70 papers
40 with a material AI role · 52 full or independently verified.
SINGULARITY COMPASSResearch Observatory
Monitoring active
AI FOR SCIENCE · MATHEMATICS
Open Problem Closure Radar
A daily watch for papers that claim to close, partially resolve, refute or materially advance named open problems. The radar separates the mathematical claim from the role AI actually played.
A paper saying “we answer” is not automatically treated as a settled theorem. Special cases remain partial until the whole problem is closed.
Human-only results are useful context, but they do not move ASI Readiness. AI-linked results matter only when the contribution is documented.
16PARTIAL
40AI-LINKED
The purpose is to detect acceleration early without turning arXiv claims into breakthroughs before verification.
RADAR
Latest open-problem claims
PARTIALAI CO-DEVELOPED
27 Aug 2026Commutative algebra
Fröberg’s conjecture for quintics and septics in four variables
Fröberg’s Conjecture for Quintics and Septics in Four Variables
Primary v3 preprint; an independent catalog reproduced printed endpoint computations and ran supplied verifiers, but did not verify the complete mathematical reduction.
PRIMARY PAPER ↗SIGNIFICANCE7.5/10
EVIDENCE74/100
FULLAI-ASSISTED
27 Aug 2026Categorical logic
Heyting algebra realization as subterminal lattices of elementary topoi
Failure of Higher-Order Truth within Intuitionistic Propositional Logic
Primary preprint gives a counterexample settling the universal realization question negatively. It does not classify all realizable Heyting algebras. AI assistance is author-disclosed but underspecified; no independent verification or peer review.
PRIMARY PAPER ↗SIGNIFICANCE7.4/10
EVIDENCE78/100
PARTIALAI CO-DEVELOPED
27 Aug 2026Hyperbolic geometry
Large systoles in every sufficiently large genus
A note on surfaces with large systoles
Primary preprint confirms the claimed theorem and AI disclosure. No independent correctness verification, peer review or reproduction found; the optimal asymptotic constant remains open.
PRIMARY PAPER ↗SIGNIFICANCE7.7/10
EVIDENCE62/100
FULLAI-LED
27 Aug 2026theoretical computer science
Provable Hadamard Quantization
Pairwise-Independent Dithering for Single-Stage Hadamard Quantization
Eliminates the second quantization stage and reduces the leading constant by about 5.93x; reproduced with Gemini 3.7 Flash.
PRIMARY PAPER ↗SIGNIFICANCE8.5/10
EVIDENCE88/100
PARTIALAI-LED
27 Aug 2026theoretical computer science
Maximal Inner Product Embeddings
Near-Optimal Dimension Lower Bounds for Single-Vector Embeddings of Maximum Inner Product Similarity
Nearly closes the gap; automated Gemini proof and author verification; reproduced with Gemini 3.7 Flash.
PRIMARY PAPER ↗SIGNIFICANCE8.4/10
EVIDENCE88/100
FULLAI-LED
27 Aug 2026theoretical computer science
Sparse Convex Optimization condition-number barrier
The Condition-Number Barrier in Sparse Least Squares
Conditional lower bound; automated Gemini proof and author verification. Not a Flash reproduction in the detailed report.
PRIMARY PAPER ↗SIGNIFICANCE8.4/10
EVIDENCE88/100
PARTIALAI-LED
27 Aug 2026theoretical computer science
Prefix-Matrix Factorizations
A Near-Optimal Lower Bound for Prefix-Matrix Factorizations
Near-optimal lower bound; automated Gemini proof and author verification. Not a Flash reproduction in the detailed report.
PRIMARY PAPER ↗SIGNIFICANCE8.2/10
EVIDENCE88/100
PARTIALAI-LED
27 Aug 2026theoretical computer science
Coresets for Lp Subspace Approximation
Nearly Optimal Strong Coresets for l_p Subspace Approximation
Improved bounds; human expert review reported by Google. Flash-specific reproduction is first-party and not externally reproduced.
PRIMARY PAPER ↗SIGNIFICANCE8.2/10
EVIDENCE84/100
PARTIALAI-LED
27 Aug 2026mathematics
Knuth Cycles Conjecture — simpler even-case constructions
Teamwork proofs for two simpler constructions of the even integer case
First proofs for two simpler even-case constructions; Google reports the 40-page proof was formally verified in Lean. Partial scope, not a full solution of every form of the conjecture.
PRIMARY PAPER ↗SIGNIFICANCE8.8/10
EVIDENCE92/100
CLAIMEDAI-LED
27 Aug 2026mathematics
Erdos Unit Distance Problem
Teamwork reproduction of the unit-distance exponent breakthrough
Repository says Gemini 3.1 Pro and explicitly notes an incorrect formula, incomplete argument and minor rigor gaps. Not a Gemini 3.7 Flash reproduction.
PRIMARY PAPER ↗SIGNIFICANCE8.7/10
EVIDENCE62/100
FULLAI-LED
26 Aug 2026Partial differential equations / regularity theory
De Giorgi continuity conjecture for non-uniformly elliptic equations
On the sharp Hölder exponent in the De Giorgi–Nash–Moser theory
V2 attributes the initial proof of Theorem 1.2 essentially autonomously to GPT-5.6 Pro. The author reports days of understanding and verification and wrote the final proof. No independent verification or peer review was found.
PRIMARY PAPER ↗SIGNIFICANCE8.8/10
EVIDENCE70/100
PARTIALAI CO-DEVELOPED
26 Aug 2026Theoretical computer science / probability
Rapid mixing for spin systems on graphs of girth at least five
A Spectral Local-to-Global Principle for Spin Systems on Graphs with Girth At Least Five
Primary preprint only; no peer review or independent verification. The theorem materially lowers the girth requirement but does not settle the general q≥Δ+2 conjecture.
PRIMARY PAPER ↗SIGNIFICANCE8.2/10
EVIDENCE78/100
PARTIALAI CO-DEVELOPED
25 Aug 2026Theoretical computer science / combinatorial optimization
Polynomial-time stable matching in network hypergraphs
Polynomial-time Stable Matching in Network Hypergraphs
Primary preprint only; no peer review or external independent verification. The network-hypergraph case is resolved, but the broader unimodular and normal-hypergraph problems remain open.
PRIMARY PAPER ↗SIGNIFICANCE7.6/10
EVIDENCE80/100
CLAIMEDAI CO-DEVELOPED
23 Aug 2026Differential and complex geometry
Hopf problem: does S^6 admit a complex structure?
A complex structure on S^6
Levent Alpoge claims a positive construction and publicly credits Claude/Opus 5 with substantial involvement. Independent expert verification is pending. This problem has a long history of incorrect claimed solutions, so no closure is recorded yet.
PRIMARY PAPER ↗SIGNIFICANCE9.5/10
EVIDENCE62/100
PARTIALAI-ASSISTED
23 Aug 2026Arithmetic geometry / number theory
Are Mordell–Weil ranks of elliptic curves over Q unbounded?
Elliptic Curve Rank Leaderboard — Curve #302
Curve #302 has 31 exactly certified independent rational points, so rank >=31 unconditionally. This is a new record and material evidence on the broader rank frontier, but it does not settle the folklore unbounded-rank question. ICARM commentary attributes discovery to Claude, Levent Alpöge and Ava Howell; detailed division of labor is not yet public.
PRIMARY PAPER ↗SIGNIFICANCE8.9/10
EVIDENCE96/100
PARTIALAI CO-DEVELOPED
23 Aug 2026analytic number theory
Riemann zeta critical-line / simple-zero lower-bound program
Zeta Lab state of record: 67.30530% candidate lower bound for simple zeros on the critical line
The project reports a 67.30530% candidate lower bound with a public interval/certificate pipeline and supporting kernel-checked theorems. The project itself states one substantial analytic bridge remains unproved/reviewed and the eight-point generalization is stated rather than proved; therefore this is partial progress, not a closure of RH or a fully verified theorem.
PRIMARY PAPER ↗SIGNIFICANCE7.5/10
EVIDENCE66/100
FULLNO MATERIAL AI ROLE
20 Aug 2026Differential geometry
Bray volume conjecture
On the proof of Bray's conjecture
The authors state that their theorem confirms Bray's 1997 conjecture. Primary preprint only; independent review/verification not yet established. No documented AI contribution.
PRIMARY PAPER ↗SIGNIFICANCE6.5/10
EVIDENCE78/100
FULLAI CO-DEVELOPED
20 Aug 2026Quantum information / shadow tomography
Fractional colouring conjecture for triply efficient Pauli shadow tomography
Counterexamples to the fractional coloring conjecture for triply efficient shadow tomography
The paper constructs states and observables showing no universal constant bounds chi_f epsilon^2, disproving Conjecture 13 of King, Gosset, Kothari and Babbush. The paper states “Found with GPT Sol 5.6” and says the model was used to derive the main results. VibeMathed checked the disclosure but not the constructions; independent review is pending.
PRIMARY PAPER ↗SIGNIFICANCE6.3/10
EVIDENCE84/100
PARTIALAI-LED
20 Aug 2026Mathematical physics / PDE / probability
Arnold fast-dynamo problem / smooth fast dynamo on T^3
An AI-discovered smooth random fast dynamo on T^3
The preprint gives the first smooth random fast-dynamo construction and explicitly credits ChatGPT 5.6 Sol Ultra with the central proof idea. This is not a full solution of the deterministic smooth fast-dynamo problem: the flow is random and the full-probability event can depend on resistivity. Independent expert verification is pending.
PRIMARY PAPER ↗SIGNIFICANCE8.5/10
EVIDENCE84/100
FULLAI CO-DEVELOPED
20 Aug 2026Network information theory
Whether Marton's inner bound achieves the broadcast-channel capacity region
Sub-optimality of Marton's Inner Bound for the Two-Receiver Broadcast Channel
Primary paper inspected. The main sub-optimality claim is unconditional and numerically certified in the paper. AI models materially assisted the search for the counterexamples; no independent full review yet.
PRIMARY PAPER ↗SIGNIFICANCE7.4/10
EVIDENCE86/100
FULLAI-ASSISTED
20 Aug 2026Number theory / arithmetic geometry
Find an elliptic curve over Q of rank 30
Elliptic Curve Rank Leaderboard — Curve #273
The concrete open problem listed by AIM is satisfied by a curve certified to have at least 30 independent rational points. This is a full closure of that finite target, not a solution of the broader question of whether elliptic-curve ranks over Q are unbounded. AI involvement is publicly reported but not yet documented sufficiently to classify beyond unclear. Primary ICARM leaderboard commentary explicitly attributes the rank-30 discovery to Claude with Levent Alpöge and Ava Howell; exact division of labor is not documented, so classified conservatively as assisted.
PRIMARY PAPER ↗SIGNIFICANCE8.8/10
EVIDENCE88/100
FULLAI-LED
19 Aug 2026Exact exponential algorithms
Koivisto question: exact linear-extension counting below the 2^n barrier
Breaking the 2^n Barrier for Counting Linear Extensions with a Short Elementary Algorithm
The paper gives a deterministic exact O*(1.89^n) algorithm and explicitly resolves Koivisto’s Dagstuhl 2013 question. The disclosure says Claude Opus 5 discovered the core new algorithmic and proof ideas, with the research prompt generated by ChatGPT 5.6 Sol. VibeMathed checked the disclosure on 2026-08-21; independent review is pending.
PRIMARY PAPER ↗SIGNIFICANCE7.3/10
EVIDENCE86/100
INDEPENDENTLY VERIFIEDAI ROLE UNCLEAR
19 Aug 2026Functional analysis / linear dynamics
Generalized Hyperbolicity Conjecture for Shadowing
Resolving the Generalized Hyperbolicity Conjecture for Shadowing
The paper refutes the conjecture on general Banach spaces and proves the converse on separable Hilbert spaces. Theorem A is explicitly noted as independently proved by Messaoudi et al.; removal of separability in the Hilbert-space positive result remains open. No documented AI contribution was found in the paper, so AI role is unclear and this record has no ASI or AI-for-Science score effect.
PRIMARY PAPER ↗SIGNIFICANCE7.4/10
EVIDENCE92/100
FULLAI-LED
19 Aug 2026Discrete geometry
Kára–Pór–Wood Big-Line-Big-Clique conjecture, first open case (4 collinear or 6-clique)
Large Finite Point Sets Have 4 Collinear Points or a 6-Clique
The paper resolves the first open case of the conjecture. Its disclosure says GPT-5.6 Sol Pro supplied a relatively detailed proof after 222 minutes; Bonnet checked and simplified it and rewrote the paper. VibeMathed verified the disclosure against the paper on 2026-08-21, but the proof is not independently reviewed.
PRIMARY PAPER ↗SIGNIFICANCE7.6/10
EVIDENCE86/100
FULLAI-ASSISTED
19 Aug 2026Quantum information / computational complexity
Gaussian boson sampling hiding conjecture
Proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezed input modes
Primary paper opened and inspected. Acknowledgments state GPT-5.5 Thinking/Pro and GPT-5.6 Sol contributed proof ideas and methods; human authors checked and validated all results. Independent external verification not yet established.
PRIMARY PAPER ↗SIGNIFICANCE7.7/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
19 Aug 2026Numerical linear algebra
Worst-case entry growth in Gaussian elimination under complete and rook pivoting
Entry growth in Gaussian elimination
The preprint states that it settles several open problems, including the asymptotic behavior of the maximum growth factor under complete and rook pivoting, proving both quasi-polynomial in dimension. No documented AI contribution was found in the abstract/source reviewed; no ASI impact is assigned.
PRIMARY PAPER ↗SIGNIFICANCE7.5/10
EVIDENCE65/100
FULLAI ROLE UNCLEAR
19 Aug 2026Mathematical analysis / special functions
Csordas–Dimitrov logarithmic concavity conjecture for the Riemann Xi kernel
Second-Level Concavity of the Riemann Xi Kernel
The preprint explicitly states that it proves the Csordas–Dimitrov conjecture/Open Problem 4.14 by two methods. No documented AI contribution was found in the abstract/source reviewed, so ai_role remains unclear. This does not assert the Riemann Hypothesis.
PRIMARY PAPER ↗SIGNIFICANCE6.5/10
EVIDENCE65/100
FULLAI-ASSISTED
19 Aug 2026harmonic analysis
Eceizabarrena–Da Rocha Conjecture 4.5
Norm bounds on Fourier series with polynomial spectra and constrained coefficients
Theorem 3 explicitly answers Conjecture 4.5 and determines the sharp L4 growth order. The author acknowledges ChatGPT 5.6 Plus as a research tool in developing and checking technical parts of Theorem 3, including arithmetic estimates and reference discovery, while independently checking the proof.
PRIMARY PAPER ↗SIGNIFICANCE6.2/10
EVIDENCE90/100
FULLAI-ASSISTED
19 Aug 2026Operator theory
Separation between ordinary and strong Kreiss constants (Chalmoukis–Tsikalas–Yakubovich Question 6.1)
A solution to the inverse generator problem and related questions
Primary arXiv v2 inspected: Theorem 1.4(i) explicitly states that it solves Question 6.1 and gives an essentially optimal dimension-dependent separation. AI was materially involved in Proposition 2.1, the finite-dimensional construction from which the result is deduced, but the theorem itself is not independently verified.
PRIMARY PAPER ↗SIGNIFICANCE5.4/10
EVIDENCE82/100
PARTIALAI ROLE UNCLEAR
19 Aug 2026Cryptography / finite fields
Kasami APN function conjecture
On a conjecture on the Kasami APN function: reductions, structure theorems, a proof for k mod n in {1,2,n-2,n-1}, and exhaustive verification for n<=13
The paper proves the conjecture for several residue classes, including a complete proof for k=2, and exhaustively verifies n<=13; it does not close the full conjecture. No documented AI contribution was found in the abstract, so ai_role remains unclear.
PRIMARY PAPER ↗SIGNIFICANCE5.3/10
EVIDENCE86/100
FULLAI ROLE UNCLEAR
19 Aug 2026Extremal graph theory
Ma conjecture on C_[4,r]-saturation numbers
Minimizing the number of edges in C_[4,6]-saturated graphs
The paper proves an upper bound that contradicts Ma's 2025 conjecture for every r>=6 and determines the r=6 saturation number exactly. No documented AI contribution was found in the paper abstract, so ai_role is unclear rather than inferred.
PRIMARY PAPER ↗SIGNIFICANCE5.6/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
19 Aug 2026Algebraic geometry
Generators of the automorphism group of the complex Fermat quartic K3 surface
Sixteen generators of the automorphism group of the Fermat quartic surface
The preprint describes the generator problem as longstanding and presents an explicit first solution with 16 finite-order geometric generators. No documented AI contribution was found in the abstract/source reviewed; no ASI impact is assigned.
PRIMARY PAPER ↗SIGNIFICANCE6.5/10
EVIDENCE65/100
FULLAI ROLE UNCLEAR
19 Aug 2026differential geometry
Bangert question on codimension-one minimizing foliations
Minimal foliations, codimension-one stable norms, and a question of Bangert
The paper constructs nonflat tori satisfying the stated foliation property in every dimension n>=3, giving a negative answer to Bangert’s 1994 question. No documented AI contribution was found in the paper during this check.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE88/100
INDEPENDENTLY VERIFIEDAI CO-DEVELOPED
19 Aug 2026Set theory / forcing
Erdős Problem #501: infinite independent sets for families of small outer measure
Erdős Problem #501 in Lean 4: the closed case and the independence of the first question
Both independence directions and the statement-faithfulness bridge are formalized in Lean. The primary repository reports no sorryAx dependencies in targets and only standard axioms; VibeMathed independently audited the repository and marks the result Lean-verified. This meets the Compass threshold for independently_verified. The new contribution removes the large-cardinal hypothesis, while much of the surrounding mathematics predates this work.
PRIMARY PAPER ↗SIGNIFICANCE7.0/10
EVIDENCE92/100
FULLAI-LED
19 Aug 2026Differential / algebraic geometry
Yau–Tian–Donaldson conjecture for cscK metrics
Disproof of the Yau–Tian–Donaldson conjecture
The preprint explicitly constructs a K-polystable smooth polarized projective fivefold with no cscK metric and states that this disproves the original cscK YTD conjecture. The appendix documents a collaborative AI-generated proof and a fresh improved-Danus run that reportedly solved the original problem in 5h29m without the key human intervention. Independent expert verification is pending; Fano and uniform/completed YTD variants are not affected.
PRIMARY PAPER ↗SIGNIFICANCE9.5/10
EVIDENCE82/100
FULLAI-ASSISTED
19 Aug 2026Differential geometry
C^infinity Carathéodory conjecture on umbilic points
Proof of the smooth Carathéodory–Loewner counterexample
Candidate counterexample to the smooth C^infinity case only; the real-analytic Carathéodory theorem remains untouched. VibeMathed audited the pinned Lean development on 2026-08-21: 8013-line proof tree, zero sorry and zero declared axioms, but the commit is not merged and upstream PRs remain drafts, so statement/repository verification is still pending. AI role is assistance/checking of a human construction; Codex helped formalization, not discovery.
PRIMARY PAPER ↗SIGNIFICANCE5.5/10
EVIDENCE76/100
FULLNO MATERIAL AI ROLE
18 Aug 2026Differential geometry
Chern–do Carmo–Kobayashi conjecture on minimal submanifolds
On Chern's conjecture for minimal submanifolds of the sphere
The paper provides counterexamples that falsify the universal conjecture for broad parameter ranges. No AI contribution is documented on the arXiv record; no independent verification was found in this run. Human-only result: context for mathematical progress, not an ASI signal.
PRIMARY PAPER ↗SIGNIFICANCE7.3/10
EVIDENCE88/100
FULLAI CO-DEVELOPED
18 Aug 2026Harmonic analysis
Stein’s dimension-free weak-(1,1) Riesz transform problem
A dimension-free weak-type (1,1) bound for the vector Riesz transform on R^n
Claim is a full resolution of Stein’s 1986 endpoint dimension-free problem. AI contribution is explicitly documented in the paper; independent expert/peer verification of the analytic proof is pending.
PRIMARY PAPER ↗SIGNIFICANCE8.4/10
EVIDENCE82/100
FULLAI-ASSISTED
18 Aug 2026Algebraic geometry / toric geometry
Sato weak F-equivalence conjecture
Counterexamples to Sato's Weak F-Equivalence Conjecture and a Gorenstein Refinement
The paper explicitly says it disproves Sato's weak F-equivalence conjecture in every dimension d>=3 and states the results were developed with assistance from GPT-5.6 Sol. The exact depth of AI contribution is not independently audited; no independent mathematical verification was found in this run.
PRIMARY PAPER ↗SIGNIFICANCE6.7/10
EVIDENCE90/100
FULLAI ROLE UNCLEAR
18 Aug 2026A-hypergeometric systems / algebraic analysis
Okuyama–Saito intrinsic perturbation question
Obstructions to intrinsic perturbation for A-hypergeometric series
The paper answers the Okuyama–Saito question affirmatively by exhibiting obstruction examples and states that it settles a case left open by Okuyama–Saito. No documented AI contribution was found in the paper metadata/abstract checked in this run, so ai_role remains unclear.
PRIMARY PAPER ↗SIGNIFICANCE5.4/10
EVIDENCE80/100
FULLNO MATERIAL AI ROLE
18 Aug 2026Algebra / Hochschild cohomology
Snashall–Solberg conjecture for selfinjective algebras
A Symmetric Counterexample to the Snashall–Solberg Conjecture
Paper inspected. Theorem B gives a symmetric (hence selfinjective) counterexample. This does not newly refute the unrestricted conjecture, which already had known counterexamples; it closes the remaining selfinjective case identified by the authors. The paper mentions unsuccessful use of ChatGPT and Kimi for a separate Gerstenhaber-structure task, not as a contribution to the main counterexample, so ai_role=none. Independent external verification not established.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE86/100
FULLAI ROLE UNCLEAR
17 Aug 2026Partial differential equations / geometric analysis
Magnanini conjecture on critical points of the torsion function
Counterexamples to Magnanini's conjecture concerning critical points of the torsion function
The arXiv abstract explicitly states that the authors construct planar simply-connected domains disproving Magnanini's conjectured bound and also answer a question of Steinerberger. No documented AI contribution was found in the paper metadata/abstract checked in this run, so ai_role remains unclear rather than inferred.
PRIMARY PAPER ↗SIGNIFICANCE6.4/10
EVIDENCE82/100
FULLAI ROLE UNCLEAR
17 Aug 2026Operator Algebras
Ozawa question on simplicity of reduced crossed products
Simplicity of reduced crossed products
The paper explicitly states that its characterization completely resolves a question of Ozawa. No AI contribution is documented in the checked source.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
17 Aug 2026Dynamical Systems / Functional Analysis
Shadowing without generalized hyperbolicity for invertible operators
On Generalized Hyperbolicity, Stability, and Shadowing for Linear Operators
The paper states that its results, combined with a recent theorem, answer an open problem in linear dynamics by producing invertible operators with shadowing that are not generalized hyperbolic for a large class of Banach spaces. No AI contribution is documented in the checked source.
PRIMARY PAPER ↗SIGNIFICANCE5.4/10
EVIDENCE86/100
FULLAI ROLE UNCLEAR
17 Aug 2026Statistics theory
Finiteness of modes in finite isotropic Gaussian mixtures
On Finite Gaussian Mixtures: Finiteness of the Number of Modes and an Application to NPMLE
arXiv v1 proves that every finite isotropic Gaussian mixture has finitely many modes, resolving the higher-dimensional finiteness question stated as open in the paper. No independent verification located in this hourly pass; no documented AI role found in the checked metadata/abstract.
PRIMARY PAPER ↗SIGNIFICANCE6.3/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
17 Aug 2026Theoretical computer science / quantum information
Asymptotic classical value of the repeated CHSH game
Optimal bounds on the classical value of the repeated CHSH game
The primary arXiv paper proves a matching upper bound which, together with the 2008 Barak et al. lower bound, determines the asymptotic classical value of the repeated CHSH game exactly. Earlier literature explicitly described this asymptotic value as unknown. No material AI contribution is documented in the primary source checked, so this is tracked as mathematical-progress context only and does not affect ASI Readiness or AI-for-Science maturity.
PRIMARY PAPER ↗SIGNIFICANCE6.4/10
EVIDENCE86/100
FULLAI ROLE UNCLEAR
17 Aug 2026Logic
Generalized Gaifman Conjecture
Counterexamples to the Generalized Gaifman Conjecture
arXiv v1 states a negative answer to Shelah and Usvyatsov's Generalized Gaifman Conjecture; no independent verification located in this hourly pass. No documented AI role found in the checked paper metadata/abstract.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE86/100
FULLAI ROLE UNCLEAR
16 Aug 2026Analysis of PDEs
Brezis open problem 2.2
On Brezis' open problem 2.2
arXiv v1 gives an affirmative answer to Brezis open problem 2.2 for the stated Ginzburg–Landau minimizer problem; no independent verification located in this hourly pass. No documented AI role found in the checked paper metadata/abstract.
PRIMARY PAPER ↗SIGNIFICANCE6.2/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
16 Aug 2026Metric geometry / optimization
Maximum-area small polygon problem (even orders)
The Maximum-Area Small Polygon Problem
arXiv v1 claims an exact solution of the previously open even-order cases n>=8; combined with classical odd-order and known n=4,6 cases this yields an exact solution for all n>=3. No independent verification located in this hourly pass; no documented AI role found in the checked metadata/abstract.
PRIMARY PAPER ↗SIGNIFICANCE6.6/10
EVIDENCE88/100
FULLAI-LED
16 Aug 2026Probability / harmonic analysis
Talagrand's convolution conjecture
Weak-Type Bounds for Convolution on the Boolean Hypercube
The preprint explicitly claims to prove Talagrand's 1989 conjecture and states that the proof was discovered by the Odin Automatic AI Research Agent. Final proofs were reorganized by the authors. Independent expert review remains pending.
PRIMARY PAPER ↗SIGNIFICANCE8.1/10
EVIDENCE82/100
FULLAI-ASSISTED
16 Aug 2026Quantum Information / Mathematical Physics
Lesniewski–Ruskai Conjecture 4.9
A minimal qutrit counterexample to Conjecture 4.9 of Lesniewski and Ruskai
The paper gives an explicit exact qutrit counterexample and states dimension three is minimal among full matrix algebras. AI-use disclosure says GPT-5.6 Sol assisted literature retrieval, exact symbolic arithmetic checks and preparation of an initial draft; responsibility for mathematical statements remains with the author. This is documented AI assistance but not evidence that AI generated the core discovery.
PRIMARY PAPER ↗SIGNIFICANCE5.9/10
EVIDENCE90/100
FULLAI ROLE UNCLEAR
15 Aug 2026Commutative Algebra
Bi-UF Positive Conjecture
The Bi-UF Positive Conjecture Holds
The arXiv paper explicitly states and proves the 2021 Bi-UF Positive Conjecture. No AI contribution is documented in the paper metadata/abstract checked in this run.
PRIMARY PAPER ↗SIGNIFICANCE5.6/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
15 Aug 2026Probability
Wide-sense regenerative structure for Harris recurrent continuous-time Markov processes
A Harris recurrent continuous-time Markov process without wide-sense regenerative structure
arXiv v1 gives a counterexample and a negative answer to an open problem first raised in the 1990s and later posed in Glynn (2011). No independent verification located in this hourly pass; no documented AI role found in the checked metadata/abstract.
PRIMARY PAPER ↗SIGNIFICANCE6.0/10
EVIDENCE87/100
FULLAI ROLE UNCLEAR
14 Aug 2026Combinatorics / Information Theory
Tu–Deng conjecture
Proof of the TuDeng Conjecture
arXiv v1 explicitly claims a complete proof of the 2011 Tu–Deng conjecture; no independent verification located in this hourly pass. No documented AI contribution found in the paper metadata/abstract checked.
PRIMARY PAPER ↗SIGNIFICANCE6.6/10
EVIDENCE88/100
FULLAI ROLE UNCLEAR
14 Aug 2026Functional analysis / Grothendieck inequalities
König constant / high-dimensional König-form question
The König constant is one
The arXiv preprint proves the defined König constant equals 1 and states this gives a negative answer to the high-dimensional aspect of the Braverman–Makarychev–Makarychev–Naor question. This is a primary preprint claim; no independent verification or peer review was located in this watch pass. The paper does not document a material AI contribution in the available abstract, so AI role remains unclear and it must not affect AI-for-Science or ASI scores.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE72/100
FULLAI ROLE UNCLEAR
13 Aug 2026Functional analysis / Banach spaces
Banach isometric conjecture
A solution to Banach's isometric conjecture
The primary arXiv paper states that it proves every remaining odd-dimensional case; together with Gromov's even-dimensional result, this completes Banach's isometric conjecture in the real case. No material AI role is documented in the primary source checked here, so the result is tracked as mathematical-progress context only and does not affect ASI Readiness or AI-for-Science maturity.
PRIMARY PAPER ↗SIGNIFICANCE8.2/10
EVIDENCE88/100
PARTIALAI ROLE UNCLEAR
13 Aug 2026Mathematical analysis
Generalized Chang–Yang conjecture
A positive answer to the generalized Chang-Yang conjecture on S^N
Paper proves the generalized Chang–Yang conjecture only for axially symmetric functions for N≥3; this is a restricted case, not closure of the full conjecture.
PRIMARY PAPER ↗SIGNIFICANCE8.0/10
EVIDENCE90/100
FULLAI ROLE UNCLEAR
12 Aug 2026Group theory
Kourovka Problem 21.87
Generation of finite groups from subgroups of coprime index
The paper gives an affirmative answer to Kourovka Problem 21.87. The arXiv listing notes supporting proof-audit materials, but no documented AI contribution was identified in the arXiv record.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE84/100
FULLAI CO-DEVELOPED
12 Aug 2026Graph theory / reconstruction
Strong Graph Reconstruction Conjecture / Bowler–Brown–Fenner deck-overlap bound
Nonisomorphic Graphs Can Share an Arbitrarily Large Fraction of Their Vertex-Deleted Cards
Paper gives an explicit 78-vertex counterexample (51 common cards versus the proposed bound 50) and asymptotic families with overlap fraction approaching 1. Paper itself does not disclose AI use. VibeMathed records author public statements that GPT-5.6 Sol proved many intermediate theorems while the decisive construction idea/direction was human-supplied; therefore AI role is co_developed, not ai_led. VibeMathed checked the paper and linked repository but did not independently verify the construction; Kelly–Ulam reconstruction conjecture remains untouched.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE82/100
FULLAI ROLE UNCLEAR
12 Aug 2026Combinatorics / graph theory
Total regularity problem for almost mixed Moore graphs
On the Total Regularity of Almost Mixed Moore Graphs
The paper states that it settles the open problem posed by Tuite and Erskine concerning total regularity of almost mixed Moore graphs and derives a classification consequence. No documented AI contribution found in the arXiv record.
PRIMARY PAPER ↗SIGNIFICANCE5.0/10
EVIDENCE84/100
PARTIALAI ROLE UNCLEAR
12 Aug 2026Probability / convex geometry
Ellipsoid fitting conjecture
Sharp Phase Transition for Ellipsoid Fitting
The paper claims resolution up to a vanishing factor and establishes the sharp phase transition at d^2/4. Because the statement retains an asymptotically vanishing factor rather than an exact finite-d threshold, classified as partial rather than full. No documented AI contribution found in the arXiv record.
PRIMARY PAPER ↗SIGNIFICANCE6.5/10
EVIDENCE88/100
PARTIALAI CO-DEVELOPED
11 Aug 2026Functional analysis / theoretical computer science
Grothendieck constant
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
The exact value remains open. The collaboration materially tightened both sides of the interval and determined the previously unknown tenths digit. The methodology paper states that the AI research system discovered and first proved the lower bound K_G >= 6π/11; the human authors subsequently verified and revised the proof. The upper-bound framework included prior human/AI work and human steering, so co_developed is more accurate than AI-led.
PRIMARY PAPER ↗SIGNIFICANCE8.4/10
EVIDENCE92/100
FULLAI CO-DEVELOPED
11 Aug 2026Enumerative combinatorics
Spahn–Zeilberger third challenge: holonomicity of restricted permutation counts
Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics, with an Account of the Human-Machine Methodology Employed
The v2 paper reports an affirmative solution. It states that Claude generated the mathematical ideas, proofs and verification code, while the human author selected problems, executed computations and enforced the verification protocol. VibeMathed checked the disclosure on 2026-08-21; scripts were not independently rerun.
PRIMARY PAPER ↗SIGNIFICANCE5.9/10
EVIDENCE84/100
FULLAI CO-DEVELOPED
11 Aug 2026Enumerative combinatorics
Five-dimensional Geode Challenge of Amdeberhan, Kauers and Zeilberger
Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics, with an Account of the Human-Machine Methodology Employed
The v2 paper reports the five-dimensional Geode challenge as settled. It states that Claude generated mathematical ideas, proofs and verification code, while the human author selected problems, executed computations and enforced the verification protocol. VibeMathed checked the disclosure on 2026-08-21; independent review is pending.
PRIMARY PAPER ↗SIGNIFICANCE5.8/10
EVIDENCE84/100
FULLAI ROLE UNCLEAR
11 Aug 2026Metric geometry / combinatorics / number theory
Five-distance conjectured bound for convex norms
The Five Distance Theorem For A Convex Norm
The paper proves the five-distance upper bound for every strictly convex norm in R^2 and explicitly settles the conjectured bound for all l_p norms with 1<p<infinity. No documented AI contribution found in the arXiv record.
PRIMARY PAPER ↗SIGNIFICANCE5.5/10
EVIDENCE86/100
PARTIALAI CO-DEVELOPED
11 Aug 2026Analytic number theory
Riemann Hypothesis — critical-line proportion bound
Critical-line proportion bound for Riemann zeta zeros (67.2%)
Claude-assisted research reportedly raises the proved critical-line proportion from about 41.6% to 67.2%. This is a substantial partial result related to the Riemann Hypothesis, not a proof of RH. Human checking and Lean formalization were reported; external peer review remains incomplete. VibeMathed approved the entry on 2026-08-21 and classifies the result as Lean-checked with the statement-to-formalization correspondence still unaudited; this is new verification evidence, not a new mathematical event.
PRIMARY PAPER ↗SIGNIFICANCE9.0/10
EVIDENCE90/100
FULLAI ROLE UNCLEAR
06 Aug 2026Differential geometry
Existence of non-equivariant embedded Gromov tori
The Existence of Non-Equivariant Gromov Tori
arXiv v1 claims a definitive negative answer for n>=3 to the previously open embedding question for Gromov tori, after the immersion case had already been settled. No independent verification located in this hourly pass; no documented AI role found in the checked metadata/abstract.
PRIMARY PAPER ↗SIGNIFICANCE5.7/10
EVIDENCE86/100
FULLAI-ASSISTED
06 Aug 2026Functional analysis / semigroup theory
Inverse generator problem on Hilbert spaces
A solution to the inverse generator problem and related questions
Primary arXiv v2 inspected: Theorem 1.2 resolves the Hilbert-space inverse generator problem negatively. AI disclosure documents ChatGPT 5.6 Pro assistance on counterexample exploration, Proposition 2.1 basis construction, and constant optimization. No independent mathematical verification yet.
PRIMARY PAPER ↗SIGNIFICANCE7.1/10
EVIDENCE84/100
FULLAI-LED
20 Jul 2026Mathematical physics
Full replica symmetry breaking in the zero-field Sherrington–Kirkpatrick spin glass
Full-RSB in the zero-field Sherrington–Kirkpatrick spin glass
Primary preprint only for the complete theorem. Independent audit finds the Lean artifact conditional on seven analytic inputs; no independent review of the full analytic proof.
PRIMARY PAPER ↗SIGNIFICANCE8.7/10
EVIDENCE64/100
INDEPENDENTLY VERIFIEDAI CO-DEVELOPED
20 Jul 2026Algebraic geometry / polynomial automorphisms
Jacobian Conjecture
Counterexamples to the Jacobian conjecture in dimensions greater than two
Alpöge’s explicit C^3 map was independently checked in exact arithmetic and formally verified. The general conjecture is refuted for all n>=3, while the n=2 case remains open. AI involvement is explicit in the original announcement, which credits Claude Fable 5 with work leading to the construction.
PRIMARY PAPER ↗SIGNIFICANCE9.2/10
EVIDENCE98/100