Erdős Problem #959
Prior state unknown→proved
superlinear lower bound M(n) ≥ n^{1 + 1/(50000 log log n)}, improving Ω(n log n); the exact order remains open
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Open registry federation
Mathematical findings
136 source-grounded records. Verification labels remain separate from source authentication and publication status.
Imported from VibeMathed under CC BY 4.0. Each record links to its registry entry and named primary source. Registry verification is preserved verbatim.
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.
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Erdős Problem #469
Prior state unknown→proved
Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?
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Erdős Problem #1026: Monotonic Subsequence Sums
Prior state unknown→proved
For a sequence of $n$ distinct reals, determine the largest constant $c$ such that some monotonic subsequence always has sum exceeding $(c-o(1))\cdot(1/\sqrt{n})$ times the total sum. Resolved as $c = 1$.
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Erdős Problem #131
Prior state unknown→proved
The new content is the upper bound; the matching N^(1/5) construction is prior work of Erdős and Csaba. erdosproblems.com has not accepted the claim
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Erdős Problem #1039
Prior state unknown→proved
order of magnitude determined; the exact asymptotic constant remains open
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Erdős Problem #1188
Prior state unknown→proved
Estimate the number $F(x)$ of minimal distinct covering systems whose moduli all lie in $[1, x]$. The candidate proof gives $\log\log F(x)/\log x \to 1$, i.e. $F(x) = \exp(x^{1+o(1)})$.
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Erdős Problem #897
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #897.” The registry entry and named primary source contain the available statement and scope.
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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 $1/3$.
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Erdős Problem #769
Prior state unknown→disproved
the conjectured lower bound is disproved; good bounds for c(n) remain open
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Erdős Problem #865
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #865.” The registry entry and named primary source contain the available statement and scope.
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Erdős Problem #369
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #369.” The registry entry and named primary source contain the available statement and scope.
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Erdős Problem #306
Prior state unknown→proved
If $a/b \in \mathbb{Q}_{>0}$ and $b$ is squarefree, can $a/b$ always be written as a finite sum of reciprocals of distinct products of two distinct primes?
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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.
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Erdős Problem #966
Prior state unknown→proved
Erdős reported in 1975 that Spencer had shown existence but gave no reference; no proof was on record before the AI solution
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Erdős Problem #1197
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #1197.” The registry entry and named primary source contain the available statement and scope.
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Erdős Problem #38
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #38.” The registry entry and named primary source contain the available statement and scope.
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
Elizalde-Luo Pattern-Avoidance Conjecture
Prior state unknown→proved
Is the number of nonnesting permutations of $\{1,1,\dots,n,n\}$ avoiding both $1132$ and $3312$ equal to $3^n - 3 \cdot 2^{n-1} + 1$ for every $n \ge 1$?
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Optimal Strategies in the All-Heads Coin Game
Prior state unknown→proved
In the all-heads coin game a player starts with $n$ coins, each showing heads with probability $p$; each round all remaining coins are flipped, the player must set aside at least one head (losing if none shows), and wins once all coins are set aside. Determine optimal strategies and the winning probability $w_{n,p}$. Resolved: for $p=\tfrac12$ every strategy achieves $w_{n,1/2}=\tfrac12$; for $p>\tfrac12$ the sing…
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Written on the Wall II, Graph Conjecture 144
Prior state unknown→proved
The Formal Conjectures pull request flipping this from open to solved is still open rather than merged, so the canonical repository has not yet accepted it.
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Hamilton Decompositions of the Directed 3-Torus
Prior state unknown→proved
For $D_3(m) = \vec{C}_m \square \vec{C}_m \square \vec{C}_m$, can the full arc set be partitioned into three directed Hamilton cycles for every integer $m \ge 3$?
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Written on the Wall II, Graph Conjecture 143
Prior state unknown→proved
For every finite connected graph, is $\operatorname{girth}(G) + 1$ at most the product of its largest induced-tree order and its second-smallest degree?
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Written on the Wall II, Graph Conjecture 103
Prior state unknown→disproved
For every connected graph $G$, is $\alpha(G) \le \lfloor b(G) - \log(\operatorname{ecc}_{avg}(G)) \rfloor$, where $b(G)$ is the largest induced-bipartite-subgraph order? An $11$-vertex counterexample - a triangle with four leaves on each of two vertices - has $\alpha = 9$ against bound $8$.
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Written on the Wall II, Graph Conjecture 322
Prior state unknown→proved
The formalization proves the statement under the weaker hypothesis n >= 2; the pull request marking the conjecture solved is open, not merged
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Written on the Wall II, Graph Conjecture 217
Prior state unknown→proved
VibeMathed records this result as “Written on the Wall II, Graph Conjecture 217.” The registry entry and named primary source contain the available statement and scope.
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Written on the Wall II, Graph Conjecture 109
Prior state unknown→disproved
Must every connected graph satisfy the proposed upper bound on its independence number in terms of residue and largest induced-bipartite-subgraph order? The family $\overline{K}_{2r+1} \vee (K_r \sqcup K_r)$ violates it for every $r \ge 3$.
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Written on the Wall II, Graph Conjecture 2
Prior state unknown→proved
For a finite connected graph $G$, let $L_s(G)$ be the maximum number of leaves in a spanning tree and $\ell(G)$ the average local independence number. Must $L_s(G) \ge 2(\ell(G) - 1)$?
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Equilibria of the Vlasov-Maxwell-Landau System
Prior state unknown→proved
Under smoothness, positivity, decay and score assumptions, are all steady solutions of the Coulomb Vlasov-Maxwell-Landau system on $\mathbb{T}^3 \times \mathbb{R}^3$ necessarily spatially uniform Maxwellians?
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