Original problem prompt
- Primary Lean formalization repository
- Independent Jim Geelen, OpenAI's proof of the Cycle Double Cover Theorem
- Independent Sang-il Oum, An exposition of OpenAI's proof
- Independent IBS seminar by Sang-il Oum
- Independent Wolfram MathWorld status summary
AI involvement: The originating package credits GPT-5.6 Sol Ultra for proof generation and Codex for assistance with the write-up.
Change history
Added on 2026-07-22 with formal-verification and independent-exposition signals, while retaining a non-peer-reviewed status.
Correlated two-sided Gaussian tests can defeat the Benjamini–Hochberg guarantee
Evidence tier 1
Peer reviewed: No
AI role: Yes
An explicit correlated Gaussian factor model, backed by an interval-arithmetic certificate, has asymptotic false discovery rate above 0.0104 when Benjamini–Hochberg is run at nominal level 0.01. A follow-on paper extends the negative result.
- Problem or result
- False-discovery-rate control for Benjamini–Hochberg under unrestricted Gaussian correlation
- Authors
- Edgar Dobriban
- Institutions
- University of Pennsylvania
- Result date
- Preprint submitted July 13, 2026
Why it matters: The result closes a precise theoretical question about one of the most widely used multiple-testing procedures.
Limits: It does not invalidate Benjamini–Hochberg under independence or accepted positive-dependence conditions. The counterexample uses a special unrestricted dependence setting, and its exhibited excess is small.
Sources and record details
- Primary Edgar Dobriban, The Benjamini–Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests
- Independent Lihua Lei, No Universal Multiplicative FDR Bound for the BH Procedure
- Independent Independent technical explainer with scope caveats
AI involvement: The paper states that GPT-5.6 Pro produced the proof and that Dobriban carefully checked it.
Change history
Added on 2026-07-22 with the dependence assumptions and small numerical excess made explicit to prevent overstatement.
A near-quadratic lower bound in derivative-free convex optimization
Evidence tier 1
Peer reviewed: No
AI role: Yes
The paper proves an Ω(d²/log(d+1)) lower bound for a specified deterministic exact-value-oracle problem at accuracy on the order of d⁻¹ᐟ². This nearly matches the known upper bound up to polylogarithmic factors.
- Problem or result
- Oracle-complexity gap for deterministic derivative-free convex optimization
- Authors
- Phillip Kerger
- Institutions
- Affiliation not stated on the inspected arXiv record
- Result date
- Preprint submitted July 14, 2026
Why it matters: It sharply narrows a complexity gap dating to the 1990s and limits what derivative-free methods can achieve in the stated oracle model.
Limits: The theorem concerns a specific deterministic oracle model and accuracy regime. Lean verification supports deductive correctness, but independent specialists still need to assess statement correspondence, novelty and the surrounding literature.
Sources and record details
- Primary Phillip Kerger, Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization
- Primary Author disclosure and discussion
- Independent Cautious secondary explainer
AI involvement: Kerger reports that GPT-5.6 Sol Pro generated the main argument, which he checked and formalized in Lean.
Change history
Added on 2026-07-22 as a formally checked but very recent preprint whose novelty and scope still need specialist review.
Erdős Problem #90: the planar unit-distance conjecture is false
Evidence tier 1
Peer reviewed: No
AI role: Yes
Arbitrarily large planar point sets can determine at least n^(1+c) unit-distance pairs for an absolute c greater than zero, contradicting the proposed n^(1+o(1)) growth. A companion paper gives an explicit exponent greater than 1.014.
- Problem or result
- Erdős Problem #90, the planar unit-distance conjecture
- Authors
- Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang and Melanie Matchett Wood
- Institutions
- Multi-institution collaboration
- Result date
- Announced and submitted May 20, 2026
Why it matters: The disproved near-linear-growth conjecture had guided the unit-distance problem for decades.
Limits: The extremal unit-distance problem remains open. A large gap persists between the new lower bound and the classical O(n^(4/3)) upper bound.
Sources and record details
- Primary OpenAI research announcement
- Primary Original proof PDF
- Primary Alon et al., Remarks on the disproof of the unit distance conjecture
- Primary Will Sawin, An explicit lower bound for the unit distance problem
- Independent Erdős Problems #90
- Independent Nature news coverage
AI involvement: An OpenAI model generated the construction and proof; a group of mathematicians produced a shorter human-verified account.
Change history
Added on 2026-07-22 as a human-verified disproof while preserving that the broader extremal problem remains unsolved.
Erdős Problems #1196 and #1217: primitive sets and divisibility chains
Evidence tier 1
Peer reviewed: No
AI role: Yes
The authors resolve 1966 Erdős–Sárközy–Szemerédi conjectures concerning dense primitive subsets of sufficiently large integers and long divisibility chains. They develop a Markov-chain and von Mangoldt framework for the proofs.
- Problem or result
- Erdős Problems #1196 and #1217
- Authors
- Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang and Terence Tao
- Institutions
- Multi-institution collaboration
- Result date
- Preprint submitted May 1, 2026
Why it matters: The work settles two named Erdős problems and introduces machinery that may apply beyond them.
Limits: The paper also gives a short proof related to the already resolved Erdős primitive-set conjecture #164. That result must not be presented as a third newly solved problem.
Sources and record details
- Primary Alexeev et al., Primitive sets and von Mangoldt chains
- Primary Terence Tao's technical discussion
AI involvement: The paper credits GPT-5.4 Pro with suggesting the Markov-chain idea; the human authors developed and checked the proofs.
Change history
Added on 2026-07-22 with #1196 and #1217 separated from the paper's alternate treatment of already resolved #164.
Erdős Problem #728: a Lean-formalized resolution of the reconstructed intended statement
Evidence tier 1
Peer reviewed: No
AI role: Yes
The proof establishes an infinite family of middle-range factorial-divisibility triples whose logarithmic gap lies between any prescribed positive constant multiples of log n. A Lean proof is translated into conventional mathematical prose.
- Problem or result
- Erdős Problem #728
- Authors
- Nat Sothanaphan; GPT-5.2 Pro and Aristotle operated by Kevin Barreto
- Institutions
- Harmonic for Aristotle; see the paper for author affiliation
- Result date
- Submitted January 12, 2026; revised through January 26, 2026
Why it matters: The authors describe it as the first problem in the Erdős Problems database regarded as fully resolved autonomously by an AI system.
Limits: The historical wording of #728 was ambiguous, so the project formalized a reconstructed intended statement. Related older literature also complicates an unqualified novelty claim.
Sources and record details
- Primary Nat Sothanaphan, Resolution of Erdős Problem #728
- Independent Erdős Problems project blog
- Independent Problem #728 discussion and formulation notes
AI involvement: GPT-5.2 Pro and Harmonic's Aristotle performed the formal proof search, with Kevin Barreto operating the system and Sothanaphan writing the exposition.
Change history
Added on 2026-07-22 with an explicit formulation and prior-literature warning rather than an unqualified autonomous-solution claim.
Near-diagonal Ramsey lower bounds improve exponentially
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
For every fixed C greater than 1, the authors improve the exponential base in the classical Erdős lower bound for r(ℓ,Cℓ). This is the first exponential improvement over the 1947 bound in that near-diagonal regime.
- Problem or result
- Classical lower bounds for near-diagonal Ramsey numbers
- Authors
- Jie Ma, Wujie Shen and Shengjie Xie
- Institutions
- University of Science and Technology of China; Tsinghua University
- Result date
- Submitted July 17, 2025; revised April 26, 2026
Why it matters: The work breaks decades of stasis and introduces a geometric random-coloring method that has already produced follow-on results.
Limits: The numerical improvement can be extremely small and does not determine Ramsey numbers. It does not improve the equal-size diagonal case C=1.
Sources and record details
- Primary Ma, Shen and Xie, An exponential improvement for Ramsey lower bounds
- Independent Quanta, After 80 Years, Mathematicians Give Famed 'Erdős Method' an Upgrade
- Independent Follow-on paper, Gaussian random graphs and Ramsey numbers
AI involvement: No generative-AI role was disclosed.
Change history
Added on 2026-07-22 as a major bound improvement, not as a solved Ramsey-number problem.
The Kakeya set conjecture in three dimensions
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
Every Kakeya set in R³, meaning a set containing a unit line segment in every direction, has both Hausdorff and Minkowski dimension 3.
- Problem or result
- Three-dimensional Kakeya set conjecture
- Authors
- Hong Wang and Joshua Zahl
- Institutions
- NYU Courant and University of British Columbia at announcement
- Result date
- Preprint submitted February 24, 2025
Why it matters: The theorem resolves the three-dimensional case of a central problem linking harmonic analysis, geometric measure theory, partial differential equations and number theory.
Limits: Higher-dimensional cases remain open. No peer-reviewed publication was located for the long and technically demanding preprint.
Sources and record details
- Primary Hong Wang and Joshua Zahl, Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions
- Independent Quanta, Once-in-a-Century Proof Settles Math's Kakeya Conjecture
AI involvement: No generative-AI role was disclosed.
Change history
Added on 2026-07-22 with the result confined to three dimensions and higher dimensions explicitly left open.
Hilbert's tenth problem for rings of integers of number fields
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
Two independent teams prove that no algorithm can always decide whether an arbitrary polynomial equation has a solution in the ring of integers of a given number field.
- Problem or result
- Hilbert's tenth problem over rings of integers of number fields
- Authors
- Peter Koymans and Carlo Pagano; independently Levent Alpöge, Manjul Bhargava, Wei Ho and Ari Shnidman
- Institutions
- Utrecht University and Concordia University for the first team; see the second manuscript for its exact affiliations
- Result date
- One proof published online December 1, 2025, in a March 2026 volume; independent proof forthcoming in JAMS
Why it matters: The work extends the negative solution of Hilbert's tenth problem from ordinary integers to the rings of integers of all number fields.
Limits: The quantified domain is rings of integers of number fields. It should not be broadened casually to every ring described as involving algebraic integers.
Sources and record details
- Primary Koymans and Pagano, Hilbert's tenth problem via additive combinatorics
- Primary Alpöge, Bhargava, Ho and Shnidman, Rank stability in quadratic extensions and Hilbert's tenth problem
- Primary Published Inventiones Mathematicae article
- Independent Quanta, New Proofs Probe the Limits of Mathematical Truth
- Independent Princeton publication record
- Independent Peter Koymans publication list
- Independent Carlo Pagano publication list
AI involvement: No generative-AI role was disclosed.
Change history
- — Added as two independent proof routes with the ring-of-integers domain stated precisely.
- — Corrected the review status: the Alpöge–Bhargava–Ho–Shnidman proof is published in Inventiones Mathematicae, and both authors list the independent Koymans–Pagano proof as forthcoming in JAMS.
Erdős's large sum-free subset conjecture
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
Every n-element set of integers contains a sum-free subset of size at least n/3 + c log log n for an absolute positive c. The guaranteed excess over n/3 therefore tends to infinity.
- Problem or result
- Erdős's 1965 large sum-free subset conjecture
- Authors
- Benjamin Bedert
- Institutions
- University of Oxford at the time of the work
- Result date
- Preprint submitted February 12, 2025
Why it matters: The result settles a simple-to-state, 60-year-old problem connecting additive combinatorics and harmonic analysis.
Limits: The theorem proves an unbounded improvement of the stated order. It does not determine the optimal excess term.
Sources and record details
- Primary Benjamin Bedert, Large sum-free subsets of sets of integers
- Independent Quanta, Graduate Student Solves Classic Problem About the Limits of Addition
AI involvement: No generative-AI role was disclosed.
Change history
Added on 2026-07-22 with the unbounded-excess theorem distinguished from determination of the optimal term.
The bunkbed conjecture is false
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The authors construct an explicit finite planar graph with 7,222 vertices that violates the bunkbed percolation inequality.
- Problem or result
- Bunkbed conjecture in percolation
- Authors
- Nikita Gladkov, Igor Pak and Aleksandr Zimin
- Institutions
- University of California, Los Angeles and Massachusetts Institute of Technology at publication
- Result date
- Preprint October 3, 2024; published June 13, 2025
Why it matters: The peer-reviewed counterexample overturns an intuitively compelling conjecture studied for roughly four decades.
Limits: The disproof does not show that every bunkbed-type inequality fails. Restricted graph classes and related variants may remain true.
Sources and record details
- Primary Gladkov, Pak and Zimin, The bunkbed conjecture is false
- Primary Peer-reviewed PNAS article
- Independent Quanta, Math's 'Bunkbed Conjecture' Has Been Debunked
AI involvement: No generative-AI role was disclosed; computation and search aided discovery, while the final proof is mathematical.
Change history
Added on 2026-07-22 as the only peer-reviewed published disproof in the initial 16-card mathematics set.
A counterexample to the Mizohata–Takeuchi conjecture
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
The paper constructs counterexamples for hypersurfaces not contained in a hyperplane, disproving the Mizohata–Takeuchi conjecture in its stated generality and the related formulation of Stein's conjecture discussed in the paper.
- Problem or result
- Mizohata–Takeuchi conjecture
- Authors
- Hannah Mira Cairo
- Institutions
- Work developed while studying mathematics at UC Berkeley
- Result date
- Preprint submitted February 10, 2025
Why it matters: The result changes which weighted estimates researchers can plausibly pursue in Fourier restriction theory.
Limits: Stronger or more restricted replacement statements may survive. The counterexample should not be described as ending the wider restriction-theory research program.
Sources and record details
- Primary Hannah Mira Cairo, A Counterexample to the Mizohata–Takeuchi Conjecture
- Independent Quanta profile and expert context
AI involvement: No generative-AI role was disclosed.
Change history
Added on 2026-07-22 as a counterexample to the conjecture as stated, with restricted successor statements left open.
The Friedlander–Iwaniec Gaussian-primes conjecture
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
For each n congruent to 0 or 4 modulo 6, the authors obtain an asymptotic count of primes of the form p² + nq² with p and q prime. The case n=4 settles the Friedlander–Iwaniec Gaussian-primes conjecture.
- Problem or result
- Friedlander–Iwaniec Gaussian-primes conjecture
- Authors
- Ben Green and Mehtaab Sawhney
- Institutions
- University of Oxford and Columbia University at announcement
- Result date
- Preprint submitted October 5, 2024; accepted July 22, 2025
Why it matters: The proof overcomes a long-standing parity barrier for simultaneous prime-variable constraints in sieve theory.
Limits: The theorem applies to specified congruence classes of n. It is not a complete classification of all quadratic forms that take prime values. Version three corrected a partial-summation error in Section 8.3 and a minor inaccuracy in Section 8.7. Acta Mathematica lists the paper as accepted and awaiting publication; no final issue or DOI was located.
Sources and record details
- Primary Acta Mathematica, accepted papers awaiting publication
- Primary Ben Green and Mehtaab Sawhney, Primes of the form p²+nq²
- Independent Quanta, Mathematicians Uncover a New Way to Count Prime Numbers
- Independent Mehtaab Sawhney publication list
AI involvement: No generative-AI role was disclosed.
Change history
- — Added with the n modulo 6 restriction and the special n=4 conjecture case stated explicitly.
- — Corrected the review status after the journal's accepted-paper list and the author's publication list showed that the paper was accepted by Acta Mathematica on July 22, 2025; final publication is still pending. Also disclosed the partial-summation error and minor inaccuracy corrected in arXiv version three.
Modularity theorems for a positive proportion of abelian surfaces
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
Under specified local, image and ordinary or distinguished hypotheses, the paper proves modularity for a positive proportion of abelian surfaces over the rational numbers.
- Problem or result
- Modularity of abelian surfaces over the rational numbers
- Authors
- George Boxer, Frank Calegari, Toby Gee and Vincent Pilloni
- Institutions
- Imperial College London, University of Chicago and CNRS/Université Paris-Saclay affiliations are represented
- Result date
- Preprint submitted February 28, 2025
Why it matters: The work extends modularity machinery central to the proof of Fermat's Last Theorem from elliptic curves toward two-dimensional abelian varieties.
Limits: This is not a theorem that every abelian surface over the rational numbers is modular. The positive-proportion and hypothesis restrictions are essential.
Sources and record details
- Primary Boxer, Calegari, Gee and Pilloni, Modularity theorems for abelian surfaces
- Independent Quanta, The Core of Fermat's Last Theorem Just Got Superpowered
AI involvement: No generative-AI role was disclosed.
Change history
Added on 2026-07-22 with positive-proportion and technical hypotheses preserved against broader headline claims.
The moving sofa problem: a claimed optimality proof
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
The paper claims that Gerver's 18-section shape has the largest possible area, approximately 2.2195, among planar sofas that can move around a right-angled unit-width hallway corner.
- Problem or result
- Moving sofa problem
- Authors
- Jineon Baek
- Institutions
- Yonsei University at announcement
- Result date
- Preprint submitted November 29, 2024
Why it matters: If accepted, the proof resolves a famous geometric optimization problem posed in 1966.
Limits: No journal publication was located, and arXiv still showed the original version at the last check. The result should remain labeled as a claimed proof while the long, technical argument is reviewed.
Sources and record details
- Primary Jineon Baek, Optimality of Gerver's Sofa
- Independent Quanta, The Largest Sofa You Can Move Around a Corner
AI involvement: No generative-AI role was disclosed.
Change history
Added on 2026-07-22 as a provisional claimed proof rather than a confirmed solution.
A claimed proof of Godbersen's mixed-volume conjecture
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
The authors claim the sharp Godbersen bound for the mixed volume of a convex body and its reflection, confirming the conjectured simplex value. They also prove an Lp Rogers–Shephard inequality and classify the equality cases among convex polytopes.
- Problem or result
- Godbersen's 1938 conjecture on mixed volumes of a convex body and its reflection
- Authors
- Jan Kotrbatý and Mohamed A. Mouamine
- Institutions
- Mathematical Institute of Charles University
- Result date
- Preprint submitted July 22, 2026
Why it matters: The conjecture has stood since 1938 and sits inside the Brunn–Minkowski theory of convex bodies and mixed volumes.
Limits: This is a same-day version-one preprint. No independent specialist assessment, journal acceptance or formal verification was located. The paper's uniqueness statement is for convex polytopes; it does not claim a full equality-case classification for every convex body.
Sources and record details
AI involvement: No substantive AI role was disclosed in the inspected manuscript.
Change history
- — Added as a version-one preprint claim pending independent specialist review.
Claimed counterexamples to the Duval–Reiner majorization conjecture
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
Huang reports strict counterexamples to the majorization assertion for every index r at least 5 in some uniformity and for every uniformity q at least 3 at some index. The paper separately proves the universal second partial-sum inequality and classifies its equality cases.
- Problem or result
- Duval–Reiner majorization assertion for simplicial up-Laplacian spectra
- Authors
- Jing Huang
- Institutions
- Guangzhou University
- Result date
- Preprint submitted July 22, 2026
Why it matters: The result would delimit how far graph Laplacian majorization extends to higher-dimensional uniform simplicial families.
Limits: The counterexamples appear in a same-day version-one preprint. No independent recomputation, specialist assessment or journal review was located by the maintenance cutoff.
Sources and record details
- Primary Jing Huang, The Duval–Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality
- Independent Earlier partial result on the second partial-sum case
AI involvement: No substantive AI role was disclosed in the inspected manuscript.
Change history
- — Added as a version-one preprint disproof claim pending independent verification.
A counterexample to Thakur's conjecture on Carlitz–Wieferich primes
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
The paper gives an explicit degree-five Carlitz–Wieferich prime over the field with 19 cubed elements. Because 19 does not divide five, the example contradicts the conjectured degree-divisibility condition.
- Problem or result
- Thakur's conjectural degree-divisibility condition for Carlitz–Wieferich primes in odd characteristic
- Authors
- David Niedbala Giraudin
- Institutions
- Independent researcher, Meaux, France
- Result date
- Version 2 submitted July 22, 2026
Why it matters: It overturns a conjectural pattern in function-field arithmetic that had survived earlier proofs in small degrees and extensive computations.
Limits: Version 2 corrected an unrelated exactness theorem to a conjecture. The counterexample remains in the manuscript, and the author reports an independent Magma check by Dinesh Thakur, but no separate verification artifact or journal review was located.
Sources and record details
AI involvement: No substantive AI role was disclosed in the inspected manuscript.
Change history
- — Added from version 2. The entry discloses that former Theorem 4.2 was corrected from an exactness statement to a conjecture; the counterexample itself remains.
4 tracked records
Computer science breakthroughs
Separating QMA from QCMA with a classical oracle
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The authors constructed a classical-oracle setting in which QMA, the class with quantum witnesses, is strictly larger than QCMA, whose witnesses are classical. The proof uses a decision problem called spectral Forrelation.
- Problem or result
- Whether quantum proofs can be strictly more powerful than classical proofs checked by a quantum verifier
- Authors
- John Bostanci, Jonas Haferkamp, Chinmay Nirkhe and Mark Zhandry
- Institutions
- Columbia, Saarland/Harvard, University of Washington, Stanford and NTT Research
- Result date
- November 12, 2025; published at STOC 2026 on June 9, 2026
Why it matters: It supplies the oracle separation quantum-complexity researchers had sought for roughly two decades and introduces techniques that may be useful beyond this problem.
Limits: This is a relativized oracle separation, not an unconditional proof that QMA differs from QCMA in the ordinary unrelativized setting. It is not a demonstrated hardware advantage.
Sources and record details
- Primary Final ACM STOC 2026 proceedings record
- Primary Primary paper on arXiv
- Primary Author publication record confirming STOC 2026 Best Paper
- Independent Quanta Magazine explanation
- Independent Ruhr University report on the STOC Best Paper Award
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
July 22, 2026 — Added the final ACM STOC 2026 proceedings record and changed “accepted” to “published.” The theorem statement and verification status are unchanged.
Simulating Time With Square-Root Space
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
Williams proved that every multitape Turing-machine computation running in time t can be simulated in O(sqrt(t log t)) space. This substantially improves the previous O(t/log t) universal bound.
- Problem or result
- The general relationship between computation time and memory, including the 50-year-old Hopcroft–Paul–Valiant simulation bound
- Authors
- R. Ryan Williams
- Institutions
- Massachusetts Institute of Technology
- Result date
- February 25, 2025; published at STOC 2025
Why it matters: The theorem is the first major improvement in half a century on a foundational time-versus-space simulation.
Limits: It does not prove P is different from PSPACE. Its formal scope is multitape Turing machines and related models, not immediate memory savings for production software.
Sources and record details
- Primary Final ACM STOC 2025 proceedings record
- Primary Primary paper on arXiv
- Independent Quanta Magazine explanation
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
July 22, 2026 — Added the ACM STOC 2025 version of record; result and status unchanged.
Breaking the Sorting Barrier for Directed Single-Source Shortest Paths
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The authors gave a deterministic O(m log^(2/3) n)-time algorithm for directed single-source shortest paths in the comparison-addition model. It is the first to beat Dijkstra's O(m + n log n) bound on sparse directed graphs in that model.
- Problem or result
- Single-source shortest paths in directed graphs with non-negative real edge weights
- Authors
- Ran Duan, Jiayi Mao, Xiao Mao, Xinkai Shu and Longhui Yin
- Institutions
- Tsinghua University, Stanford University and Max Planck Institute for Informatics
- Result date
- April 23, 2025; published at STOC 2025
Why it matters: The result shows that the sorting-like overhead in Dijkstra's method is not an unavoidable barrier for this foundational graph problem.
Limits: The improvement is asymptotic and model-specific to non-negative real weights in the comparison-addition model. It does not establish faster performance on current routing workloads or small-integer-weight graphs.
Sources and record details
- Primary Open proceedings record
- Primary Primary preprint on arXiv
- Independent Quanta Magazine explanation
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry.
Optimal Bounds for Open Addressing Without Reordering
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The authors constructed open-addressed hash tables with better-than-expected search bounds, disproving the central conjecture in Andrew Yao's “Uniform Hashing Is Optimal.” They also proved matching lower bounds for the models studied.
- Problem or result
- Expected search and insertion costs in open-addressed hash tables without reordering
- Authors
- Martín Farach-Colton, Andrew Krapivin and William Kuszmaul
- Institutions
- New York University, University of Cambridge and Carnegie Mellon University
- Result date
- FOCS 2024; arXiv version January 4, 2025
Why it matters: The paper replaces a presumed 40-year-old barrier for one of computer science's most basic data structures with optimal bounds.
Limits: The result concerns a defined open-addressing model without reordering. It does not show that every real-world hash-table implementation should be replaced, and immediate engineering performance was not demonstrated.
Sources and record details
- Primary Primary paper on arXiv
- Primary IEEE FOCS 2024 proceedings record
- Independent Quanta Magazine explanation
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry.
5 tracked records
Physics breakthroughs
Hybrid calculation of hadronic vacuum polarization in muon g − 2 to 0.48%
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
A hybrid lattice-QCD and experimental calculation determined the leading hadronic-vacuum-polarization contribution to 0.48% precision. With other Standard Model terms included, the prediction differs from the final experimental value by only 0.5 standard deviations.
- Problem or result
- The discrepancy between measured and predicted values of the muon's anomalous magnetic moment
- Authors
- A. Boccaletti, Sz. Borsanyi, A. Cotellucci, M. Davier, Z. Fodor and collaborators
- Institutions
- University of Wuppertal, Forschungszentrum Jülich, Université Paris-Saclay/CNRS, Aix-Marseille University/CNRS and partners
- Result date
- April 22, 2026
Why it matters: The calculation strongly weakens the former interpretation of muon g − 2 as evidence for undiscovered particles.
Limits: It does not remove every theory-level disagreement: tensions remain among some electron–positron datasets and between certain dispersive and lattice determinations. The careful conclusion is that the former anomaly is largely reconciled under the updated lattice-led prediction.
Sources and record details
- Primary Hybrid theory calculation in Nature
- Independent Muon g − 2 experimental measurement in Physical Review Letters
- Independent Forschungszentrum Jülich technical context
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry; the 2026 theory result materially changed the interpretation of the June 2025 experimental precision update.
Direct observation of the Migdal effect induced by neutron bombardment
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
A purpose-built detector recorded six correlated nuclear-recoil and electron-track candidates among almost one million events, producing a reported significance above 5σ. The measured cross-section ratio agrees within uncertainty with theory.
- Problem or result
- Direct laboratory validation of the Migdal effect in neutral-particle collisions
- Authors
- Difan Yi, Qian Liu, Shi Chen and collaborators
- Institutions
- University of Chinese Academy of Sciences, Guangxi University, Central China Normal University, Lanzhou University and partners
- Result date
- January 14, 2026
Why it matters: The observation supplies an empirical anchor for light-dark-matter searches that use the Migdal effect to extend their sensitivity.
Limits: This was a controlled neutron–nucleus experiment, not a dark-matter detection. The signal rests on six candidate events, so replication in other target materials and recoil regimes remains important.
Sources and record details
- Primary Primary paper in Nature
- Independent Nature Physics specialist commentary
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry.
Observation of charge–parity symmetry breaking in baryon decays
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
LHCb measured significant asymmetries between a beauty baryon's decay rate and that of its antibaryon. This is the first observation of CP violation in baryon decay.
- Problem or result
- Whether CP violation, previously observed in mesons, can be observed in baryon decays
- Authors
- LHCb Collaboration
- Institutions
- International LHCb collaboration at CERN
- Result date
- March 25, 2025; published July 16, 2025
Why it matters: The result opens a new class of matter–antimatter asymmetry measurements and a new test bed for the Standard Model.
Limits: CP violation is already part of the Standard Model, and this result alone does not explain the universe's matter excess. It is not by itself evidence for a new force or particle.
Sources and record details
- Primary LHCb paper in Nature
- Independent CERN result explanation
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry; preliminary reporting was followed by the peer-reviewed Nature publication.
Direct observation of coherent elastic antineutrino–nucleus scattering
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
CONUS+ inferred 395 ± 106 reactor-antineutrino signal events, consistent with the Standard Model expectation of 347 ± 59. The reported significance was 3.7σ.
- Problem or result
- Detecting coherent elastic neutrino–nucleus scattering with low-energy reactor antineutrinos
- Authors
- N. Ackermann, H. Bonet, A. Bonhomme, C. Buck and the CONUS Collaboration
- Institutions
- Max Planck Institute for Nuclear Physics and the Brokdorf and Leibstadt nuclear plants
- Result date
- Preprint April 1, 2025; published July 30, 2025
Why it matters: Reactor CEνNS enables compact neutrino detectors and a clean low-energy test of the Standard Model.
Limits: CEνNS was first observed by COHERENT in 2017 with higher-energy accelerator neutrinos; the novelty is the reactor-antineutrino signal in the fully coherent regime. Its 3.7σ strength is below the conventional 5σ particle-physics discovery threshold.
Sources and record details
- Primary CONUS+ paper in Nature
- Independent Max Planck Institute technical explanation
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry.
Observation of a B_c*+ meson with the ATLAS detector
Evidence tier 1
Peer reviewed: No
AI role: No disclosed role
ATLAS reported a new state above 8σ significance with a mass and mass gap matching expectations for the long-predicted B_c*+ meson. The collaboration submitted the result to Physical Review Letters.
- Problem or result
- Completing the lowest-lying spectrum of the meson made from a bottom antiquark and a charm quark
- Authors
- ATLAS Collaboration
- Institutions
- International ATLAS collaboration at CERN
- Result date
- May 15, 2026
Why it matters: The state fills a basic gap in the heavy-meson spectrum and tests calculations of how the strong force binds two different heavy quark flavours.
Limits: This is a new composite hadron, not a new elementary particle or evidence beyond the Standard Model. At the cutoff date it remained an official collaboration preprint submitted to a journal.
Sources and record details
- Primary ATLAS collaboration preprint
- Independent CERN result explanation
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
July 22, 2026 — Rechecked arXiv and INSPIRE. No refereed version or journal DOI was found; provisional/preprint-only status retained.
5 tracked records
Astronomy and astrophysics
Discovery of an Exterior Third Planet Orbiting β Pictoris
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
JWST spectroscopy revealed the carbon-monoxide fingerprint, position and motion of a third giant planet in the Beta Pictoris system. A separate VLT/JWST imaging team independently confirmed the object.
- Problem or result
- Finding planets hidden within the bright debris disk around the young star Beta Pictoris
- Authors
- Aidan Gibbs, Jean-Baptiste Ruffio, Alexis Bidot and collaborators
- Institutions
- University of California San Diego, Space Telescope Science Institute and partners
- Result date
- July 15, 2026
Why it matters: The discovery demonstrates a way to find planets amid bright circumstellar dust and creates only the second known system with at least three directly imaged planets.
Limits: The planet's mass, orbit, temperature and atmospheric abundances remain model dependent. It is a young giant planet, not an Earth analogue or a biosignature result.
Sources and record details
- Primary Discovery paper in The Astrophysical Journal Letters
- Independent NASA Webb mission explanation
- Independent ESO independent confirmation
AI involvement: No generative-AI research assistance was disclosed; standard data-processing and modelling software were used.
Change history
Initial entry; qualifies for New and updated this week.
Water D/H in 3I/ATLAS as a probe of formation conditions in another planetary system
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
ALMA constrained the water deuterium-to-hydrogen ratio in interstellar comet 3I/ATLAS to more than 6.6 × 10^-3. That lower bound is over 40 times Earth's ocean value and over 30 times typical Solar System comet values.
- Problem or result
- Measuring an isotopic formation tracer in material from outside the Solar System
- Authors
- Luis E. Salazar Manzano, Teresa Paneque-Carreño, Martin A. Cordiner and collaborators
- Institutions
- University of Michigan, NASA Goddard, JPL/Caltech, UC Berkeley, Observatoire de Paris/CNRS, NRAO and partners
- Result date
- April 23, 2026
Why it matters: The result provides a direct chemical constraint on planetary material formed around another star and points to unusually cold or weakly processed formation conditions.
Limits: The result is a lower bound derived from HDO detection and H2O non-detection, not a precise ratio. The birth-environment inference depends on chemical and excitation modelling and does not identify the comet's home star.
Sources and record details
- Primary Primary paper in Nature Astronomy
- Independent Le Monde specialist reporting
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry.
Observation of an ultra-high-energy cosmic neutrino with KM3NeT
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
KM3NeT detected KM3-230213A, a through-going muon event consistent with a cosmic neutrino whose estimated energy is about 220 PeV. It is the highest-energy cosmic neutrino observed to date.
- Problem or result
- Extending neutrino observations into the ultra-high-energy regime and identifying their cosmic sources
- Authors
- KM3NeT Collaboration
- Institutions
- International KM3NeT collaboration
- Result date
- Observed February 13, 2023; published February 12, 2025
Why it matters: The event opens an observational window in which cosmogenic neutrinos and extreme cosmic accelerators may become distinguishable.
Limits: This is one event, its source has not been identified and origin scenarios remain speculative. A March 2025 author correction fixed a surname only and did not alter the scientific result.
Sources and record details
- Primary KM3NeT paper in Nature
- Primary Nature author correction
- Independent Le Monde specialist reporting
AI involvement: No AI assistance was disclosed in the paper or linked reporting.
Change history
Initial entry; the non-substantive author-name correction is recorded explicitly.
GW231123: a Binary Black Hole Merger with Total Mass 190–265 M⊙
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The collaboration interpreted GW231123 as a black-hole merger with a total source-frame mass of 190–265 solar masses, the most massive such merger it had reported. Later peer-reviewed analyses found that component masses and spins depend strongly on waveform and possible signal-overlap assumptions.
- Problem or result
- Characterizing a short, high-mass gravitational-wave signal with strongly model-dependent source properties
- Authors
- LIGO Scientific, Virgo and KAGRA Collaborations
- Institutions
- International LIGO–Virgo–KAGRA network
- Result date
- Primary preprint July 10, 2025; interpretation updated May 26, 2026
Why it matters: A secure characterization would probe how very massive black holes form and grow through hierarchical mergers or other channels.
Limits: The detection is secure, but the event is extremely short and its exact source properties remain model dependent. A two-signal model is favoured in one likelihood comparison but has low prior probability and only modest background significance, while other studies attribute the discrepancies to waveform systematics.
Sources and record details
- Primary Peer-reviewed Astrophysical Journal Letters version of record
- Primary LIGO–Virgo–KAGRA primary analysis
- Independent Peer-reviewed overlapping-signal analysis
- Independent Peer-reviewed waveform-systematics analysis
- Independent LIGO Lab result context
AI involvement: No generative-AI assistance was disclosed for the primary merger claim; a separate lensing analysis used deep-learning inference.
Change history
July 22, 2026 — Added the peer-reviewed ApJ Letters version of record. A new formation-channel preprint was reviewed but does not alter the entry’s model-dependent interpretation caveat.
A planetary-mass exosatellite candidate around CD-35 2722 B
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
High-resolution radial-velocity monitoring with VLT/CRIRES+ found an approximately 170-day wobble in the young brown dwarf CD-35 2722 B. The preferred interpretation includes an orbiting companion with a minimum mass of about 0.9 Jupiter masses.
- Problem or result
- Detecting a natural satellite outside the Solar System
- Authors
- Kevin Hoy, Alice Zurlo, P. A. Peña R. et al.
- Institutions
- European Southern Observatory; Universidad Diego Portales; Millennium Nucleus on Young Exoplanets and their Moons; collaborating observatories
- Result date
- Published July 22, 2026
Why it matters: The result is strong peer-reviewed evidence for a planetary-mass satellite around an extrasolar substellar object and demonstrates a radial-velocity route to satellite systems beyond the Solar System.
Limits: The host is a brown dwarf orbiting a star, not a planet, so calling the object an exomoon is partly definitional. The satellite interpretation still needs independent or astrometric confirmation, and radial velocity supplies a minimum rather than a true mass.
Sources and record details
- Primary Nature, Planetary-mass exosatellite detected around the substellar companion of a star
- Primary Initial pre-peer-review manuscript
- Independent European Southern Observatory research summary
- Independent Physics World analysis
AI involvement: No substantive AI role was disclosed in the inspected paper or official research summary.
Change history
July 22, 2026 — Added from the final peer-reviewed Nature paper. Values follow the published article rather than the earlier preprint; the satellite interpretation remains provisional pending independent confirmation.
5 tracked records
Medicine and public health
A one-time in-vivo CRISPR treatment cut hereditary-angioedema attacks by 87% in a phase 3 trial
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
In the randomized phase 3 HAELO trial, 80 participants received one 50-mg intravenous dose of lonvoguran ziclumeran or placebo. From weeks 5 through 28, mean monthly attack rates were 0.26 versus 2.10, an estimated 87% relative reduction.
- Problem or result
- Hereditary angioedema causes unpredictable, potentially life-threatening swelling attacks and usually requires continuing preventive treatment.
- Authors
- Danny M. Cohn et al.; HAELO Investigators
- Institutions
- International HAELO clinical sites; Intellia Therapeutics
- Result date
- June 13, 2026
Why it matters: It is the first placebo-controlled phase 3 result to show a large clinical benefit from a single systemic CRISPR treatment that edits cells inside the body.
Limits: The treatment remains investigational, the rare-disease cohort was small, and median follow-up was about 7.5 months. Long-term durability, off-target editing, late adverse effects and permanent kallikrein-suppression risks remain unresolved; Intellia funded the study.
Sources and record details
- Primary NEJM primary paper
- Primary ClinicalTrials.gov HAELO record
AI involvement: No substantive AI role was reported.
Change history
- — Phase 3 results published online in the New England Journal of Medicine.
The first bespoke in-vivo base-editing medicine was designed and given to one infant
Evidence tier 2
Peer reviewed: Yes
AI role: No disclosed role
Researchers created a lipid-nanoparticle-delivered adenine base editor for one infant's pathogenic CPS1 variant. After two infusions, the child tolerated more dietary protein and required about half the baseline nitrogen-scavenger dose during the short observation reported in the paper.
- Problem or result
- Carbamoyl-phosphate synthetase 1 deficiency is an ultra-rare genetic disorder that can cause dangerous ammonia accumulation, brain injury and death.
- Authors
- Kiran Musunuru, Rebecca C. Ahrens-Nicklas et al.
- Institutions
- Children's Hospital of Philadelphia; University of Pennsylvania; Innovative Genomics Institute; Broad Institute and collaborators
- Result date
- May 15, 2025
Why it matters: The case proves that an n-of-1 programmable genetic medicine can be designed, manufactured, reviewed and delivered on a clinically meaningful timescale.
Limits: This was one infant with no control group and only seven weeks of reported post-treatment observation. The fraction of liver cells edited was not directly measured, so the result does not establish a cure, durable efficacy, scalability or long-term safety.
Sources and record details
- Primary NEJM primary case report
- Primary Open full text
- Independent Nature specialist reporting
AI involvement: No substantive AI role was reported.
Change history
- — Peer-reviewed n-of-1 treatment report published online.
The first gene therapy for OTOF-related genetic hearing loss won accelerated FDA approval
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The peer-reviewed CHORD report found that nine of 12 children met the week-24 auditory endpoint, six could hear soft speech without assistive devices and three reached average normal hearing sensitivity. The FDA later reviewed an ongoing single-arm study with 24 treated children, 20 of whom were efficacy-evaluable, and granted accelerated approval to Otarmeni after 80% of evaluable participants improved.
- Problem or result
- People with biallelic OTOF variants can have severe-to-profound congenital hearing loss because inner hair cells cannot transmit auditory signals normally.
- Authors
- Vassili Valayannopoulos et al.; CHORD Study Group
- Institutions
- Multicentre CHORD trial sites in North America and Europe; Regeneron Pharmaceuticals
- Result date
- April 23, 2026
Why it matters: Otarmeni is the first approved disease-modifying treatment for OTOF-related deafness and the first FDA-approved dual-AAV gene therapy.
Limits: Accelerated approval rests on a single-arm rare-disease trial and a hearing-sensitivity surrogate; continued approval may depend on durability and confirmation of speech-development and quality-of-life benefits. The indication is limited to molecularly confirmed biallelic OTOF variants with preserved outer hair-cell function and no prior implant in the treated ear.
Sources and record details
- Primary NEJM CHORD primary paper
- Primary FDA approval announcement
- Primary FDA product and review documents
- Independent International expert consensus on hereditary-hearing-loss gene therapy
AI involvement: No substantive AI role was reported.
Change history
- — CHORD results published online in the New England Journal of Medicine.
- — FDA granted accelerated approval to Otarmeni, formerly DB-OTO.
Twice-yearly lenacapavir prevented nearly all HIV infections in two phase 3 trials and became a WHO-recommended PrEP option
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
PURPOSE 1 recorded zero HIV infections among 2,134 participants assigned twice-yearly lenacapavir, compared with infections in both daily-oral-PrEP groups; PURPOSE 2 showed similarly high prevention efficacy in a broader gender population. The FDA approved injectable lenacapavir for prevention in June 2025, and WHO recommended it as an additional PrEP choice in July 2025.
- Problem or result
- Daily oral HIV pre-exposure prophylaxis is highly effective when taken consistently, but adherence and access barriers reduce its real-world impact.
- Authors
- Linda-Gail Bekker et al., PURPOSE 1 Study Team; Colleen F. Kelley et al., PURPOSE 2 Study Team
- Institutions
- Multicountry PURPOSE trial networks; Gilead Sciences
- Result date
- July 14, 2025
Why it matters: A six-month injection can remove much of the day-to-day adherence burden that limits oral PrEP.
Limits: Public-health impact depends on price, equitable access, clinic capacity and timely HIV testing. Injection-site reactions occur, infection during the long pharmacologic tail can select resistance, and both phase 3 trials were manufacturer-sponsored.
Sources and record details
- Primary PURPOSE 1 primary paper
- Primary PURPOSE 2 primary paper
- Primary WHO guideline
- Independent Nature specialist reporting on PURPOSE 1
AI involvement: No substantive AI role was reported.
Change history
- — PURPOSE 1 efficacy result reported.
- — PURPOSE 2 result published.
- — FDA approval reported by WHO.
- — WHO recommended twice-yearly injectable lenacapavir as an additional PrEP choice.
Gene-edited donor islet cells survived and secreted insulin without immunosuppression for 14 months in one patient
Evidence tier 2
Peer reviewed: Yes
AI role: No disclosed role
Gene-edited allogeneic pancreatic islets transplanted into the forearm muscle of one man with longstanding type 1 diabetes continued to show beta-cell function through 14 months without systemic immunosuppression. The investigators reported no detected immune response against the allograft.
- Problem or result
- Donor islet replacement can restore insulin production, but immune rejection normally requires chronic immunosuppression.
- Authors
- Per-Ola Carlsson, Xiaomeng Hu, Hanne Scholz et al.
- Institutions
- Uppsala University; UCSF; University of Oslo and Oslo University Hospital; Karolinska Institutet; Sana Biotechnology
- Result date
- Initial report August 4, 2025; follow-up July 10, 2026
Why it matters: Functional donor-cell survival without immunosuppressive drugs addresses the central barrier to off-the-shelf islet replacement.
Limits: This remains a one-person, uncontrolled early-phase result using a low cell dose; the participant did not become insulin-independent. Fourteen months does not establish population-level efficacy, lifetime immune evasion, malignancy or infection safety, or performance at a therapeutic dose. The registry still lists two planned participants and has stale completion dates.
Sources and record details
- Primary NEJM primary case report
- Primary NEJM 14-month follow-up
- Primary ClinicalTrials.gov study record
- Independent Independent research commentary record
AI involvement: No substantive AI role was reported.
Change history
- — First-in-human result published online in the New England Journal of Medicine.
- — Peer-reviewed NEJM follow-up reported beta-cell function and no detected graft-directed immune response through 14 months; status and evidence tier remain unchanged because the evidence still concerns one low-dose participant.
2 tracked records
Biology and biotechnology
AI plus evolutionary constraints produced compact, active RNA-guided genome editors
Evidence tier 2
Peer reviewed: Yes
AI role: Yes
Researchers combined machine-learning inverse folding with evolutionary and structural constraints to design synthetic TnpB nucleases. Experimentally screened variants matched or exceeded natural TnpB activity in bacterial, plant and human cells, and cryo-EM revealed stabilizing contacts created by the designs.
- Problem or result
- Many powerful genome editors are difficult to package and deliver, while unconstrained AI protein designs often fail when tested experimentally.
- Authors
- Petr Skopintsev, Isabel Esain-Garcia, Evan C. DeTurk et al.
- Institutions
- Innovative Genomics Institute; University of California, Berkeley; University of California, Los Angeles
- Result date
- July 16, 2026
Why it matters: The study closes a credible loop from AI sequence generation to cell activity and structural explanation while producing editors smaller than commonly used Cas9 proteins.
Limits: This is laboratory and cell evidence, not a therapeutic result. Editing activity does not establish genome-wide specificity, delivery, immunogenicity or safety, and only a small fraction of generated candidates passed experimental screening.
Sources and record details
- Primary Science primary paper
- Primary Preprint and methods context
- Primary Cryo-EM structure record
- Independent Nature specialist reporting
AI involvement: Machine-learning inverse folding was a core sequence-design method, combined with evolutionary and structural constraints.
Change history
- — Preprint posted.
- — Peer-reviewed version published in Science.
A Streptomyces megacluster encodes a naturally coordinated multi-drug antibiotic system
Evidence tier 2
Peer reviewed: Yes
AI role: No disclosed role
A conserved Streptomyces biosynthetic megacluster was shown to produce four natural-product families plus streptavidin that converge on bacterial biotin metabolism through complementary mechanisms. Stravidin S2 and alpha-Me-KAPA acted synergistically and improved efficacy in a mouse model of multidrug-resistant E. coli infection.
- Problem or result
- Conventional antibiotic discovery often isolates one molecule at a time and may miss naturally co-evolved combinations that attack a pathway at several points.
- Authors
- R. Gordzevich, M. Xu, W. Wang et al.
- Institutions
- McMaster University Institute of Infectious Disease Research; Biochemistry and Biomedical Sciences; David Braley Centre for Antibiotic Discovery
- Result date
- June 24, 2026
Why it matters: The work reveals naturally encoded combination therapy as an underexplored antibiotic-discovery strategy.
Limits: The efficacy evidence is preclinical; pharmacokinetics, toxicity, dosing, manufacturing and resistance evolution in humans are unknown. These compounds are not an approved treatment.
Sources and record details
- Primary Nature primary paper
- Primary Code archive
- Independent Nature editorial reporting
AI involvement: No substantive AI role was reported.
Change history
- — Mechanistic and mouse-efficacy study published in Nature.
2 tracked records
Chemistry and materials
Ball milling destroyed diverse PFAS classes while recovering reusable fluoride
Evidence tier 2
Peer reviewed: Yes
AI role: No disclosed role
Potassium phosphate salts and solvent-free mechanochemical milling mineralized several PFAS classes, including PTFE, PVDF, PFOA and PFOS. The process recovered fluorine as KF and K2PO3F for reuse and also treated consumer materials and PFAS-loaded activated carbon.
- Problem or result
- Many PFAS remediation methods transfer contamination, consume large amounts of energy or work on only a narrow subset of persistent fluorochemicals.
- Authors
- Long Yang, Zijun Chen, Christopher A. Goult et al.
- Institutions
- University of Oxford; Colorado State University
- Result date
- March 26, 2025
Why it matters: The method couples broad fluorochemical destruction to recovery of useful fluorine rather than merely concentrating or transferring the waste.
Limits: The work is laboratory scale, and energy demand, reactor wear, lifecycle emissions, cost, heterogeneous waste handling and residue management need independent scale-up testing. A patent has been filed, and the result does not mean the global PFAS problem is solved.
Sources and record details
- Primary Nature primary paper
- Independent Nature Research Briefing
AI involvement: No substantive AI role was reported.
Change history
- — Laboratory destruction and fluoride-recovery method published in Nature.
A hybrid chemical-biological process converted lignin to adipic acid at a record reported single-product yield
Evidence tier 2
Peer reviewed: Yes
AI role: No disclosed role
Reductive processing of poplar lignin produced alkyl-aromatic mixtures that catalytic oxidation converted to aromatic carboxylic acids at up to 73 wt%. Engineered Pseudomonas putida funnelled the mixture toward muconolactone and then adipic acid at up to 26 wt% relative to starting lignin.
- Problem or result
- Lignin is abundant but chemically heterogeneous, making it difficult to convert into one high-value product rather than low-value heat or a complex mixture.
- Authors
- Kathryn M. Mains, Chad T. Palumbo, Davide Rigo et al.
- Institutions
- National Laboratory of the Rockies; Oak Ridge National Laboratory; MIT; University of Wisconsin-Madison
- Result date
- June 10, 2026
Why it matters: Combining refinery-like redox chemistry with microbial funnelling offers a plausible route from lignin to one high-volume nylon precursor.
Limits: This is not a commercial refinery: feedstock variability, catalyst recovery, solvent and hydrogen demand, fermentation economics, purification, lifecycle carbon and scale remain open. The demonstrated yield is below the paper's 57 wt% theoretical maximum, and several authors filed a patent application.
Sources and record details
- Primary Nature primary paper
- Primary Sequence-data accession
- Independent Nature News and Views
AI involvement: No substantive AI role was reported.
Change history
- — Hybrid chemical-biological lignin-conversion study published in Nature.
1 tracked records
Earth science
Antarctic ice extended direct greenhouse-gas measurements to three million years ago
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
Discontinuous Allan Hills ice snapshots spanning about 3.1 to 0.5 million years ago showed no marked mean methane change and an approximately 20-ppm carbon-dioxide decline from 2.9 to 1.2 million years ago, followed by values stable within about 10 ppm across the mid-Pleistocene transition. Corrected 2.8- to 3.1-million-year samples yielded mean CO2 of 250 plus or minus 10 ppm.
- Problem or result
- Direct measurements of ancient atmospheric gases from ice had not previously reached far enough into the late Pliocene to constrain greenhouse-gas history over three million years.
- Authors
- Julia Marks-Peterson, Sarah Shackleton, John Higgins et al.
- Institutions
- Oregon State University-led COLDEX collaboration with Woods Hole, Princeton, Scripps/UC San Diego, Tongji, Maine, UC Santa Barbara and Shanghai Jiao Tong
- Result date
- March 18, 2026
Why it matters: Ancient air trapped in ice provides a more direct atmospheric measurement than many proxies and opens a new observational window on long-term climate evolution.
Limits: These are discontinuous blue-ice snapshots, not a continuous three-million-year core. Post-depositional effects and accumulation assumptions complicate interpretation, and the findings do not imply that today's rapid anthropogenic CO2 rise is harmless.
Sources and record details
- Primary Nature primary paper
- Primary Author correction
- Primary Public data
- Independent Nature News and Views
AI involvement: No substantive AI role was reported.
Change history
- — Greenhouse-gas snapshot record published in Nature.
- — Author correction published and incorporated into the tracker summary.
1 tracked records
Human evolution
Proteins and mitochondrial DNA identified the Harbin cranium as Denisovan
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
Mitochondrial DNA recovered from dental calculus clustered with early Denisovan lineages, while protein sequences from the cranium independently supported Denisovan affinity. Together the studies provide the first direct molecular link between a near-complete Middle Pleistocene skull and Denisovans.
- Problem or result
- Denisovans were known mainly from genomes and a small number of fragmentary fossils, leaving their cranial anatomy and the identity of several Asian fossils unresolved.
- Authors
- Qiaomei Fu, Peng Cao, Qingyan Dai et al.
- Institutions
- Chinese Academy of Sciences; University of the Chinese Academy of Sciences; University of Richmond; Max Planck Institute for Evolutionary Anthropology; Hebei GEO University
- Result date
- June 18, 2025
Why it matters: A substantially complete cranium gives researchers a far richer anatomical candidate for Denisovans and connects Asian fossils to molecular lineages.
Limits: Mitochondrial DNA follows only the maternal lineage and is not a nuclear genome; species labels such as Homo longi remain debated. The skull's discovery history, possible population mixing and the limits of molecular affinity mean the result does not settle every morphological or taxonomic question.
Sources and record details
- Primary Cell mitochondrial-DNA paper
- Primary Science proteome paper
- Independent Nature specialist reporting
- Independent Nature Ecology and Evolution commentary
AI involvement: No substantive AI role was reported.
Change history
- — Companion palaeoproteomic and mitochondrial-DNA identifications published.
5 tracked records
Claims to watch, corrections and disputes
Dark oxygen at the deep seafloor is formally disputed and under editorial review
Evidence tier 4
Peer reviewed: Yes
AI role: No disclosed role
The original paper reported rising oxygen concentrations in 25 benthic-chamber incubations over polymetallic-nodule fields and proposed a nodule-associated electrochemical source. A peer-reviewed critique raised replication, sensor, entrained-air and thermodynamic objections, and Nature Geoscience added an Editor's Note stating that concerns were under consideration.
- Problem or result
- The original study reported oxygen production in dark abyssal incubations, a result that would challenge assumptions about deep-ocean chemistry if it were real.
- Authors
- Andrew K. Sweetman, Alycia J. Smith, Danielle S. W. de Jonge et al.
- Institutions
- International deep-sea research collaboration in the Clarion-Clipperton Zone
- Result date
- July 22, 2024; disputed April 8, 2026
Why it matters: If independently reproduced, oxygen production without light in abyssal ecosystems would have major implications for deep-ocean chemistry and early-life environments.
Limits: The claim is not established and must remain outside the confirmed-breakthrough feed while editorial review and independent tests continue. Several critique authors disclosed affiliations or interests connected to deep-sea-mining companies or projects, so that conflict must be shown alongside the methodological objections.
Sources and record details
- Primary Original Nature Geoscience paper and Editor's Note
- Primary Original data
- Independent Peer-reviewed methodological critique
- Independent Nature reporting on new robotic tests
AI involvement: No substantive AI role was reported.
Change history
- — Original dark-oxygen claim published in Nature Geoscience.
- — Peer-reviewed critique published in Frontiers in Marine Science.
- — Nature Geoscience added an Editor's Note stating that concerns were under consideration.
- — Rechecked the article, Editor's Note and critique. No correction, retraction or resolved editorial response was found; disputed status retained.
The autonomous A-Lab paper was corrected after its novelty claims were challenged
Evidence tier 4
Peer reviewed: Yes
AI role: Yes
The corrected record says the A-Lab successfully synthesized 36 of 57 targeted compounds and clarifies that the targets were new to the laboratory, not necessarily new to science. Previous experimental reports existed for many of the same or closely related compositions.
- Problem or result
- The original public story presented an autonomous laboratory as rapidly realizing novel inorganic materials, making the novelty and identification of its targets central to the claimed advance.
- Authors
- Nathan J. Szymanski, Bernardus Rendy, Yuxing Fei et al.
- Institutions
- Lawrence Berkeley National Laboratory; University of California, Berkeley; Google DeepMind
- Result date
- Correction published January 19, 2026
Why it matters: The autonomous platform remains important, but the correction materially narrows the novelty framing that drove the original breakthrough coverage.
Limits: The paper was corrected, not retracted. Independent chemistry reporting says some critics still consider the treatment of structural disorder insufficiently addressed, so the tracker should preserve the correction history rather than repeat the original novelty claim.
Sources and record details
- Primary Original Nature article, updated
- Primary Formal Nature correction
- Independent Chemical and Engineering News integrity reporting
AI involvement: Machine learning, language models, active learning and autonomous experiment planning were core components of the A-Lab platform.
Change history
- — Original A-Lab article published in Nature.
- — Nature published an author correction and updated the article's target-novelty framing and synthesis accounting.
- — Rechecked the correction record. No retraction or later formal amendment was found; corrected, not retracted, status retained.
Microsoft Majorana 1 topological-qubit interpretation
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
The peer-reviewed Microsoft paper demonstrated a single-shot interferometric fermion-parity measurement in an InAs–Al hybrid device. It did not unequivocally distinguish topological Majorana zero modes from trivial low-energy Andreev states.
- Problem or result
- Whether Microsoft's InAs–Al device data demonstrate a topological superconducting regime or Majorana zero modes
- Authors
- Microsoft Azure Quantum; critique by Henry F. Legg
- Institutions
- Microsoft Azure Quantum, University of St Andrews and University of Basel
- Result date
- Original paper February 19, 2025; critique and reply June 24, 2026
Why it matters: A verified topological regime would be important for fault-tolerant quantum computing, but the published evidence does not yet establish one.
Limits: A 2026 peer-reviewed critique argues that the selected transport regime appears disordered and gapless, suggesting trivial mechanisms; Microsoft published a simultaneous reply disputing that conclusion. Required wording: peer-reviewed device measurement; claimed topological/Majorana interpretation unverified and actively contested.
Sources and record details
- Primary Original Microsoft paper in Nature
- Primary Peer-reviewed Nature critique
- Primary Microsoft peer-reviewed reply
- Independent APS Physics analysis
AI involvement: No AI assistance was disclosed for the scientific experiment or analysis in the linked papers.
Change history
July 22, 2026 — Rechecked the published critique and reply. A separate Majorana 2 preprint was reviewed but does not resolve the Majorana 1 interpretation dispute; status unchanged.
DESI evidence for evolving dark energy
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
DESI's three-year data, combined with CMB and supernova datasets, produced a 2.8σ–4.2σ preference for time-varying dark energy depending on the dataset and model. Several 2026 analyses found weaker or cosmological-constant-consistent results; the full DES Year 6 multi-probe analysis also reported only a weak, combination-dependent preference.
- Problem or result
- Whether dark energy changes over cosmic time rather than behaving as a cosmological constant
- Authors
- DESI Collaboration and independent cosmology teams
- Institutions
- Dark Energy Spectroscopic Instrument collaboration and partner institutions
- Result date
- March 19, 2025; countervailing analyses published in 2026
Why it matters: Confirmed evolving dark energy would require a major revision of the standard cosmological model.
Limits: No combination reached 5σ, and the inference changes with dataset, calibration and parameterization. Required wording: evidence suggesting evolving dark energy, model- and dataset-dependent; not a discovery.
Sources and record details
- Primary DESI Data Release 2 cosmology papers
- Primary DESI official interpretation
- Independent Model-independent reconstruction in JCAP
- Independent Revised-supernova analysis in European Physical Journal C
- Independent Dark Energy Survey Year 6 cosmology results
- Independent DES Year 6 multi-probe analysis
AI involvement: No AI assistance was disclosed as a contributor to the core cosmological result.
Change history
July 22, 2026 — Added the DES Year 6 multi-probe analysis for balance. Its weak, combination-dependent support does not change the provisional/model-dependent status; full five-year DESI results remain expected in 2027.
K2-18 b DMS/DMDS molecular and biosignature claim
Evidence tier 1
Peer reviewed: Yes
AI role: No disclosed role
A 2025 JWST analysis reported about 3σ evidence for dimethyl sulfide and/or dimethyl disulfide in K2-18 b's atmosphere. Independent reductions found the MIRI result sensitive to binning and instrumental systematics and did not recover statistically significant DMS/DMDS evidence.
- Problem or result
- Whether JWST spectra establish dimethyl sulfide or dimethyl disulfide in K2-18 b's atmosphere
- Authors
- Nikku Madhusudhan and collaborators; independent reanalyses by Rafael Luque and collaborators
- Institutions
- University of Cambridge and independent JWST-analysis teams
- Result date
- Original analysis April 16, 2025; independent reanalyses from May 2025
Why it matters: A well-verified atmospheric biosignature on a temperate exoplanet would be a landmark result, which makes strict molecular and instrumental verification essential.
Limits: The molecules were degenerate, the significance was below the usual discovery threshold and plausible atmospheric or instrumental alternatives remain. Required wording: tentative and disputed molecular retrieval; not a biosignature detection and not evidence that life has been found.
Sources and record details
- Primary Original DMS/DMDS analysis
- Primary Independent reanalysis finding insufficient evidence
- Primary Final Astrophysical Journal Letters paper for the original claim
- Primary Final Astronomy & Astrophysics version of the reanalysis
- Independent Subsequent peer-reviewed systematic analysis in The Astronomical Journal
AI involvement: No AI assistance was disclosed as a contributor to the linked spectral-retrieval studies.
Change history
July 22, 2026 — Rechecked the original claim, independent reanalysis and systematic study. Added final journal links where available; the disputed/insufficient-evidence status is unchanged.
Methodology and evidence standards
Every record links to its strongest available primary evidence. Independent interpretation is added when it clarifies scope or verification. Institutional announcements can establish what an organization says, but they do not independently confirm that organization’s claim.
| Tier | Meaning | How it is used |
|---|---|---|
| 1 | Primary paper, formal artifact, regulator decision, dataset or official collaboration report | The controlling evidence for the result actually reported |
| 2 | Strong independent specialist interpretation or credible early peer-reviewed evidence | Scope, significance and unresolved questions |
| 3 | Institutional announcement, preprint-only claim or incomplete evidence | Provisional records and follow-up triggers |
| 4 | Materially disputed, corrected, under editorial review or retracted | Displayed separately; never presented as an established breakthrough |
Mathematical wording: “Proved,” “disproved,” “solved” and “settled” are used only when the exact statement, dimensional scope, proof artifact and review state justify them. A machine-checked proof verifies the encoded theorem and proof; specialists must still check that the encoding matches the intended problem.
Medical wording: A laboratory result, single patient, phase 3 trial, regulatory approval and public-health recommendation are different milestones. The tracker states which one occurred.
Weekly update log
22 July 2026 — follow-up source correction
Corrected the Friedlander–Iwaniec Gaussian-primes entry after the official Acta Mathematica accepted-paper list and Mehtaab Sawhney’s publication list showed that the paper was accepted on 22 July 2025. The tracker now marks it as accepted and awaiting final publication, rather than as an unreviewed preprint, and discloses the partial-summation error and minor inaccuracy corrected in arXiv version three. No new record was added in this follow-up pass.
22 July 2026 — weekly maintenance pass
Added three mathematics records as provisional claims: a claimed proof of Godbersen’s conjecture, counterexamples to the Duval–Reiner majorization assertion, and a counterexample to Thakur’s Carlitz–Wieferich-prime conjecture whose version-two correction is disclosed. Added the peer-reviewed CD-35 2722 B planetary-mass exosatellite candidate with its interpretation still marked provisional. Corrected the Hilbert’s tenth record to show one published proof and an independent proof forthcoming in JAMS; added a new scholarly analysis of the Jacobian counterexample without calling it peer review; updated the QMA-versus-QCMA oracle separation to its final STOC 2026 publication record; and extended the UP421 donor-islet record to its peer-reviewed 14-month follow-up. Rechecked every provisional, disputed, claimed-proof and preprint-only entry. The broad new Gromov–Ros proof claim remains off the tracker pending independent assessment. Source links were refreshed for several conference, astronomy and dispute records.
22 July 2026 — inaugural edition
Created the permanent tracker, established the evidence-tier system and added the first 24-month foundation. Mathematics received the broadest pass, including Erdős problems, conjecture disproofs, formal proofs and AI-assisted work. Physics, computer science, astronomy, medicine, biology, chemistry, Earth science and human evolution were added only where primary evidence supported a field-level advance. Disputed and corrected claims were separated from ordinary results.
Suggest a result or correction
Send the exact theorem, paper, preprint, dataset, regulator record or correction notice through the Kingy.ai contact page. Include a primary-source link and explain whether the item is published, preprint-only, formally verified, disputed or corrected.