algebra Feb 3, 2026 Significance 10/100 Registry: lean checked
Prior state unknown → proved
Does the conjectured universal formula for normalized alternating syzygy power sums of numerical semigroup rings hold for every index?
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number-theory Jun 1, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
Does there exist an integer polynomial f f f of degree at least two and a set A ⊆ Z A \subseteq \mathbb{Z} A ⊆ Z such that every integer has a unique representation n = a + f ( k ) n = a + f(k) n = a + f ( k ) ? A manuscript claims the thirteenth powers admit a tiling complement.
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number-theory Apr 22, 2026 Significance 10/100 Registry: 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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geometry-topology Feb 13, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
Question 8 of the First Proof experiment (Abouzaid et al.) asks whether a polyhedral Lagrangian surface with exactly four faces meeting at every vertex necessarily admits a Lagrangian smoothing. The research report assembles ChatGPT-suggested constructions into an affirmative argument for orientable surfaces in ( R 4 , ω ) (\mathbb{R}^4, \omega) ( R 4 , ω ) : smooth the edges, verify the vertex links are unknots with rot 0 and tb -1, and…
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number-theory Jul 21, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?
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analysis Apr 9, 2026 Significance 10/100 Registry: 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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combinatorics Apr 16, 2026 Significance 10/100 Registry: lean checked
Prior state unknown → disproved
Erdős asked whether every n n n -point set in Euclidean space whose pairwise distances are mutually at least 1 apart must have diameter at least ( 1 + o ( 1 ) ) n 2 (1+o(1))n^2 ( 1 + o ( 1 )) n 2 . Disproved: an explicit high-dimensional construction beats the conjectured constant.
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algebra Jul 21, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
answered for 3-cocycles, inside a broader partial classification of twisted Deligne products
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combinatorics Jul 23, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
For a finite forbidden triple system G G G , what exact uncountable chromatic cardinalities occur among G G 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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geometry-topology Feb 3, 2026 Significance 10/100 Registry: lean checked
Prior state unknown → proved
For odd k k k with gcd ( n , k ) = gcd ( n + 1 , k ) = 1 \gcd(n,k) = \gcd(n+1,k) = 1 g cd( n , k ) = g cd( n + 1 , k ) = 1 , is N k ( n ) ≡ ⌊ ( k + 1 ) / 4 ⌋ ( m o d 2 ) N_k(n) \equiv \lfloor (k+1)/4 \rfloor \pmod 2 N k ( n ) ≡ ⌊( k + 1 ) /4 ⌋ ( mod 2 ) , where N k ( n ) N_k(n) N k ( n ) counts pairs 1 ≤ b i ≤ ( k − 1 ) / 2 1 \le b_i \le (k-1)/2 1 ≤ b i ≤ ( k − 1 ) /2 with b 1 + b 2 ≥ ( k + 1 ) / 2 b_1 + b_2 \ge (k+1)/2 b 1 + b 2 ≥ ( k + 1 ) /2 and b 2 ≡ n b 1 ( m o d k ) b_2 \equiv n b_1 \pmod k b 2 ≡ n b 1 ( mod k ) ? Conjectured by Chen and Gendron; its proof removes a conditional step in the genus-zero and genus-one spin-parity classification.
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number-theory May 1, 2026 Significance 10/100 Registry: 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.
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number-theory Jul 13, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
How large must y ( ε , n ) y(\varepsilon, n) y ( ε , n ) be so that every interval ( x , x + y ) (x, x+y) ( x , x + y ) contains at most ε y \varepsilon y ε y integers having a divisor in ( n , 2 n ) (n, 2n) ( n , 2 n ) ? The candidate proof gives the sharp fixed- ε \varepsilon ε order y = Θ ε ( n ) y = \Theta_\varepsilon(n) y = Θ ε ( n ) , uniformly in the translate.
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number-theory Apr 9, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → disproved
VibeMathed records this result as “Erdős Problem #1141.” The registry entry and named primary source contain the available statement and scope.
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number-theory Jun 10, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
main exponent determined; sharper subpolynomial factors remain open
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number-theory Jan 11, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
VibeMathed records this result as “Erdős Problem #401.” The registry entry and named primary source contain the available statement and scope.
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probability-statistics Jul 21, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
Is the density of Chernoff's distribution - the law of argmax t { W ( t ) − t 2 } \operatorname{argmax}_t \{W(t) - t^2\} argmax t { W ( t ) − t 2 } for two-sided Brownian motion W W W - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?
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combinatorics Apr 9, 2026 Significance 10/100 Registry: 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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geometry-topology Jul 13, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
the infinite-chromatic subquestion is proved; the rest of the problem remains open
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number-theory Jul 14, 2026 Significance 10/100 Registry: site confirmed
Prior state unknown → disproved
A monic prime P P P of F q [ T ] \mathbb{F}_q[T] F q [ T ] is a c c c -Wieferich prime if ρ P ( 1 ) ≡ 1 m o d P 2 \rho_P(1) \equiv 1 \bmod P^2 ρ P ( 1 ) ≡ 1 mod P 2 for the Carlitz module ρ \rho ρ . On limited data and proofs in degrees 2 2 2 and 3 3 3 , Thakur suggested in 2015 that in odd characteristic every c c c -Wieferich prime has degree divisible by p p p . It is false: an explicit irreducible c c c -Wieferich prime has degree not divisible by p p p , and the resulting common factor has a clos…
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geometry-topology Feb 1, 2026 Significance 10/100 Registry: expert verified
Prior state unknown → disproved
the strongest form is disproved via configurations where every point sees at most about 3n/4 distinct distances; the weaker improvement remains open
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combinatorics Apr 23, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
VibeMathed records this result as “Erdős Problem #1014.” The registry entry and named primary source contain the available statement and scope.
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number-theory Jun 21, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
Zhi-Wei Sun conjectured a closed evaluation of a truncated Legendre-symbol determinant. For every prime p ≡ 3 ( m o d 4 ) p \equiv 3 \pmod 4 p ≡ 3 ( mod 4 ) it equals ⌊ ( p − 2 ) / 3 ⌋ 2 x \lfloor (p-2)/3 \rfloor^2 x ⌊( p − 2 ) /3 ⌋ 2 x , proved by reducing to inverse data for Chapman's full Legendre-symbol matrix and evaluating that with Vsemirnov's factorization and a Schur-Pfaffian resolvent identity.
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analysis Apr 21, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → disproved
Answered negatively in a preprint that also settles the p=2 case of problem #995; erdosproblems.com still lists the problem open
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geometry-topology Feb 1, 2026 Significance 10/100 Registry: 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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quantum-information-computing Jul 27, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
What is the optimal uniform continuity bound for quantum conditional entropy in trace distance, depending only on the dimension of the conditioned system? The sharp bound h 2 ( δ ) + δ log ( d 2 − 1 ) h_2(\delta) + \delta \log(d^2 - 1) h 2 ( δ ) + δ log ( d 2 − 1 ) up to δ = 1 − d − 2 \delta = 1 - d^{-2} δ = 1 − d − 2 , conjectured by Wilde, is proved.
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geometry-topology Jul 13, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → disproved
the conjectured lower bound is disproved; good bounds for c(n) remain open
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probability-statistics Jul 13, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
Do the one-species current marginals of type-D ASEP have the predicted Tracy-Widom long-time asymptotics despite the model's two-species interactions?
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number-theory Jul 25, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
If A ( x ) A(x) A ( x ) counts integers satisfying the Sylow divisor condition, determine the constant c c c in A ( x ) / x = exp ( − ( c + o ( 1 ) ) log x log log x ) A(x)/x = \exp(-(c + o(1)) \sqrt{\log x} \log\log x) A ( x ) / x = exp ( − ( c + o ( 1 )) log x log log x ) . The claimed exact value is c = 1 / ( 2 log 2 ) c = 1/(2\sqrt{\log 2}) c = 1/ ( 2 log 2 ) .
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number-theory Apr 25, 2026 Significance 10/100 Registry: 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.
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combinatorics Jun 10, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
A cyclic meander induces a cyclic permutation on its 2 n 2n 2 n marked intersection points. Schwartz's conjecture on the quadratic growth of the associated meander number is resolved.
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number-theory Jul 8, 2026 Significance 10/100 Registry: lean verified
Prior state unknown → proved
h₄(n) = 4 for every n ≥ 331,777, with improved global bounds; the broader problem remains open
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number-theory Jul 24, 2026 Significance 10/100 Registry: lean verified
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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number-theory Jun 5, 2026 Significance 10/100 Registry: 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.
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number-theory Jul 1, 2026 Significance 10/100 Registry: site confirmed
Prior state unknown → proved
Let F ( n ) F(n) F ( n ) be the largest A ⊆ { 1 , … , n } A\subseteq\{1,\dots,n\} A ⊆ { 1 , … , n } with a ∤ b c a\nmid bc a ∤ b c for distinct a , b , c ∈ A a,b,c\in A a , b , c ∈ A . Is F ( n ) = π ( n ) + ( C + o ( 1 ) ) n 2 / 3 ( log n ) − 2 F(n)=\pi(n)+(C+o(1))\,n^{2/3}(\log n)^{-2} F ( n ) = π ( n ) + ( C + o ( 1 )) n 2/3 ( log n ) − 2 for some constant C C C ?
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number-theory Apr 15, 2026 Significance 10/100 Registry: unreviewed
Prior state unknown → proved
Identifies the exponent as a variational sunflower-capacity constant, sharpening the Tang-Zhang bounds; the value of that constant itself remains open, as does site acceptance
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combinatorics May 3, 2026 Significance 10/100 Registry: 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.
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