Open registry federation

Mathematical findings

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

All 639 unreviewed 405 lean verified 136 site confirmed 59 lean checked 25 expert verified 12 contested 2

Imported from VibeMathed under CC BY 4.0. Each record links to its registry entry and named primary source. Registry verification is preserved verbatim.

geometry-topologyJul 28, 2026Significance 15/100Registry: unreviewed

General Position for Planar Line Arrangements and $HD_2(p,3)$

Prior state unknown→proved

improved bounds; the exact Hadwiger-Debrunner numbers remain open

Source authenticatedGeneral Position for Planar Line Arrangements and

HD_2(p,3)

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

mathematical-physicsJul 30, 2026Significance 15/100Registry: unreviewed

Maxwell's Three-Charge Equilibrium Bound

Prior state unknown→proved

the sharp bound for three charges; the general Maxwell bound was separately disproved in July 2026

Source authenticatedMaxwell's Three-Charge Equilibrium Bound →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationAug 5, 2026Significance 15/100Registry: unreviewed

Tight Bound for Online Vertex Cover under Edge Arrivals

Prior state unknown→proved

What is the optimal competitive ratio for online vertex cover when edges arrive one at a time? The paper proves a tight factor-2 lower bound via a reduction in the blueprint framework of Assadi, Jiang and Xiang, closing the gap left by prior work.

Source authenticatedTight Bound for Online Vertex Cover under Edge Arrivals →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyMay 21, 2026Significance 15/100Registry: unreviewed

Mauri and Moraga's Question on Log Calabi-Yau Pairs with Big Boundary

Prior state unknown→disproved

Mauri and Moraga posed a two-part question about log Calabi-Yau pairs whose boundary decomposes into big divisors. Both parts have negative answers.

Source authenticatedMauri and Moraga's Question on Log Calabi-Yau Pairs with Big Boundary →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

quantum-information-computingJul 31, 2026Significance 15/100Registry: unreviewed

Online Shadow Tomography Matching the Classical Bounds

Prior state unknown→proved

Online Shadow Tomography with $\log m$ dependence, while retaining $\mathrm{poly}(\log(d)/\epsilon)$ dependence. Also, matching the best classical bounds for Adaptive Data Analysis

Source authenticatedOnline Shadow Tomography Matching the Classical Bounds →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisJun 16, 2026Significance 15/100Registry: unreviewed

Vinzant's Conjecture on Phase Retrieval Injectivity

Prior state unknown→proved

part (1) of the conjecture

Source authenticatedVinzant's Conjecture on Phase Retrieval Injectivity →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

mathematical-physicsFeb 12, 2026Significance 15/100Registry: unreviewed

Single-Minus Gluon Tree Amplitudes

Prior state unknown→disproved

nonzero on half-collinear complex kinematics, with a closed formula

Source authenticatedSingle-Minus Gluon Tree Amplitudes →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationMay 28, 2026Significance 15/100Registry: unreviewed

The Arborescence-Sampling Barrier for Eulerian Tours

Prior state unknown→proved

Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at $mn$ -type running times coming from arborescence sampling. A randomized algorithm achieves $\widetilde{O}(m^{3/2})$ worst case, breaking that barrier on sparse graphs.

Source authenticatedThe Arborescence-Sampling Barrier for Eulerian Tours →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisMay 25, 2026Significance 15/100Registry: unreviewed

Strong Convergence of Cesaro Means of Firmly Nonexpansive Iterates

Prior state unknown→disproved

Iterates of a firmly nonexpansive operator converge weakly but not strongly, by Genel and Lindenstrauss. Whether their Cesaro means converge strongly was open. They need not: an explicit curve gives a counterexample.

Source authenticatedStrong Convergence of Cesaro Means of Firmly Nonexpansive Iterates →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsAug 1, 2026Significance 15/100Registry: unreviewed

Ehrhart Positivity of Schubitopes

Prior state unknown→disproved

Monical, Tokcan and Yong conjectured that Schubitopes, the generalized permutahedra arising as Newton polytopes of Schubert polynomials and of Demazure characters of $\mathrm{GL}_n$ , are Ehrhart positive. Disproved by an explicit Schubitope whose Ehrhart polynomial has a negative coefficient in its monomial expansion.

Source authenticatedEhrhart Positivity of Schubitopes →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyJul 6, 2026Significance 15/100Registry: unreviewed

Counterexample to the Odd-Dimensional Rank Bound for Abelian p-Group Actions

Prior state unknown→disproved

Moraga conjectured, and Kollár and Zhuang recorded, an odd-dimensional extension of the rank bound for faithful abelian $p$ -group actions on smooth Calabi–Yau varieties. The paper disproves it.

Source authenticatedCounterexample to the Odd-Dimensional Rank Bound for Abelian p-Group Actions →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyJul 29, 2026Significance 15/100Registry: unreviewed

Completeness of Fixed-Order Atom-Centered Descriptors

Prior state unknown→disproved

The key ingredients were already in the literature, decades old and in distant fields; what was missing was anyone connecting them to this question.

Source authenticatedCompleteness of Fixed-Order Atom-Centered Descriptors →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisJul 7, 2026Significance 15/100Registry: unreviewed

Stable Phase Retrieval for Spans of Independent Random Variables

Prior state unknown→proved

After $L^2$ normalization, stable phase retrieval holds over the $L^2$ -spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided $L^1$ bound. This confirms the characterization conjectured by Calderbank, Daubechies, Freeman and Freeman.

Source authenticatedStable Phase Retrieval for Spans of Independent Random Variables →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsJul 23, 2026Significance 15/100Registry: unreviewed

Monical's Saturated Newton Polytope Conjecture

Prior state unknown→disproved

If a chromatic symmetric function is Schur positive, must every finite-variable specialization $X_G(x_1, \dots, x_k)$ have a saturated Newton polytope? A $12$ -vertex bipartite graph realizes weights $(6,6,0)$ and $(8,2,2)$ but omits their midpoint $(7,4,1)$ .

Source authenticatedMonical's Saturated Newton Polytope Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsMar 12, 2026Significance 15/100Registry: unreviewed

Pach's Tangency Conjecture: Improved Bounds

Prior state unknown→proved

Exponent improvements toward Pach's conjecture, which remains open.

Source authenticatedPach's Tangency Conjecture: Improved Bounds →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsJul 14, 2026Significance 15/100Registry: unreviewed

Brualdi's Question on Hamiltonicity of Interchange Graphs

Prior state unknown→proved

The interchange graph $G(R,S)$ has the $(0,1)$ -matrices with row sums $R$ and column sums $S$ as vertices, adjacent when they differ by a single $2\times 2$ interchange. Brualdi asked whether $G(R,S)$ is always Hamiltonian. It satisfies more: it is maximally Hamiltonian, Hamilton-laceable when bipartite and Hamilton-connected when not.

Source authenticatedBrualdi's Question on Hamiltonicity of Interchange Graphs →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsJul 2, 2026Significance 15/100Registry: unreviewed

North-East Lattice Paths with Few Collinear Vertices

Prior state unknown→proved

Both bounds move, and the gap stays enormous: the lower bound rises from $\exp(\Omega(\log^2 k))$ to $\exp(\Omega(k^{1/3}))$ and the upper falls from $\exp(O(k^4))$ to $\exp(O(k^2))$ , so $A(k)$ is still undetermined between an exponent of $k^{1/3}$ and one of $k^2$ . The paper's own closing discussion argues its lower-bound construction is near the limit of the method and that beating it needs additional randomness,…

Source authenticatedNorth-East Lattice Paths with Few Collinear Vertices →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyMay 24, 2026Significance 15/100Registry: unreviewed

Positivity of Chern Classes of Symmetric Powers

Prior state unknown→proved

The total Chern class of $\mathrm{Sym}^d(\mathbb{C}^n)$ as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.

Source authenticatedPositivity of Chern Classes of Symmetric Powers →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationJun 16, 2026Significance 15/100Registry: unreviewed

The Yun-Sra-Jadbabaie SS-RS-GD Inequalities

Prior state unknown→proved

Yun, Sra and Jadbabaie posed as a COLT 2021 open question whether, for well-conditioned symmetric matrices, the operators encoding the expected iterate of single-shuffle SGD, random-reshuffle SGD and gradient descent on a quadratic finite sum satisfy $\|W_{ss}\| \le \|W_{rs}\| \le \|W_{gd}\|$ . They do.

Source authenticatedThe Yun-Sra-Jadbabaie SS-RS-GD Inequalities →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

probability-statisticsMay 12, 2026Significance 15/100Registry: unreviewed

Gaussian Completely Monotone Conjecture

Prior state unknown→disproved

also refutes the McKean and Toscani conjectures

Source authenticatedGaussian Completely Monotone Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisJul 29, 2026Significance 15/100Registry: unreviewed

The Modified Lyons–Sidorova Conjecture for Bounded-Variation Paths

Prior state unknown→proved

This is the MODIFIED conjecture, not the original Lyons-Sidorova one, and it is proved for continuous bounded-variation paths. Prior work had a line-image result under the stronger assumption of infinite radius on every subinterval; this removes that assumption.

Source authenticatedThe Modified Lyons–Sidorova Conjecture for Bounded-Variation Paths →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algebraJun 22, 2026Significance 15/100Registry: unreviewed

Baker's Question on Smooth Hyperplane Sections over Finite Fields

Prior state unknown→disproved

Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must acquire a smooth rational hyperplane section after every sufficiently high-dimensional linearly nondegenerate embedding. Poonen predicted no for every positive-dimensional variety, and that prediction is correct.

Source authenticatedBaker's Question on Smooth Hyperplane Sections over Finite Fields →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

probability-statisticsMay 18, 2026Significance 15/100Registry: unreviewed

Log-Convexity of Fisher Information Along Heat Flow

Prior state unknown→disproved

For every smooth positive density $f$ on $\mathbb{R}^d$ , must the Fisher information $t \mapsto I(f * \gamma_t)$ be log-convex along the heat flow?

Source authenticatedLog-Convexity of Fisher Information Along Heat Flow →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationAug 5, 2026Significance 15/100Registry: unreviewed

The Approximation Ratio for Boolean Max-k-CSP

Prior state unknown→proved

Removes the constant factor from the previous best guarantee; whether $k/2^k$ is optimal is not settled here.

Source authenticatedThe Approximation Ratio for Boolean Max-k-CSP →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationAug 7, 2026Significance 15/100Registry: unreviewed

Facial Distance Patterns in Planar Graphs

Prior state unknown→proved

Three immediate consequences follow for undirected unweighted planar graphs: better compression of the Okamura-Seymour metric, less space for constant-time exact distance oracles, and a faster distributed algorithm.

Source authenticatedFacial Distance Patterns in Planar Graphs →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyJun 30, 2026Significance 15/100Registry: unreviewed

Ziegler's Cross-Polytope Conjecture (simplicial 0/1-polytopes)

Prior state unknown→disproved

Ziegler proved every simplicial $d$ -dimensional 0/1-polytope has at most $2d$ vertices, and asked whether attaining $2d$ vertices forces central symmetry (i.e. a 0/1 cross-polytope). Known true for $d \le 6$ ; open since ~2000.

Source authenticatedZiegler's Cross-Polytope Conjecture (simplicial 0/1-polytopes) →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algebraAug 7, 2026Significance 15/100Registry: unreviewed

The Generalized Vanishing Conjecture

Prior state unknown→disproved

Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, $\Lambda^m(P^m) = 0$ for all large $m$ forces $\Lambda^m(P^m Q) = 0$ for all large $m$ . Refuted by an explicit five-variable counterexample.

Source authenticatedThe Generalized Vanishing Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyJun 9, 2026Significance 15/100Registry: unreviewed

The Sharp Threshold for the Dyn-Farkhi Conjecture

Prior state unknown→proved

pins the sharp threshold; the conjecture itself was already known false above dimension two

Source authenticatedThe Sharp Threshold for the Dyn-Farkhi Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algebraAug 14, 2026Significance 15/100Registry: unreviewed

The Quartic Hessian Conjecture in Dimension Four

Prior state unknown→proved

The Hessian conjecture $HC_n$ asks whether every polynomial $f$ with $\det \mathrm{Hess}(f) \in \mathbb{C}^\times$ has a polynomial gradient inverse. It is known for $n \le 3$ , false for $n \ge 5$ , and open exactly in dimension four, where it implies the plane Jacobian conjecture. Proved for every quartic polynomial in dimension four: the quartic case reduces to $f = P(x_1,x_2,x_3) + x_4 Q(x_1,x_2,x_3) + a x_4^2$ wi…

Source authenticatedThe Quartic Hessian Conjecture in Dimension Four →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisJul 19, 2026Significance 15/100Registry: unreviewed

A Unital Banach Algebra That Is Not a Calkin Algebra

Prior state unknown→proved

The realisation problem asks which unital Banach algebras arise as the Calkin algebra $\mathcal{B}(X)/\mathcal{K}(X)$ of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.

Source authenticatedA Unital Banach Algebra That Is Not a Calkin Algebra →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

mathematical-physicsJul 8, 2026Significance 15/100Registry: unreviewed

Remodeling for the Affine Binary Dihedral Calabi–Yau Threefold

Prior state unknown→proved

A variant rather than the BKMP conjecture itself: the target lies outside the toric setting the conjecture addresses.

Source authenticatedRemodeling for the Affine Binary Dihedral Calabi–Yau Threefold →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algebraJul 23, 2026Significance 15/100Registry: unreviewed

The Liu-Morin Extension Conjecture

Prior state unknown→proved

Han's conjecture itself remains open; this settles the Liu-Morin extension case

Source authenticatedThe Liu-Morin Extension Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsAug 4, 2026Significance 15/100Registry: unreviewed

The Bandelt-Dress Quartet Distance Conjecture

Prior state unknown→proved

The quartet distance counts the four-leaf subsets on which two binary phylogenetic trees display different topologies. Bandelt and Dress conjectured the maximum over trees on $n$ leaves. Proved: it is $(2/3 + o(1))\binom{n}{4}$ , by reducing arbitrary pairs of trees to caterpillars through a common-root planarization and an identity on five-leaf trees.

Source authenticatedThe Bandelt-Dress Quartet Distance Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsMay 8, 2026Significance 15/100Registry: unreviewed

The Escobar-Klein-Weigandt Conjecture on Cohen-Macaulay ASM Varieties

Prior state unknown→proved

Escobar, Klein and Weigandt proved that gradedness of an ASM weak order interval, constancy of Coxeter length across its fibres, and equidimensionality of the associated ASM varieties are mutually equivalent, and conjectured (Conjecture 3.21) that Cohen-Macaulayness of those varieties belongs on the same list. Proved, via a $0$ -Hecke monoid action on the MacNeille completion of Bruhat order and vertex-decomposabilit…

Source authenticatedThe Escobar-Klein-Weigandt Conjecture on Cohen-Macaulay ASM Varieties →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

quantum-information-computingJul 15, 2026Significance 15/100Registry: unreviewed

Quantum Memory Advantage for Process Tomography

Prior state unknown→proved

Does quantum memory give a query-complexity advantage for learning an unknown quantum channel, when protocols without it must measure after each channel use and keep only a classical transcript? It does, and the paper also determines how little coherent memory suffices for the advantage to appear.

Source authenticatedQuantum Memory Advantage for Process Tomography →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationAug 3, 2026Significance 15/100Registry: unreviewed

The Axiotis-Sviridenko Condition-Number Conjecture

Prior state unknown→proved

Conditional on the randomized exact-volume Small-Set Expansion Hypothesis, and stated for least-squares objectives rather than sparse convex optimization in general.

Source authenticatedThe Axiotis-Sviridenko Condition-Number Conjecture →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review