combinatoricsJun 5, 2026Significance 15/100Registry: unreviewed
Prior state unknown→proved
asymptotic in k; the paper also shows the analogous statement is false for d = 2
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quantum-information-computingJul 31, 2026Significance 15/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Online Shadow Tomography Matching the Classical Bounds. Consult the linked registry entry for the original report and scope.
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combinatoricsJul 21, 2026Significance 15/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Pak-Slonim Conjecture on Stretched Schubert Structure Constants. Consult the linked registry entry for the original report and scope.
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algorithms-optimizationAug 14, 2026Significance 15/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Convergence of Three-Block ADMM with Identity Third Block. Consult the linked registry entry for the original report and scope.
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number-theoryMar 31, 2026Significance 15/100Registry: lean checked
Prior state unknown→disproved
VibeMathed recorded: Sárközy's Conjecture on Sums and Products Modulo a Prime. Consult the linked registry entry for the original report and scope.
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combinatoricsMay 21, 2026Significance 14/100Registry: lean verified
Prior state unknown→proved
the stronger question W(k)1/k→∞ remains open
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logic-foundationsAug 19, 2026Significance 14/100Registry: lean verified
Prior state unknown→independent
Independent of ZFC, which is why this entry is the first to carry that result rather than proved or disproved. Both directions are formalized: Hechler's 1972 construction gives a model where the answer is no, and adding c+ random reals over a model of CH gives one where it is yes.
The credit is shared and mostly human. Newelski, Pawlikowski and Seredynski settled the problem's second question in 1987,…
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combinatoricsAug 11, 2026Significance 14/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: The Five-Dimensional Geode Challenge of Amdeberhan, Kauers and Zeilberger. Consult the linked registry entry for the original report and scope.
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number-theoryJul 31, 2026Significance 14/100Registry: unreviewed
Prior state unknown→proved
The sharp valuation bounds and optimal γ(m) are proved for ALL loop quivers m≥2, hence for the extremal BPS invariants of all twist knots (both rows, matching every twist-knot entry of GKS Table 1). Scope limits: the m=3/figure-eight divisibility 2nr/r∈Z was previously proved by Basor–Conrey–Morrison (arXiv:1703.00990), whose per-r 2-adic characterization for m=3 is finer than the uni…
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combinatoricsAug 11, 2026Significance 14/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: The First Rigorous Solid Standard Young Tableaux Challenge. Consult the linked registry entry for the original report and scope.
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probability-statisticsJul 13, 2026Significance 14/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Benjamini-Hochberg FDR Under Correlated Gaussian Tests. Consult the linked registry entry for the original report and scope.
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algebraAug 25, 2026Significance 14/100Registry: site confirmed
Prior state unknown→proved
Let S=k[x1,x2,x3,x4] over any characteristic-zero field. For each d∈{5,7} and every r≥1, the paper proves that r general degree-d forms satisfy Fröberg’s predicted Hilbert series
HSS/(F1,…,Fr)(t)=[(1−t)4(1−td)r]+.
The genuinely new ranges are 6≤r≤11 for quintics and 6≤r≤21 for septics. These are reduced to finitely many exac…
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algebraJul 20, 2026Significance 14/100Registry: lean verified
Prior state unknown→proved
VibeMathed recorded: Kourovka Problem 20.125 - Noninjective Rota-Baxter Operator. Consult the linked registry entry for the original report and scope.
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number-theoryJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
Proves positive lower density. The Formal Conjectures encoding asks for Set.HasPosDensity, a density that exists and is positive; erdosproblems.com says Erdos most likely meant lower density.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
VibeMathed recorded: Kourovka Problem 21.8 - Horizontal Class Transpositions. Consult the linked registry entry for the original report and scope.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→disproved
VibeMathed recorded: Kourovka Problem 21.147 - Relatively Convex Subgroups. Consult the linked registry entry for the original report and scope.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
VibeMathed recorded: Kourovka Problem 21.24 - Cograph Power Graphs Are Chordal. Consult the linked registry entry for the original report and scope.
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combinatoricsJun 23, 2026Significance 13/100Registry: unreviewed
Prior state unknown→proved
settles two numbered Erdos problems at once
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analysisJul 1, 2026Significance 13/100Registry: site confirmed
Prior state unknown→proved
VibeMathed recorded: Erdős Problem #119. Consult the linked registry entry for the original report and scope.
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number-theoryJul 29, 2026Significance 13/100Registry: unreviewed
Prior state unknown→disproved
VibeMathed recorded: Improved Bounds for Distinct Multiples in Intervals. Consult the linked registry entry for the original report and scope.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→disproved
VibeMathed recorded: Kourovka Problem 21.150 - Rank Inequality for p-Group Extensions. Consult the linked registry entry for the original report and scope.
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number-theoryJul 19, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
The headline is the constant, and its two halves have different histories. The lower bound, liminf(f(n)−2n)/(n/logn)≥4029639598/25970038185, is not new here: it is Mausberg's thirteen-layer valuation cut, posted to the erdosproblems.com forum in May 2026 and credited as such in the paper. Its author wrote there that it "does not prove an upper bound, nor does it prove that an asymptotic constant exists."…
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combinatoricsJul 23, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
VibeMathed recorded: Erdős Problem #593. Consult the linked registry entry for the original report and scope.
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combinatoricsSep 5, 2026Significance 12/100Registry: lean checked
Prior state unknown→disproved
Let H be the Berlekamp–van Lint–Seidel graph on 243 vertices, the Cayley graph of Z35 with strongly regular parameters
(243,22,1,2),
and let G=H.
The proof establishes
γ(G)=3
because every pair has a common neighbor in H, while an H-triangle gives a dominating triple in G.
It then proves
γ∞(G)=3
by showing that the family of all dominating triples…
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geometry-topologyAug 17, 2026Significance 12/100Registry: unreviewed
Prior state unknown→disproved
Disproved. An explicit 32-leaf tree has least isometric ℓ∞-dimension six, not the conjectured five, and keeps dimension six under every assignment of positive edge lengths, so the weighted sharp-threshold conjecture falls too. Every tree with at most 31 leaves does attain ⌈log2t⌉, so 32 is the first failure; Brigham et al. had checked through 21. The proof is finite and exact: six explici…
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algebraAug 18, 2026Significance 12/100Registry: lean checked
Prior state unknown→proved
For pairwise distinct real numbers x1,…,xN and an integer D≥1, Ma proves the complete classification
det[(xj−xi)D]i,j=1N=0⟺D≥N−1 and (N is even or D is even).
This fully resolves Colombo’s original conjecture for even N. The new part is the even-size, odd-exponent branch, strengthened to the strict Pfaffian…
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theoretical-computer-scienceSep 3, 2026Significance 12/100Registry: site confirmed
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…
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number-theoryAug 1, 2026Significance 12/100Registry: lean checked
Prior state unknown→proved
New theorems, not a formalisation of known results. In base ten the bare existence of a square with any admissible digit sum was recorded in the recreational literature (Murthy–Ashbacher 2005); the theorem here is the quantitative all-base version — roots coprime to b (excluding their trailing-zero trick), exp(c_b√q) representations of controlled size — and that statement is what is machine-checked, with effective b…
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analysisApr 16, 2026Significance 12/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Wickstead's Conjecture on Positive Projections. Consult the linked registry entry for the original report and scope.
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number-theoryApr 23, 2026Significance 12/100Registry: lean verified
Prior state unknown→proved
VibeMathed recorded: Erdős Problem #202. Consult the linked registry entry for the original report and scope.
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theoretical-computer-scienceJul 10, 2026Significance 12/100Registry: unreviewed
Prior state unknown→proved
VibeMathed recorded: Klopp-Zadik Question on Polynomial-Time Node-Private Recovery. Consult the linked registry entry for the original report and scope.
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analysisJun 22, 2026Significance 12/100Registry: lean verified
Prior state unknown→proved
Both parts claimed answered affirmatively, with a Lean formalization; two proof claims are filed on erdosproblems.com but the problem is still listed open
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algorithms-optimizationAug 9, 2026Significance 12/100Registry: unreviewed
Prior state unknown→proved
Improves every prior result for p >= 2 and matches the classical extragradient method at p = 1.
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theoretical-computer-scienceJul 24, 2026Significance 12/100Registry: unreviewed
Prior state unknown→proved
the PIR consequence is conditional on a number-theoretic conjecture implied by either the generalized repunit conjecture or Schinzel's hypothesis H, and is unconditional for s <= 15
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combinatoricsDec 16, 2025Significance 12/100Registry: unreviewed
Prior state unknown→proved
An improved lower bound on the maximal product; the sharp maximizer for the 1958 question remains unknown.
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number-theoryMay 21, 2026Significance 12/100Registry: lean verified
Prior state unknown→proved
parts (i) and (ii) resolved - a near-linear-density construction exists, refuting the N^{1-c} decay; the reciprocal-sum part remains open
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