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Mathematical findings

639 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.

number-theoryJul 13, 2026Significance 10/100Registry: lean verified

Erdős Problem #267

Prior state unknown→proved

If $n_1 < n_2 < \cdots$ with $n_{k+1}/n_k \ge c > 1$ , must $\sum_k 1/F_{n_k}$ be irrational? The proposed proof closes the range $1 < c < 2$ left open by earlier criteria.

Source authenticatedErdős Problem #267 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryJun 18, 2026Significance 10/100Registry: unreviewed

Erdős Problem #451

Prior state unknown→proved

the conjectured superpolynomial growth is established; the sharper order remains open

Source authenticatedErdős Problem #451 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryJul 13, 2026Significance 10/100Registry: lean verified

If each integer has at most $r$ representations $m = pa$ with $p$ prime and $a \in A \subseteq [1, N]$ , what is the best upper bound for $\sum_{a \in A} 1/a$ ? The candidate proof gives the matching order $\Theta_r(\log N / \log\log N)$ .

Source authenticatedErdős Problem #538 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryJun 14, 2026Significance 10/100Registry: lean verified

Erdős Problem #326

Prior state unknown→proved

Affirmative answer claimed, contrary to the negative answer Erdős and Graham conjectured; erdosproblems.com still lists the problem open

Source authenticatedErdős Problem #326 →

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combinatoricsAug 2, 2026Significance 10/100Registry: unreviewed

Hoa's Conjecture on Maximal Non-Hamiltonian Graphs

Prior state unknown→disproved

A graph $G$ is maximal non-Hamiltonian if it is non-Hamiltonian but $G + e$ is Hamiltonian for every nonedge $e$ . In 1994 Vu Dinh Hoa conjectured a property of $G - V(C)$ for a longest cycle $C$ of such a graph. Disproved by an explicit base graph on 56 vertices, extended to larger orders.

Source authenticatedHoa's Conjecture on Maximal Non-Hamiltonian Graphs →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryMay 3, 2026Significance 10/100Registry: lean verified

Erdős Problem #351

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #351.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #351 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryApr 27, 2026Significance 10/100Registry: unreviewed

Erdős Problem #1101

Prior state unknown→proved

a subexponential good sequence is constructed; the polynomial-growth question remains open

Source authenticatedErdős Problem #1101 →

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combinatoricsJul 15, 2026Significance 10/100Registry: unreviewed

The Small Davenport Constant of the Heisenberg Group of Order 125

Prior state unknown→proved

Settles the case p=5. The posed formula for every odd prime remains open.

Source authenticatedThe Small Davenport Constant of the Heisenberg Group of Order 125 →

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number-theoryApr 23, 2026Significance 10/100Registry: lean verified

Erdős Problem #1190

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #1190.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #1190 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

theoretical-computer-scienceApr 16, 2026Significance 10/100Registry: unreviewed

Avidor-Zwick Question on Low-Dimensional Max-Cut SDP

Prior state unknown→proved

For fixed $d$ , can every $d$ -dimensional feasible solution of the triangle-strengthened Max-Cut SDP be rounded in polynomial time with ratio strictly larger than $\alpha_{GW}$ ? A rounding achieving $\alpha_{GW} + 2^{-O(d)}$ answers yes.

Source authenticatedAvidor-Zwick Question on Low-Dimensional Max-Cut SDP →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryJul 13, 2026Significance 10/100Registry: lean verified

Erdős Problem #336

Prior state unknown→proved

If $h(r)$ is the maximal finite exact order attainable by an additive basis of order at most $r$ , what is $\lim_{r \to \infty} h(r)/r^2$ ? The candidate proof identifies the sharp limit $1/3$ .

Source authenticatedErdős Problem #336 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

probability-statisticsJun 28, 2026Significance 10/100Registry: unreviewed

Mossel-Peres Multivariable Bernoulli Factory Claim

Prior state unknown→disproved

the published multivariable claim fails; the single-variable theorem stands

Source authenticatedMossel-Peres Multivariable Bernoulli Factory Claim →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

differential-equationsApr 21, 2026Significance 10/100Registry: unreviewed

Sharp Convergence Rates for Viscous Hamilton-Jacobi Homogenization

Prior state unknown→proved

Sharp global and almost-everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations, settling the sharpness question left open by the first-order theory.

Source authenticatedSharp Convergence Rates for Viscous Hamilton-Jacobi Homogenization →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryFeb 4, 2026Significance 10/100Registry: lean verified

Erdős Problem #347

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #347.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #347 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisApr 1, 2026Significance 10/100Registry: unreviewed

Erdős Problem #514

Prior state unknown→proved

an escape path dominating every power of |z| with bounded initial length is constructed, and universal positive-power lower bounds are ruled out; the broader variant remains open

Source authenticatedErdős Problem #514 →

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combinatoricsJul 23, 2026Significance 10/100Registry: site confirmed

The Target-Free Clique Conjecture for Threshold-Linear Networks

Prior state unknown→disproved

The target-free clique conjecture asserts that the supports of stable fixed points of a nondegenerate combinatorial threshold-linear network are exactly its target-free cliques, the bidirected cliques no outside vertex receives an edge from every member of. An explicit six-neuron counterexample refutes it.

Source authenticatedThe Target-Free Clique Conjecture for Threshold-Linear Networks →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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

Erdős Problem #543

Prior state unknown→disproved

VibeMathed records this result as “Erdős Problem #543.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #543 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryMar 2, 2026Significance 10/100Registry: lean verified

Erdős Problem #457

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #457.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #457 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyApr 27, 2026Significance 10/100Registry: unreviewed

Erdős Problem #953

Prior state unknown→proved

What is the largest possible measure of a subset of a radius- $R$ disk in $\mathbb{R}^2$ containing no pair of points at a positive integer distance? A Poisson-Bessel kernel argument gives $M(R) \ll R^{1/2}$ ; with Sárközy's lower construction, $M(R) = R^{1/2 + o(1)}$ .

Source authenticatedErdős Problem #953 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsApr 21, 2026Significance 10/100Registry: site confirmed

Erdős Problem #603

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.

Source authenticatedErdős Problem #603 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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

Erdős Problem #321

Prior state unknown→proved

What is the largest $A\subseteq\{1,\dots,N\}$ such that all subset sums $\sum_{n\in S}1/n$ (over $S\subseteq A$ ) are distinct?

Source authenticatedErdős Problem #321 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algebraApr 4, 2026Significance 10/100Registry: lean verified

Anderson's Quasi-Completeness Question

Prior state unknown→disproved

Is every weakly quasi-complete Noetherian local ring quasi-complete? Asked by D. D. Anderson in 2014. The ring $A = k^p[[X, Y]][k]$ with $k = \mathbb{F}_p(u_1, u_2, \dots)$ is weakly quasi-complete but not quasi-complete.

Source authenticatedAnderson's Quasi-Completeness Question →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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

Erdős Problem #1202

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #1202.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #1202 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

theoretical-computer-scienceJul 28, 2026Significance 10/100Registry: unreviewed

The 4^k Barrier for the k-Distinct Language

Prior state unknown→proved

Can the $k$ -distinct language - words over $[n]$ of length at most $k$ with no repeated symbol - be recognized by an acyclic NFA of size $c^k n^{O(1)}$ for some $c < 4$ ? A construction of size $2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)}$ answers yes.

Source authenticatedThe 4^k Barrier for the k-Distinct Language →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryAug 15, 2026Significance 10/100Registry: lean checked

Composites Among $[\xi 7^n]$ and Right-Truncatable Primes in Base 7

Prior state unknown→proved

For every real $\xi>0$ the sequence of integer parts $[\xi 7^{n}]$ , $n=0,1,2,\dots$ , contains infinitely many composite numbers. Second, there is no infinite right truncatable prime in base~ $7$ .

Source authenticatedComposites Among

[\xi 7^n]

and Right-Truncatable Primes in Base 7 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

algorithms-optimizationAug 6, 2026Significance 10/100Registry: unreviewed

Balanced EF1 and fPO Allocations

Prior state unknown→proved

The paper records how the collaboration actually went: the authors first aimed at a counterexample showing EF1 and PO incompatible under matroid constraints, and when the model surfaced fundamental difficulties with that plan they redirected toward proving the positive result instead. The paper also extends the technique to category constraints and leaves a pseudopolynomial-time algorithm open.

Source authenticatedBalanced EF1 and fPO Allocations →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisApr 29, 2026Significance 10/100Registry: unreviewed

Erdős Problem #1133

Prior state unknown→proved

Must every sufficiently large node set admit bounded labels that force any polynomial fitting almost all labels at degree below $(1+\varepsilon)n$ to have arbitrarily large uniform norm? Claimed via Beurling density for Bernstein spaces.

Source authenticatedErdős Problem #1133 →

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probability-statisticsNov 24, 2025Significance 10/100Registry: unreviewed

Minimax Rate for Density Estimation under Wasserstein Contamination

Prior state unknown→proved

What is the minimax optimal error rate for density estimation when observations are perturbed by Wasserstein-bounded contaminations? Chao and Dobriban's 2023 preprint left a gap between upper and lower bounds; the sharp rate is now derived, closing the problem.

Source authenticatedMinimax Rate for Density Estimation under Wasserstein Contamination →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

geometry-topologyJan 13, 2026Significance 10/100Registry: lean verified

Erdős Problem #659

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #659.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #659 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryApr 26, 2026Significance 10/100Registry: site confirmed

Erdős Problem #896

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.

Source authenticatedErdős Problem #896 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

combinatoricsJun 4, 2026Significance 10/100Registry: unreviewed

Erdős Problem #623

Prior state unknown→proved

Resolved (if correct) by an independence result rather than a proof or disproof in ZFC: consistency of the positive answer is equivalent to a measurable cardinal, of the negative to ZFC alone

Source authenticatedErdős Problem #623 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

analysisJul 19, 2026Significance 10/100Registry: unreviewed

Strict Cosingularity and Adjoints for Separable Range

Prior state unknown→proved

Pełczyński's duality between strictly singular and strictly cosingular operators fails without weak compactness. Beanland asked, in work with Androulakis and later on MathOverflow, for the separable-range case: the paper answers it affirmatively and shows that for separable $X$ , $T$ is strictly cosingular exactly when $T^{*}$ is strictly singular.

Source authenticatedStrict Cosingularity and Adjoints for Separable Range →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryMay 3, 2026Significance 10/100Registry: lean verified

Erdős Problem #283

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #283.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #283 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryJun 24, 2026Significance 10/100Registry: unreviewed

Erdos Problem #1061

Prior state unknown→disproved

Let $S(x)$ count ordered pairs $(a,b)$ with $a+b \le x$ and $\sigma(a)+\sigma(b) = \sigma(a+b)$ . Erdos asked whether $S(x) \sim cx$ . The opposite extreme holds: for every $R > 0$ , $S(x)/(x(\log x)^R) \to \infty$ , so the count beats every fixed logarithmic scale.

Source authenticatedErdos Problem #1061 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryJan 10, 2026Significance 10/100Registry: lean verified

Erdős Problem #205

Prior state unknown→disproved

VibeMathed records this result as “Erdős Problem #205.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #205 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

number-theoryMar 16, 2026Significance 10/100Registry: lean verified

Erdős Problem #1148

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #1148.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #1148 →

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review