combinatoricsJul 23, 2026Significance 40/100Registry: site confirmed
Prior state unknown→disproved
This preprint was not the first disproof. A 68-vertex counterexample was posted to X on 23 July 2026 by @NeuralReformist, credited to GPT-5.6 Sol Ultra, sixteen days earlier. This site decoded that sparse6 string and checked it independently: 68 vertices, 102 edges, simple, cubic, connected, bridgeless, girth five, and no Petersen coloring under the same encoder used for the 112-vertex graph. Whether the two are i…
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combinatoricsAug 12, 2026Significance 30/100Registry: site confirmed
Prior state unknown→proved
Explicit construction of a Hadamard matrix of order 668, the smallest previously unresolved order, verified exactly by this site from the announcement plus its decoder reply. The same post encodes matrices for all twelve previously-open admissible orders below 2000 (668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948, 1964), and this site verified every one of them. The entry records the order-668 existe…
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combinatoricsAug 11, 2026Significance 30/100Registry: site confirmed
Prior state unknown→disproved
The ratio 15/31 is not claimed to be optimal, and the paper makes no claim that 31 vertices is the smallest possible counterexample. The construction produces separating triangles by design, so it says nothing about the 4-connected case.
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combinatoricsMay 26, 2026Significance 30/100Registry: site confirmed
Prior state unknown→disproved
Priority: the result was first obtained by Max Grinsztajn with GPT-5.5 Pro assistance, published 26 May 2026 and recorded as the current best bound on Tao's optimization-problems ledger. The same construction was found again independently in August 2026 by Nicholas Konz working with Claude, with a different derivation and a fuller AI disclosure; the two efforts were evidently unaware of each other, and the submitt…
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probability-statisticsJul 20, 2026Significance 25/100Registry: site confirmed
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
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combinatoricsMay 23, 2026Significance 25/100Registry: site confirmed
Prior state unknown→disproved
Simon conjectured that every skeleton of a simplex is extendably shellable. False: for every $d \ge 3$ there is a pure $d$-dimensional shellable simplicial complex that is not shelling completable.
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algebraJul 23, 2026Significance 25/100Registry: site confirmed
Prior state unknown→disproved
the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
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geometry-topologyJun 16, 2026Significance 25/100Registry: site confirmed
Prior state unknown→disproved
Wegner conjectured in 1965 that every finite family $\mathcal{R}$ of axis-parallel rectangles satisfies $\tau(\mathcal{R}) \le 2\nu(\mathcal{R}) - 1$, where $\tau$ is the minimum number of piercing points and $\nu$ the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.
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probability-statisticsMay 3, 2026Significance 20/100Registry: site confirmed
Prior state unknown→disproved
the paper proposes that the cosine matrix is the true minimizer for all p and n, and proves a stronger stochastic domination statement conditional on a new volumetric extension of Fejes Toth's zone conjecture
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combinatoricsAug 13, 2026Significance 15/100Registry: site confirmed
Prior state unknown→proved
Part III of a series, and the first unconditional positive results in it. Settled exactly: the local envelope ladder $E(2)=1$, $E(3)=9/8$ and $E(4)=(299-41\sqrt{41})/32=1.13974707\ldots$, which recasts the earlier record constants as exact envelopes of the general theory rather than isolated instances, plus exact constants for four classes - out-trees 0, two-layer hubs 1, outerplanar two-exit interval spines 1 (sh…
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combinatoricsAug 10, 2026Significance 15/100Registry: site confirmed
Prior state unknown→disproved
Teschner's universal bound b(G) <= (3/2)Delta(G) is false: the 18-vertex cubic bipartite graph has b(G) = 5 against a bound of 4.5. What survives is the restricted statement Teschner actually proved, that the bound holds for graphs of domination number at most three, and Gagarin and Zverovich's 2013 result that it holds for almost all graphs. The counterexample does not suggest a replacement bound, and the correct…
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combinatoricsJul 31, 2026Significance 15/100Registry: site confirmed
Prior state unknown→proved
Record lower bound only. The sub-2 ceiling is the codimension-two case and does not bound the record ladder (k=17 has complement mass 11). 4/3 and 2 are conjectures; the proved gap is [1.28249, 2].
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geometry-topologyJun 26, 2026Significance 15/100Registry: site confirmed
Prior state unknown→disproved
Lassak conjectured that a reduced planar convex body of thickness $\Delta$ has area at most $(\pi/4)\Delta^2$, the value for the disc. False: an explicit reduced body of thickness $1$ has area $0.786215\ldots > \pi/4 = 0.785398\ldots$, given by a closed-form support function.
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combinatoricsJul 22, 2026Significance 15/100Registry: site confirmed
Prior state unknown→disproved
Chromatic quasisymmetric functions of natural unit interval graphs were conjectured to have log-concave coefficients in the elementary basis. A connected $13$-vertex example refutes it: for the Hessenberg function $h=(2,4,4,6,7,10,10,10,10,12,12,13,13)$ and $\lambda=(6,5,1,1)$ the coefficients of $q^5,q^6,q^7$ are $1,6,38$, and $6^2 < 1 \cdot 38$. The coefficient is still positive, palindromic and unimodal, so log…
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geometry-topologyJul 9, 2026Significance 15/100Registry: site confirmed
Prior state unknown→disproved
the refined form for essential arrangements in projective three-space
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algebraMay 25, 2026Significance 15/100Registry: site confirmed
Prior state unknown→proved
two of the three remaining cases; one is still unclassified
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geometry-topologyJun 6, 2026Significance 15/100Registry: site confirmed
Prior state unknown→disproved
For a family $F$ of an odd number $n$ of unit disks in the plane, let $\mathrm{OA}(F)$ be the area covered by an odd number of disks. It was conjectured that $\mathrm{OA}(F) \ge \pi$, the area of a single disk. False: configurations exist with smaller odd area.
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algebraAug 25, 2026Significance 14/100Registry: site confirmed
Prior state unknown→proved
Let $S=k[x_1,x_2,x_3,x_4]$ over any characteristic-zero field. For each $d\in\{5,7\}$ and every $r\ge1$, the paper proves that $r$ general degree-$d$ forms satisfy Fröberg’s predicted Hilbert series
$$
\operatorname{HS}_{S/(F_1,\ldots,F_r)}(t)
=
\left[\frac{(1-t^d)^r}{(1-t)^4}\right]_+.
$$
The genuinely new ranges are $6\le r\le11$ for quintics and $6\le r\le21$ for septics. These are reduced to finitely many ex…
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analysisJul 1, 2026Significance 13/100Registry: site confirmed
Prior state unknown→proved
For unit-modulus complex numbers $z_i$, let $p_n(z)=\prod_{i\le n}(z-z_i)$ and $M_n=\max_{|z|=1}|p_n(z)|$. Erdős's prize question: is there $c>0$ with $\sum_{k\le n} M_k > n^{1+c}$?
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quantum-information-computingAug 6, 2026Significance 12/100Registry: site confirmed
Prior state unknown→proved
Five existence statements, all by explicit construction: $\mathrm{AME}(12,5)$, $\mathrm{AME}(17,11)$, $\mathrm{AME}(18,11)$, $\mathrm{AME}(17,13)$ and $\mathrm{AME}(18,13)$. The $[12,6,7]_{25}$ code came from a direct search with no symmetry imposed; its automorphism group turned out to have a regular $\mathbb{Z}_3^2$ coordinate orbit, and imposing that translation symmetry on two nine-coordinate orbits collapses…
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number-theoryApr 27, 2026Significance 11/100Registry: site confirmed
Prior state unknown→disproved
both proposed bounds fail
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analysisApr 9, 2026Significance 11/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #987.” The registry entry and named primary source contain the available statement and scope.
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combinatoricsJun 16, 2026Significance 11/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #986.” The registry entry and named primary source contain the available statement and scope.
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geometry-topologyFeb 1, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #1089.” The registry entry and named primary source contain the available statement and scope.
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algorithms-optimizationJun 12, 2026Significance 10/100Registry: site confirmed
Prior state unknown→disproved
On the basis of experiments up to 5000 nodes, Papamanthou and Tollis conjectured a relation between the longest paths produced by their MaxSTN and MinSTN algorithms for $st$-orientations of biconnected graphs. A counterexample refutes it.
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combinatoricsApr 21, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #603.” The registry entry and named primary source contain the available statement and scope.
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number-theoryApr 26, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #896.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJul 1, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
Let $S(N)$ count the distinct values of $\sum_{n\in A} 1/n$ over $A\subseteq\{1,\dots,N\}$. Estimate $S(N)$.
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combinatoricsApr 9, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #1091.” The registry entry and named primary source contain the available statement and scope.
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number-theoryApr 22, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #863.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJul 1, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
Let $F(n)$ be the largest $A\subseteq\{1,\dots,n\}$ with $a\nmid bc$ for distinct $a,b,c\in A$. Is $F(n)=\pi(n)+(C+o(1))\,n^{2/3}(\log n)^{-2}$ for some constant $C$?
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number-theoryMar 31, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #380.” The registry entry and named primary source contain the available statement and scope.
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number-theoryNov 20, 2025Significance 10/100Registry: site confirmed
Prior state unknown→proved
Resolved for all sufficiently large N via a stability theorem; small N remain a finite computation (erdosproblems.com marks the problem DECIDABLE)
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number-theoryFeb 5, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #851.” The registry entry and named primary source contain the available statement and scope.
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combinatoricsApr 28, 2026Significance 10/100Registry: site confirmed
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #1092.” The registry entry and named primary source contain the available statement and scope.
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number-theoryApr 19, 2026Significance 10/100Registry: site confirmed
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #1195.” The registry entry and named primary source contain the available statement and scope.
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