combinatoricsSep 2, 2026Significance 22/100Registry: unreviewed
Prior state unknown→proved
For every nonnegative n×n matrix A whose bipartite support graph has girth at least an even integer g≥4, Dong and Jain prove the sharp inequality
Bethe(A)≤per(A)≤22n/gBethe(A).
The factor 22n/g is optimal whenever g∣2n, attained by matrices whose support graphs are disjoint unions of g-cycles. Thus the result confirms Anari's conjectur…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologySep 3, 2026Significance 22/100Registry: unreviewed
proved→proved
the equality case; the inequality was settled separately and is tracked on its own entry
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
probability-statisticsJan 14, 2026Significance 22/100Registry: unreviewed
Prior state unknown→proved
Fully resolves the posed coordinate-wise question; the main Courtade-Kumar conjecture itself remains open outside the extended high-noise range.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyAug 27, 2026Significance 22/100Registry: unreviewed
Prior state unknown→proved
The theorem improves the best lower bound valid in *every* sufficiently large genus from asymptotic constant 2/9 to 1. The every-genus ladder it climbs is Katz-Sabourau's 19/120 and then Liu-Petri's 2/9, the latter also by a random construction. Constant 1 was already reached by Petri-Walker along a subsequence of genera, following Erdos-Sachs, so the new contribution is achieving it uniformly rather than…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyAug 10, 2026Significance 22/100Registry: unreviewed
Prior state unknown→disproved
The counterexamples come with divisibility bounds on the Hodge-theoretic index, at 2-torsion and 5-torsion, on very general hyperkahler fourfolds.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
algebraAug 4, 2026Significance 22/100Registry: unreviewed
Prior state unknown→disproved
The paper records how stuck this was: the first author had discussed the question with Caucher Birkar, Osamu Fujino, Christopher D. Hacon, Junpeng Jiao, Vladimir Lazic and Lingyao Xie, and writes that despite a general feeling that a negative answer was likely, no precise counterexample could be found. The authors also note that, given the limitations of generative AI, they may have missed related literature and wel…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisAug 9, 2026Significance 22/100Registry: unreviewed
Prior state unknown→disproved
The domain has dihedral symmetry of order 26 and is neither a disc nor centrally symmetric, and its eigenfunction changes sign - which is why an additional sign assumption rescues the statement.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisNov 19, 2025Significance 22/100Registry: unreviewed
Prior state unknown→proved
Charts the bounded-slope regime of the arithmetic Kakeya program; the conjecture itself remains open.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
quantum-information-computingAug 5, 2026Significance 22/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Completeness of Maximally Entangled States for Pseudo-Telepathy. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisAug 6, 2026Significance 22/100Registry: unreviewed
Prior state unknown→disproved
One finite-dimensional construction settles several related questions. Besides the inverse generator problem, it gives a generator whose Cayley transforms satisfy the ordinary Kreiss resolvent condition but are neither strongly Kreiss bounded nor power bounded, and it shows the Crank-Nicolson scheme is unstable in operator norm both over long times at fixed step size and under mesh refinement at fixed final time. Ve…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyAug 13, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
Courtade conjectured that for convex bodies B,C⊂Rn,
(∣B∣∣C∣)1/n+(∣B2n∣∣B2n+B+C∣)1/n≤∣B2n+B∣1/n∣B2n+C∣1/n.
The paper proves that this inequality is false in every dimension n≥3. In dimension 3, it gives an explicit geometric counterexample using two orthogonal double bodies of revolution. It then strengthens this by constructing zonoid counterexamples in every d…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
combinatoricsSep 4, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
The preprint claims an exact classification. Write C5(G) for the residues modulo five represented by cycle lengths in G. Let
E5=K6,K5,5∪H5,n;t:2≤t≤5<n,
where H5,n;t is obtained from K5,n by deleting 5−t edges incident with one vertex in the part of size n.
For every finite simple graph G with minimum degree at least five, exactly one alternative holds:…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisSep 1, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
For the space-homogeneous Boltzmann equation in dimension 3 with collision kernels
B=4π1∣v−v∗∣γ,γ∈[0,1],
the paper constructs smooth, positive, radial mixtures fR=(1−p)M1+pMR for which ∂tD(fR)>0 for sufficiently large R. Thus entropy production need not decrease even for Maxwell molecules (γ=0) or hard spheres (γ=1), negatively resolving McKean's…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
logic-foundationsSep 4, 2026Significance 20/100Registry: unreviewed
proved→proved
Let T be a complete first-order theory in discrete or continuous logic, let M≺U, and let μ∈Mx(U) be Borel-definable over M. The paper proves that the following three conditions are equivalent:
(i) μ is a frequency interpretation measure (fim) over M;
(ii) μ is definable over M and its canonical random extension rμ is generically stable over…
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologySep 3, 2026Significance 20/100Registry: unreviewed
disproved→disproved
VibeMathed recorded: Kollár and Kovács's Question on Cohomology of Fibers. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologySep 3, 2026Significance 20/100Registry: unreviewed
disproved→disproved
VibeMathed recorded: Han and Jiang's Question on klt Type in Flat Families. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
combinatoricsJul 21, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Norine's Antipodal-Colouring Conjecture. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisAug 3, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Sharpness of Denjoy's Theorem. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisJul 24, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: The Graveyard Problem for Dissipative Barrier Truncations. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyJun 26, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Erdos's Question on the Independence Ratio of Unit-Distance Graphs. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyJul 27, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Kuperberg's Six-Cylinder Conjecture. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
algebraJul 27, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
theoretical-computer-scienceJun 24, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Quadratic-Time Hardness of Furthest Pair in Superconstant Dimension. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
probability-statisticsMay 12, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Maximum Entropy of Sums of Independent Ternary Random Variables. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyApr 28, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
resolves the noncommutative half of the Kirby-list problem
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
mathematical-physicsJul 29, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Sharp Bounds on the Ground State Energy of the SYK Model. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisJul 19, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Weakly Compact Factorization Through a Space With a Basis. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
combinatoricsJul 16, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
improves the classical recurrence; the exact Schur numbers beyond S(5) remain unknown
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
theoretical-computer-scienceJul 22, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
information-theoretic; a polynomial-time implementation remains open
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisJul 16, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Belinskaya's Theorem for Measure-Preserving Flows. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Two Counterexamples in the Geometry of Numbers. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyJul 22, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
also disproves a separate finite-field conjecture of Hunter, Pohoata, Verstraete and Zhang
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
probability-statisticsJul 3, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: The Signed BAR Uniqueness Problem. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
theoretical-computer-scienceMay 4, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Odifreddi's Problem 3 on Irreducible m-Degrees. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisJul 23, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Uniqueness of the Faber–Krahn Position of Convex Bodies. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisJul 29, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
A partial result. Fuglede's conjecture remains open for finite cyclic groups generally; this settles an infinite family and, for the spectral-to-tiling direction, only under rapid growth of the prime factors.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review