Open registry federation

Mathematical findings

690 source-grounded records. Verification labels remain separate from source authentication and publication status.

All 690 unreviewed 432 lean verified 144 site confirmed 66 lean checked 33 expert verified 13 contested 2

Editorial data from VibeMathed is CC BY 4.0 licensed. Linked papers and authors’ text retain their own rights. Each record links to its registry entry and primary source. Verification labels are attributed to the registry.

number-theoryMay 31, 2026Significance 25/100Registry: unreviewed

Gaussian Mass Maximality of the Integer Lattice

Prior state unknown→proved

integral unimodular lattices of rank at most 32; the general conjecture is open

Source authenticatedGaussian Mass Maximality of the Integer Lattice →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsJul 27, 2026Significance 25/100Registry: unreviewed

Unimodality of Kazhdan-Lusztig Polynomials of Matroids

Prior state unknown→disproved

VibeMathed recorded: Unimodality of Kazhdan-Lusztig Polynomials of Matroids. Consult the linked registry entry for the original report and scope.

Source authenticatedUnimodality of Kazhdan-Lusztig Polynomials of Matroids →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisAug 5, 2026Significance 25/100Registry: lean checked

Gabor Frames of Totally Positive Functions

Prior state unknown→proved

VibeMathed recorded: Gabor Frames of Totally Positive Functions. Consult the linked registry entry for the original report and scope.

Source authenticatedGabor Frames of Totally Positive Functions →

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geometry-topologyMar 11, 2026Significance 25/100Registry: unreviewed

Kissing Number in 19 Dimensions

Prior state unknown→proved

A record lower bound; the kissing number in dimension 19 remains unknown.

Source authenticatedKissing Number in 19 Dimensions →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationAug 3, 2026Significance 25/100Registry: unreviewed

Approximating Two-Terminal Network Reliability

Prior state unknown→proved

VibeMathed recorded: Approximating Two-Terminal Network Reliability. Consult the linked registry entry for the original report and scope.

Source authenticatedApproximating Two-Terminal Network Reliability →

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probability-statisticsJul 20, 2026Significance 25/100Registry: site confirmed

Gaussian Moments Conjecture

Prior state unknown→disproved

Explicit counterexamples in dimensions 3 and 4, so GMC(n) fails for every n >= 3; GMC(1) was already known, and a separate human-authored preprint claims the remaining n = 2 case affirmatively

Source authenticatedGaussian Moments Conjecture →

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analysisAug 3, 2026Significance 25/100Registry: unreviewed

Kalton-Peck Space and its Hyperplanes

Prior state unknown→proved

VibeMathed recorded: Kalton-Peck Space and its Hyperplanes. Consult the linked registry entry for the original report and scope.

Source authenticatedKalton-Peck Space and its Hyperplanes →

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quantum-information-computingJul 28, 2026Significance 25/100Registry: unreviewed

Existence of Bipartite Bound Information

Prior state unknown→proved

VibeMathed recorded: Existence of Bipartite Bound Information. Consult the linked registry entry for the original report and scope.

Source authenticatedExistence of Bipartite Bound Information →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsAug 1, 2026Significance 25/100Registry: lean verified

Erdős Problem #146: Degeneracy Conjecture

Prior state unknown→disproved

VibeMathed recorded: Erdős Problem #146: Degeneracy Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #146: Degeneracy Conjecture →

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combinatoricsJul 10, 2026Significance 25/100Registry: unreviewed

A Counterexample to Nivat's Conjecture for a Non-Convex Window

Prior state unknown→disproved

VibeMathed recorded: A Counterexample to Nivat's Conjecture for a Non-Convex Window. Consult the linked registry entry for the original report and scope.

Source authenticatedA Counterexample to Nivat's Conjecture for a Non-Convex Window →

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geometry-topologyJul 13, 2026Significance 25/100Registry: unreviewed

Tightness of the Cohn-Elkies Bound in Dimension 36

Prior state unknown→disproved

rules out the two-point LP method in this dimension; the optimal packing in dimension 36 remains unknown

Source authenticatedTightness of the Cohn-Elkies Bound in Dimension 36 →

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combinatoricsJul 17, 2026Significance 25/100Registry: unreviewed

Feige's Hypergraph Moore-Bound Conjecture

Prior state unknown→proved

VibeMathed recorded: Feige's Hypergraph Moore-Bound Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedFeige's Hypergraph Moore-Bound Conjecture →

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number-theorySep 6, 2026Significance 22/100Registry: lean checked

$(\xi\alpha^n)_{n\ge1}$ is not uniformly distributed modulo one for Pisot $\alpha$ and $\xi$ in the Cantor set $C(\alpha)$

proved→proved

The problem is open, and the repository says so: what is proved are criteria for it and two instances, not the general case. Every compared statement that concludes Problem 10.61 does so for a quadratic setup - a real root $\alpha > 1$ of $X^2 - aX - b$ whose conjugate has modulus below one - and both instances are quadratic. The arbitrary-degree material is conditional ingredients: for the family…

Source authenticated

(\xi\alpha^n)_{n\ge1}

is not uniformly distributed modulo one for Pisot

\alpha

and

\xi

in the Cantor set

C(\alpha)

→

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologySep 5, 2026Significance 22/100Registry: unreviewed

Does there exist a bijection of $\mathbb{R}^n$ to itself such that the forward map is connected but the inverse is not?

Prior state unknown→disproved

Answered in the negative for every $n\ge 2$ . The preprint constructs a bijection $F:\mathbb R^n\to\mathbb R^n$ that maps every connected set to a connected set, is continuous exactly off the closed ray $[0,\infty)\times\{0\}^{n-1}$ , and pulls the straight segment $\{(1,0,\dots,0)\}\times[0,1]$ back to the middle-thirds Cantor set on that ray, so $F^{-1}$ is not connectedness-preserving. The construction extends a th…

Source authenticatedDoes there exist a bijection of

\mathbb{R}^n

to itself such that the forward map is connected but the inverse is not? →

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combinatoricsSep 2, 2026Significance 22/100Registry: unreviewed

Anari's Bethe permanent conjecture

Prior state unknown→proved

For every nonnegative $n\times n$ matrix $A$ whose bipartite support graph has girth at least an even integer $g\ge4$ , Dong and Jain prove the sharp inequality $\operatorname{Bethe}(A)\le\operatorname{per}(A)\le2^{2n/g}\operatorname{Bethe}(A).$ The factor $2^{2n/g}$ is optimal whenever $g\mid2n$ , attained by matrices whose support graphs are disjoint unions of $g$ -cycles. Thus the result confirms Anari's conjectur…

Source authenticatedAnari's Bethe permanent conjecture →

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geometry-topologySep 3, 2026Significance 22/100Registry: unreviewed

The Equality Case of Ehrhart's Volume Conjecture

proved→proved

the equality case; the inequality was settled separately and is tracked on its own entry

Source authenticatedThe Equality Case of Ehrhart's Volume Conjecture →

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analysisNov 19, 2025Significance 22/100Registry: unreviewed

Sum-Difference Exponents for Boundedly Many Slopes

Prior state unknown→proved

Charts the bounded-slope regime of the arithmetic Kakeya program; the conjecture itself remains open.

Source authenticatedSum-Difference Exponents for Boundedly Many Slopes →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyAug 10, 2026Significance 22/100Registry: unreviewed

The Hyperkahler Period-Index Conjecture

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 authenticatedThe Hyperkahler Period-Index Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisAug 6, 2026Significance 22/100Registry: unreviewed

The Inverse Generator Problem on Hilbert Spaces

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 authenticatedThe Inverse Generator Problem on Hilbert Spaces →

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geometry-topologyAug 27, 2026Significance 22/100Registry: unreviewed

Large systoles in every sufficiently large genus

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 authenticatedLarge systoles in every sufficiently large genus →

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probability-statisticsJan 14, 2026Significance 22/100Registry: unreviewed

Courtade and Kumar's Coordinate-wise Mutual Information Question

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 authenticatedCourtade and Kumar's Coordinate-wise Mutual Information Question →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algebraAug 4, 2026Significance 22/100Registry: unreviewed

Finite Generation for klt Generalized Pairs

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 authenticatedFinite Generation for klt Generalized Pairs →

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analysisAug 9, 2026Significance 22/100Registry: unreviewed

The Planar Berenstein Conjecture

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 authenticatedThe Planar Berenstein Conjecture →

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quantum-information-computingAug 5, 2026Significance 22/100Registry: unreviewed

Completeness of Maximally Entangled States for Pseudo-Telepathy

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 authenticatedCompleteness of Maximally Entangled States for Pseudo-Telepathy →

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combinatoricsAug 1, 2026Significance 21/100Registry: lean verified

Erdős Problem #183: Multicolor Triangle Ramsey

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #183: Multicolor Triangle Ramsey. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #183: Multicolor Triangle Ramsey →

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geometry-topologyAug 13, 2026Significance 20/100Registry: unreviewed

Courtade's conjecture on volumes of Minkowski sums with the ball

Prior state unknown→disproved

Courtade conjectured that for convex bodies $B,C\subset\mathbb R^n$ , $(|B||C|)^{1/n} + (|B_2^n||B_2^n+B+C|)^{1/n} \le |B_2^n+B|^{1/n}|B_2^n+C|^{1/n}.$ The paper proves that this inequality is false in every dimension $n\ge3$ . 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 authenticatedCourtade's conjecture on volumes of Minkowski sums with the ball →

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combinatoricsSep 4, 2026Significance 20/100Registry: unreviewed

Cycle-residue stability at minimum degree five

Prior state unknown→proved

The preprint claims an exact classification. Write $C_5(G)$ for the residues modulo five represented by cycle lengths in $G$ . Let $\mathcal E_5={K_6,K_{5,5}}\cup{H_{5,n;t}:2\le t\le5<n}$ , where $H_{5,n;t}$ is obtained from $K_{5,n}$ 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 authenticatedCycle-residue stability at minimum degree five →

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analysisSep 1, 2026Significance 20/100Registry: unreviewed

McKean Entropy-Production Conjecture

Prior state unknown→disproved

For the space-homogeneous Boltzmann equation in dimension $3$ with collision kernels $B=\frac{1}{4\pi}|v-v_*|^\gamma,\qquad \gamma\in[0,1],$ the paper constructs smooth, positive, radial mixtures $f_R=(1-p)M_1+pM_R$ for which $\partial_tD(f_R)>0$ for sufficiently large $R$ . Thus entropy production need not decrease even for Maxwell molecules ( $\gamma=0$ ) or hard spheres ( $\gamma=1$ ), negatively resolving McKean's…

Source authenticatedMcKean Entropy-Production Conjecture →

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logic-foundationsSep 4, 2026Significance 20/100Registry: unreviewed

Equivalence of generic stability notions for Keisler measures

proved→proved

Let $T$ be a complete first-order theory in discrete or continuous logic, let $M\prec\mathcal{U}$ , and let $\mu\in\mathfrak{M}_{x}(\mathcal{U})$ be Borel-definable over $M$ . The paper proves that the following three conditions are equivalent: $(i)$ $\mu$ is a frequency interpretation measure (fim) over $M$ ; $(ii)$ $\mu$ is definable over $M$ and its canonical random extension $r_{\mu}$ is generically stable over…

Source authenticatedEquivalence of generic stability notions for Keisler measures →

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geometry-topologySep 3, 2026Significance 20/100Registry: unreviewed

Han and Jiang's Question on klt Type in Flat Families

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 authenticatedHan and Jiang's Question on klt Type in Flat Families →

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geometry-topologySep 3, 2026Significance 20/100Registry: unreviewed

Kollár and Kovács's Question on Cohomology of Fibers

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 authenticatedKollár and Kovács's Question on Cohomology of Fibers →

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probability-statisticsJul 15, 2026Significance 20/100Registry: unreviewed

Cutoff for Kac's Walk on the Sphere

Prior state unknown→proved

the conjectured cutoff location of 2n log n is wrong

Source authenticatedCutoff for Kac's Walk on the Sphere →

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probability-statisticsMay 22, 2026Significance 20/100Registry: unreviewed

Optimal Vector Balancing for Zonotopes

Prior state unknown→proved

VibeMathed recorded: Optimal Vector Balancing for Zonotopes. Consult the linked registry entry for the original report and scope.

Source authenticatedOptimal Vector Balancing for Zonotopes →

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geometry-topologyMay 27, 2026Significance 20/100Registry: unreviewed

The Aluffi-Chen-Marcolli Real-Rootedness Conjecture

Prior state unknown→proved

VibeMathed recorded: The Aluffi-Chen-Marcolli Real-Rootedness Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedThe Aluffi-Chen-Marcolli Real-Rootedness Conjecture →

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theoretical-computer-scienceJun 24, 2026Significance 20/100Registry: unreviewed

Quadratic-Time Hardness of Furthest Pair in Superconstant Dimension

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 authenticatedQuadratic-Time Hardness of Furthest Pair in Superconstant Dimension →

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analysisJul 23, 2026Significance 20/100Registry: unreviewed

Uniqueness of the Faber–Krahn Position of Convex Bodies

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 authenticatedUniqueness of the Faber–Krahn Position of Convex Bodies →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review