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Mathematical findings

66 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-theorySep 3, 2026Significance 60/100Registry: site confirmed

Improved maximal prime-gap lower bound

Prior state unknown→proved

The paper proves $G(X)\gg \frac{\log X\,(\log_2 X)^2\,\log_4 X}{(\log_3 X)^2}$ for all sufficiently large $X$ . Its main new ingredient is a short-translates theorem: for any sufficiently small set $S\subseteq[1,H]$ with $|S|\le\delta x$ , one can find a short translate making every corresponding linear form composite. Combining this with an Erdős--Rankin covering argument produces prime-free intervals of the clai…

Source authenticatedImproved maximal prime-gap lower bound →

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combinatoricsJul 23, 2026Significance 40/100Registry: site confirmed

Petersen Coloring Conjecture

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 ind…

Source authenticatedPetersen Coloring Conjecture →

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combinatoricsAug 29, 2026Significance 32/100Registry: site confirmed

Dean's conjecture for $k=5$

Prior state unknown→proved

Claims the last open case of Dean's conjecture: every finite simple graph with minimum degree at least five contains a cycle of length divisible by five. Verified independently against Luo, Ma and Zhao (arXiv:2601.13552), whose abstract confirms the landscape - the conjecture was known for $k\in\{3,4\}$ and they proved every $k\ge6$ , leaving $k=5$ open. If this proof stands, Dean's conjecture holds for all $k\ge3$ .…

Source authenticatedDean's conjecture for

k=5

→

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combinatoricsMay 26, 2026Significance 30/100Registry: site confirmed

Borsuk Conjecture lowest-ever counterexample (N=63)

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 submitter…

Source authenticatedBorsuk Conjecture lowest-ever counterexample (N=63) →

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combinatoricsAug 11, 2026Significance 30/100Registry: site confirmed

Albertson–Berman Induced Forest Conjecture

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.

Source authenticatedAlbertson–Berman Induced Forest Conjecture →

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combinatoricsAug 12, 2026Significance 30/100Registry: site confirmed

Hadamard Matrix of Order 668

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 existenc…

Source authenticatedHadamard Matrix of Order 668 →

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algebraSep 3, 2026Significance 28/100Registry: site confirmed

Conway's Refinement Conjecture for Omnific Integers

Prior state unknown→proved

The repository gives a Lean proof of Conway's 1976 refinement conjecture for omnific integers: whenever $ab=cd$ with $a,b,c,d\in\mathbf{Oz}$ , there exist $e,f,g,h\in\mathbf{Oz}$ satisfying $a=ef,\quad b=gh,\quad c=eg,\quad d=fh.$ The proof is formalized twice: once using CombinatorialGames' surreal-number implementation and once with the required surreal definitions inlined over Mathlib. The development also…

Source authenticatedConway's Refinement Conjecture for Omnific Integers →

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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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algebraJul 23, 2026Significance 25/100Registry: site confirmed

The Separable Jacobian Conjecture in Characteristic 2

Prior state unknown→disproved

the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does

Source authenticatedThe Separable Jacobian Conjecture in Characteristic 2 →

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combinatoricsMay 23, 2026Significance 25/100Registry: site confirmed

Simon's Extendable Shellability Conjecture

Prior state unknown→disproved

VibeMathed recorded: Simon's Extendable Shellability Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedSimon's Extendable Shellability Conjecture →

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geometry-topologyJun 16, 2026Significance 25/100Registry: site confirmed

Wegner's Piercing Conjecture for Rectangles

Prior state unknown→disproved

VibeMathed recorded: Wegner's Piercing Conjecture for Rectangles. Consult the linked registry entry for the original report and scope.

Source authenticatedWegner's Piercing Conjecture for Rectangles →

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probability-statisticsMay 3, 2026Significance 20/100Registry: site confirmed

Litvak's Conjecture on Gaussian Minima

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

Source authenticatedLitvak's Conjecture on Gaussian Minima →

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geometry-topologyJun 6, 2026Significance 15/100Registry: site confirmed

The Odd Area Conjecture for Unit Disks

Prior state unknown→disproved

VibeMathed recorded: The Odd Area Conjecture for Unit Disks. Consult the linked registry entry for the original report and scope.

Source authenticatedThe Odd Area Conjecture for Unit Disks →

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geometry-topologyJul 9, 2026Significance 15/100Registry: site confirmed

Purdy's Inequality for Hyperplane Arrangements

Prior state unknown→disproved

the refined form for essential arrangements in projective three-space

Source authenticatedPurdy's Inequality for Hyperplane Arrangements →

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algebraMay 25, 2026Significance 15/100Registry: site confirmed

Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups

Prior state unknown→proved

two of the three remaining cases; one is still unclassified

Source authenticatedArithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups →

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combinatoricsJul 22, 2026Significance 15/100Registry: site confirmed

$e$ -Log-Concavity of Chromatic Quasisymmetric Functions

Prior state unknown→disproved

VibeMathed recorded: $e$ -Log-Concavity of Chromatic Quasisymmetric Functions. Consult the linked registry entry for the original report and scope.

Source authenticated

e

-Log-Concavity of Chromatic Quasisymmetric Functions →

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geometry-topologyJun 26, 2026Significance 15/100Registry: site confirmed

Lassak's Area Bound for Reduced Planar Bodies

Prior state unknown→disproved

VibeMathed recorded: Lassak's Area Bound for Reduced Planar Bodies. Consult the linked registry entry for the original report and scope.

Source authenticatedLassak's Area Bound for Reduced Planar Bodies →

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combinatoricsAug 10, 2026Significance 15/100Registry: site confirmed

Teschner's Bondage-Number Conjecture

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 g…

Source authenticatedTeschner's Bondage-Number Conjecture →

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combinatoricsAug 13, 2026Significance 15/100Registry: site confirmed

1.17353 planar lower bound and exact local envelopes for cost-preserving single-source unsplittable flow

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 (shar…

Source authenticated1.17353 planar lower bound and exact local envelopes for cost-preserving single-source unsplittable flow →

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combinatoricsJul 31, 2026Significance 15/100Registry: site confirmed

1.28249... Lower Bound and Partial Upper Bounds for Cost-Preserving Single-Source Unsplittable Flows

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].

Source authenticated1.28249... Lower Bound and Partial Upper Bounds for Cost-Preserving Single-Source Unsplittable Flows →

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algebraAug 25, 2026Significance 14/100Registry: site confirmed

Fröberg’s conjecture for quintics and septics in four variables

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 exac…

Source authenticatedFröberg’s conjecture for quintics and septics in four variables →

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analysisJul 1, 2026Significance 13/100Registry: site confirmed

Erdős Problem #119

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #119. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #119 →

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theoretical-computer-scienceSep 3, 2026Significance 12/100Registry: site confirmed

Unrestricted Boolean multiplicative complexity of four-term binary polynomial multiplication

proved→proved

The exact Mul4 instance is resolved: its unrestricted XOR--AND multiplicative complexity is 9. The restricted bilinear/quadratic value 9 was classical; the new theorem proves that arbitrary nonlinear Boolean reuse cannot lower it. This is a natural positive special case of the Boyar--Find question, not a solution of the general (n,m) problem. The lower bound is a conceptual structural argument. A complete Lean 4 for…

Source authenticatedUnrestricted Boolean multiplicative complexity of four-term binary polynomial multiplication →

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quantum-information-computingAug 6, 2026Significance 12/100Registry: site confirmed

Absolutely Maximally Entangled States in Five Open Cases

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 an…

Source authenticatedAbsolutely Maximally Entangled States in Five Open Cases →

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number-theoryApr 27, 2026Significance 11/100Registry: site confirmed

Erdős Problem #43

Prior state unknown→disproved

both proposed bounds fail

Source authenticatedErdős Problem #43 →

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combinatoricsJun 16, 2026Significance 11/100Registry: site confirmed

Erdős Problem #986

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #986. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #986 →

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analysisApr 9, 2026Significance 11/100Registry: site confirmed

Erdős Problem #987

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #987. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #987 →

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geometry-topologySep 6, 2026Significance 10/100Registry: site confirmed

A 44-vertex triangulation of $\mathbb{RP}^{6}$

Prior state unknown→proved

The manuscript gives an explicit centrally symmetric simplicial 7-polytope with 88 integer vertices. Its antipodal boundary quotient is a 44-vertex triangulation of real projective 6-space, with f-vector (44, 938, 7024, 22555, 34936, 25914, 7404). This improves the 45-vertex construction of Guyer, Steinerberger and Yang and gives an affirmative answer to their Question 3.2. Integer coordinates, facet lists and exac…

Source authenticatedA 44-vertex triangulation of

\mathbb{RP}^{6}

→

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number-theoryMar 31, 2026Significance 10/100Registry: site confirmed

Erdős Problem #380

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #380. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #380 →

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number-theoryApr 1, 2026Significance 10/100Registry: site confirmed

Erdős Problem #1202

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #1202. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #1202 →

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combinatoricsApr 28, 2026Significance 10/100Registry: site confirmed

Erdős Problem #1092

Prior state unknown→disproved

VibeMathed recorded: Erdős Problem #1092. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #1092 →

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number-theoryJan 21, 2026Significance 10/100Registry: site confirmed

Erdős Problem #543

Prior state unknown→disproved

VibeMathed recorded: Erdős Problem #543. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #543 →

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geometry-topologyApr 9, 2026Significance 10/100Registry: site confirmed

Erdős Problem #960

Prior state unknown→disproved

VibeMathed recorded: Erdős Problem #960. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #960 →

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number-theoryJul 1, 2026Significance 10/100Registry: site confirmed

Erdős Problem #321

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #321. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #321 →

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analysisMar 24, 2026Significance 10/100Registry: site confirmed

Erdős Problem #1153

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #1153. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #1153 →

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number-theoryMay 8, 2026Significance 10/100Registry: site confirmed

Erdős Problem #690

Prior state unknown→proved

VibeMathed recorded: Erdős Problem #690. Consult the linked registry entry for the original report and scope.

Source authenticatedErdős Problem #690 →

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