number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
For the least $t_k(n)$ with $n \mid t_k(n)(t_k(n)+1)\cdots(t_k(n)+k-1)$, do the conjectured logarithmic-saving and adjacent-length estimates hold on average? Both answered affirmatively, with $c = 1/2048$ admissible in the $t_2$ bound.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
analysisApr 9, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #990.” The registry entry and named primary source contain the available statement and scope.
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combinatoricsJul 23, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
For a finite forbidden triple system $G$, what exact uncountable chromatic cardinalities occur among $G$-free triple systems, and how do those spectra interact? The revised manuscript answers the three exact-cardinal questions and claims a complete spectrum dichotomy.
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number-theoryJul 25, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
If $A(x)$ counts integers satisfying the Sylow divisor condition, determine the constant $c$ in $A(x)/x = \exp(-(c + o(1)) \sqrt{\log x} \log\log x)$. The claimed exact value is $c = 1/(2\sqrt{\log 2})$.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
combinatoricsMay 3, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #750.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
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○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJun 10, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
main exponent determined; sharper subpolynomial factors remain open
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyFeb 25, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #846.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
If $A \subseteq \mathbb{N}$ has unbounded dyadic-shell counts and $\sum_{n \in A} \|\theta n\| = \infty$ for every $0 < \theta < 1$, must $A$ be complete - is every sufficiently large integer a sum of distinct elements of $A$?
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
geometry-topologyJan 13, 2026Significance 10/100Registry: lean verified
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○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryMay 3, 2026Significance 10/100Registry: lean verified
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○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJun 21, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
The problem statement is ambiguous: the limit-exists reading is claimed proved (Lean), while the convergence-from-hypotheses reading was disproved by a Lean-checked construction of Price that the community classes as a variant
●Source○Replay○Reproduced●Formal proof○Statement audit○External check○Expert review○Peer review
combinatoricsJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
the literal wording is refuted; the intended variant remains open
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryApr 24, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #330.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
How large must $y(\varepsilon, n)$ be so that every interval $(x, x+y)$ contains at most $\varepsilon y$ integers having a divisor in $(n, 2n)$? The candidate proof gives the sharp fixed-$\varepsilon$ order $y = \Theta_\varepsilon(n)$, uniformly in the translate.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
upper bound improved to f(n) ≤ 14n^{3/7} with an explicit logarithmic lower bound; matching bounds remain open
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryMar 30, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #125.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJun 14, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
Affirmative answer claimed, contrary to the negative answer Erdős and Graham conjectured; erdosproblems.com still lists the problem open
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number-theoryMar 2, 2026Significance 10/100Registry: lean verified
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○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryMay 1, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #694.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJun 14, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
lower bound improved to ≫ log n/(log log n · log log log n) infinitely often; the extremal order remains open
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJan 10, 2026Significance 10/100Registry: lean verified
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○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
exact largest modulus 3·2^{k-3} for k ≥ 5, near-linear least maximum, reciprocal mass Θ(log k), and an infinite divisor family; the counting asymptotic rests on the cited BBMST theorem
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJan 29, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #1051.” The registry entry and named primary source contain the available statement and scope.
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combinatoricsMay 7, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
a new density-degree inequality gives δ(G) ≤ (3/10 + o(1))|V(G)|, improving 0.328; existence of a linear construction remains open
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
If $g_3(n)$ is the largest size of $A \subseteq [1,n]$ with fewer than three representations of every product $a_1 a_2$, does its conjectured second-order normalized term converge? The candidate proof gives an explicit limit constant.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryApr 25, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #1138.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJun 5, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #696.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryApr 16, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #741.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryDec 25, 2025Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #333.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryMar 7, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #650.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryApr 27, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #42.” The registry entry and named primary source contain the available statement and scope.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
number-theoryJan 6, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
Whether there are infinitely many integers $a, b, n$ with $a, b \ge \varepsilon n$ such that $a!\cdot b!$ divides $n!\cdot(a+b-n)!$ while $a+b$ exceeds $n$ by more than $C\cdot\log n$.
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review
algorithms-optimizationApr 4, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
For smooth convex-concave min-max problems, can anchored gradient descent-ascent be scheduled so that its exact last-iterate squared-gradient residual is $O(1/t)$, closing the gap left by the 2019 analysis?
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algebraApr 4, 2026Significance 10/100Registry: lean verified
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.
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number-theoryJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
If $A$ is a forbidden-divisor set with $|A \cap [1,x]| = o(\sqrt{x})$ and $B = \{b_1 < b_2 < \cdots\}$ the sifted set, must $x^{-1} \sum_{b_i < x} (b_{i+1} - b_i)^2$ converge to a finite limit?
●Source○Replay○Reproduced○Formal proof○Statement audit○External check○Expert review○Peer review