analysisJul 29, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: The Lukic Conjecture. Consult the linked registry entry for the original report and scope.
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mathematical-physicsJul 30, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
a record upper bound; the exact constant remains unknown
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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.
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probability-statisticsJul 15, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: The Weak Simplex Conjecture. Consult the linked registry entry for the original report and scope.
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geometry-topologyAug 4, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
Chen, Nie and Xu prove a Nakai–Moishezon-type numerical criterion for a broad class of complex Hessian-type equations on compact projective manifolds. In particular, Corollary 1.3 gives a uniform version of Székelyhidi’s conjecture for complex Hessian quotient equations, while Corollary 1.5 proves the uniform version, formulated by Murakami, for complex k-Hessian equations. However, the results assume projectivity a…
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combinatoricsAug 7, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: The Anstee-Sali Conjecture on Forbidden Configurations. Consult the linked registry entry for the original report and scope.
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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
combinatoricsJun 23, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
an improved lower bound; the true order of g(r) remains open
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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
combinatoricsAug 30, 2025Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Babai and Frankl's Oddtown Question for Composite Moduli. 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 29, 2026Significance 20/100Registry: lean verified
Prior state unknown→proved
New arXiv preprint with an author-provided Lean formalization; not yet peer-reviewed.
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combinatoricsJul 14, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Record Compositions of Alternating Permutations. Consult the linked registry entry for the original report and scope.
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algorithms-optimizationJul 22, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Dinitz-Garg-Goemans 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
theoretical-computer-scienceMay 29, 2026Significance 20/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Steurer's Conjecture on Vectors with Small Average Correlation. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisMay 23, 2026Significance 20/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Brezis's Problems on Degenerate Constants in Degree Inequalities. Consult the linked registry entry for the original report and scope.
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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.
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combinatoricsSep 1, 2026Significance 18/100Registry: unreviewed
Prior state unknown→disproved
The paper disproves both the Burness–Giudici common neighbour conjecture for primitive groups of base size 2 and its later generalisation to arbitrary base size. For every integer B≥2, it constructs infinitely many primitive permutation groups of base size B whose generalised Saxl graphs contain two nonadjacent vertices with no common neighbour. At base size 2, it gives infinite counterexample families of…
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algorithms-optimizationAug 29, 2026Significance 18/100Registry: unreviewed
Prior state unknown→proved
The paper proves that there exists a randomized voting rule using only ordinal rankings with metric distortion at most 11641/5000=2.3282. This improves the previous best upper bound of 2.5 and closes about 44% of the gap to the known asymptotic lower bound of approximately 2.1126. It does not determine the optimal randomized metric distortion: for m≥4, the exact optimum and its asymptotic limit remain o…
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algebraAug 21, 2026Significance 18/100Registry: unreviewed
Prior state unknown→disproved
A negative answer to Heuer and Löh's question: the isomorphism type of a one-relator group ⟨S∣r⟩ does not determine sclS(r). The witnesses are r=aabABabABBAbaabABBAb and r′=aabABabABabABBAbaBAb, both length 20 in F2′, with ⟨a,b∣r⟩≅⟨a,b∣r′⟩ but scl(r)=1 against scl(r′)=1/2.
The mechanism is what ma…
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logic-foundationsAug 27, 2026Significance 18/100Registry: unreviewed
Prior state unknown→disproved
The paper proves that not every Heyting algebra can occur as the lattice of subterminal objects of an elementary topos. Specifically, the free Heyting algebra F2 on two generators cannot occur.
Using Bellissima’s representation F2↪O↑(K2), the authors construct an upward-closed subset A⊆K2 with A∈/F2. They show that if some elementary topos E satis…
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analysisMar 23, 2026Significance 18/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Lower Bounds for Lebesgue Constants and an Erdős-Turán Interpolation Problem. Consult the linked registry entry for the original report and scope.
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theoretical-computer-scienceAug 6, 2026Significance 18/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Approximate Counting for Spin Systems on Planar 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
theoretical-computer-scienceAug 8, 2026Significance 18/100Registry: unreviewed
Prior state unknown→proved
An average-case claim about the Gaussian model, not a contradiction of the worst-case NP-hardness of integer least squares. If it holds, no computational-statistical gap separates polynomial-time detection from exhaustive maximum likelihood at first order in this model.
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combinatoricsAug 3, 2026Significance 18/100Registry: unreviewed
Prior state unknown→disproved
one construction disproves both the product conjecture and its weak form
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number-theoryAug 7, 2026Significance 18/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: The Umans-Wang Arithmetic-Progression Divisor 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
combinatoricsMay 19, 2026Significance 17/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Conjectures of Hopkins, Sagan-Wilson and Defant et al. on Lattices, Parking Functions and the Plactic Monoid. Consult the linked registry entry for the original report and scope.
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algebraJul 20, 2026Significance 16/100Registry: lean verified
Prior state unknown→proved
VibeMathed recorded: Kourovka Problem 3.46 - Maximal Locally Soluble Normal Subgroups. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
quantum-information-computingAug 20, 2026Significance 16/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: The Fractional Colouring Conjecture for Triply Efficient Pauli Shadow Tomography. Consult the linked registry entry for the original report and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
combinatoricsAug 11, 2026Significance 16/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Conjectures 2a and 2b of Kauers and Zeilberger. Consult the linked registry entry for the original report and scope.
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geometry-topologyAug 21, 2026Significance 16/100Registry: unreviewed
Prior state unknown→disproved
Disproved on the Hopf threefold X=(C3∖{0})/⟨z↦e−1z⟩: Xia and Zhang construct a smooth Hermitian form ω and smooth functions φj with ω+ddcφj>0 whose Monge-Ampère masses tend to infinity, so the universal bounded mass property fails already in complex dimension three. The construction uses the Hopf threefold's elliptic fibration, an exact mass…
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probability-statisticsAug 27, 2026Significance 15/100Registry: lean checked
Prior state unknown→proved
No such pair exists: for every positive integer m and every n, (Dn,2m) is rate-monotonic (Theorem A), and more generally so is every inversion extension of a finite abelian group by an involution, a family containing the generalized dihedral, dicyclic and generalized quaternion groups (Theorem B). The picture is completed in the other direction: for every real p≥1 that is not an even integer there is an…
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geometry-topologyJun 1, 2026Significance 15/100Registry: unreviewed
Prior state unknown→proved
Both problems are answered affirmatively, in every dimension at once: every connectedness-preserving injection from a connected closed n-manifold into an n-manifold is a homeomorphism onto a component, so in particular every Darboux self-bijection of Sn and of every closed manifold is a homeomorphism. This removes the finite-H1 hypothesis of the 2020 theorem for 3-manifolds and extends it above dim…
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combinatoricsSep 2, 2026Significance 15/100Registry: unreviewed
Prior state unknown→proved
Knauer proves that every finite n-vertex multigraph satisfies bn(G)=O(logn), improving the previous general O(log2n) bound and matching the known Ω(logn) order. He also proves the sharper cycle-rank bound bn(G)=O(logβ(G)). Combined with a reduction of Lehner and Miraftab, this yields bn(G)=O(logg) for graphs of Euler genus g, improving the previous…
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theoretical-computer-scienceAug 24, 2026Significance 15/100Registry: unreviewed
Prior state unknown→proved
For a Bernoulli(p) source with 0<p<21, the paper proves that the best lossy compression achievable by a linear encoder is exactly the simple time-sharing strategy that losslessly compresses a fraction of the bits and estimates the rest as zero. Equivalently, every full-row-rank H∈F2k×n satisfies
nk≥h(p)(1−pD(H)).
This resolves Massey's question affirma…
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geometry-topologySep 3, 2026Significance 15/100Registry: unreviewed
disproved→disproved
VibeMathed recorded: Mauri and Moraga's Question on Log Calabi-Yau Pairs with Big Boundary. Consult the linked registry entry for the original report and scope.
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geometry-topologySep 3, 2026Significance 15/100Registry: unreviewed
proved→proved
an independent human proof of the same conjecture appeared the same week
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