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639 source-grounded records. Verification labels remain separate from source authentication and publication status.

All 639unreviewed 405lean verified 136site confirmed 59lean checked 25expert verified 12contested 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.

combinatoricsAug 11, 2026Significance 14/100Registry: unreviewed

The First Rigorous Solid Standard Young Tableaux Challenge

Prior state unknown→proved

The first rigorous solid standard Young tableaux challenge asks for a proof of a conjectured second-order recurrence for the number of solid standard Young tableaux. The conjectured recurrence is proved.

Source authenticatedThe First Rigorous Solid Standard Young Tableaux Challenge →
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algebraAug 25, 2026Significance 14/100Registry: site confirmed

Fröberg’s conjecture for quintics and septics in four variables

Prior state unknown→proved

Let S=k[x1,x2,x3,x4]S=k[x_1,x_2,x_3,x_4] over any characteristic-zero field. For each d∈{5,7}d\in\{5,7\} and every r≥1r\ge1, the paper proves that rr general degree-dd forms satisfy Fröberg’s predicted Hilbert series HS⁡S/(F1,…,Fr)(t)=[(1−td)r(1−t)4]+. \operatorname{HS}_{S/(F_1,\ldots,F_r)}(t) = \left[\frac{(1-t^d)^r}{(1-t)^4}\right]_+. The genuinely new ranges are 6≤r≤116\le r\le11 for quintics and 6≤r≤216\le r\le21 for septics. These are reduced to finitely many exac…

Source authenticatedFröberg’s conjecture for quintics and septics in four variables →
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logic-foundationsAug 19, 2026Significance 14/100Registry: lean verified

Erdős Problem #501: infinite independent sets for families of small outer measure

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+\mathfrak{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,…

Source authenticatedErdős Problem #501: infinite independent sets for families of small outer measure →
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number-theoryJul 31, 2026Significance 14/100Registry: unreviewed

Improved integrality of Donaldson–Thomas invariants of loop quivers (GKS Conjecture 1.3 for twist knots)

Prior state unknown→proved

The sharp valuation bounds and optimal γ(m)\gamma(m) are proved for ALL loop quivers m≥2m\ge2, 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=3m=3/figure-eight divisibility 2nr/r∈Z2n_r/r\in\mathbb Z was previously proved by Basor–Conrey–Morrison (arXiv:1703.00990), whose per-rr 22-adic characterization for m=3m=3 is finer than the uni…

Source authenticatedImproved integrality of Donaldson–Thomas invariants of loop quivers (GKS Conjecture 1.3 for twist knots) →
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combinatoricsAug 11, 2026Significance 14/100Registry: unreviewed

The Five-Dimensional Geode Challenge of Amdeberhan, Kauers and Zeilberger

Prior state unknown→proved

The five-dimensional case of the Geode challenge of Amdeberhan, Kauers and Zeilberger, concerning the geode factor attached to a family of multivariate generating functions. Settled in dimension five.

Source authenticatedThe Five-Dimensional Geode Challenge of Amdeberhan, Kauers and Zeilberger →
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combinatoricsMay 21, 2026Significance 14/100Registry: lean verified

Erdős Problem #138

Prior state unknown→proved

the stronger question W(k)1/k→∞W(k)^{1/k} \to \infty remains open

Source authenticatedErdős Problem #138 →
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probability-statisticsJul 13, 2026Significance 14/100Registry: unreviewed

Benjamini-Hochberg FDR Under Correlated Gaussian Tests

Prior state unknown→disproved

Does the Benjamini-Hochberg procedure always control the false-discovery rate at its nominal level for correlated two-sided Gaussian p-values? A factor model gives FDR>0.0104\mathrm{FDR} > 0.0104 at nominal level α=0.01\alpha = 0.01.

Source authenticatedBenjamini-Hochberg FDR Under Correlated Gaussian Tests →
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number-theoryJul 20, 2026Significance 13/100Registry: lean verified

Erdős Problem #424

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.

Source authenticatedErdős Problem #424 →
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analysisJul 1, 2026Significance 13/100Registry: site confirmed

Erdős Problem #119

Prior state unknown→proved

For unit-modulus complex numbers ziz_i, let pn(z)=∏i≤n(z−zi)p_n(z)=\prod_{i\le n}(z-z_i) and Mn=max⁡∣z∣=1∣pn(z)∣M_n=\max_{|z|=1}|p_n(z)|. Erdős's prize question: is there c>0c>0 with ∑k≤nMk>n1+c\sum_{k\le n} M_k > n^{1+c}?

Source authenticatedErdős Problem #119 →
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combinatoricsJun 23, 2026Significance 13/100Registry: unreviewed

Erdos Problems #593 and #1177

Prior state unknown→proved

settles two numbered Erdos problems at once

Source authenticatedErdos Problems #593 and #1177 →
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algebraJul 20, 2026Significance 13/100Registry: lean verified

Kourovka Problem 21.8 - Horizontal Class Transpositions

Prior state unknown→proved

If CT⁡(k)\operatorname{CT}_{(k)} is generated by all horizontal class transpositions with modulus at most kk, is CT⁡(k)≅Slcm⁡(2,…,k)\operatorname{CT}_{(k)} \cong S_{\operatorname{lcm}(2,\dots,k)} for every k≥4k \ge 4?

Source authenticatedKourovka Problem 21.8 - Horizontal Class Transpositions →
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number-theoryJul 19, 2026Significance 13/100Registry: lean verified

Erdős Problem #390: the second-order constant for f(n)−2nf(n)-2n

Prior state unknown→proved

The headline is the constant, and its two halves have different histories. The lower bound, lim inf⁡(f(n)−2n)/(n/log⁡n)≥4029639598/25970038185\liminf (f(n)-2n)/(n/\log n) \ge 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."…

Source authenticatedErdős Problem #390: the second-order constant for f(n)−2nf(n)-2n →
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algebraJul 20, 2026Significance 13/100Registry: lean verified

Kourovka Problem 21.150 - Rank Inequality for p-Group Extensions

Prior state unknown→disproved

For an extension G=A⋊BG = A \rtimes B of elementary abelian pp-groups with a∈Aa \in A satisfying CB(a)=1C_B(a) = 1, must H=⟨a,B⟩H = \langle a, B\rangle satisfy rank⁡(Z(H)∩H′)≤rank⁡(B)\operatorname{rank}(Z(H) \cap H') \le \operatorname{rank}(B)? An explicit extension violates the bound.

Source authenticatedKourovka Problem 21.150 - Rank Inequality for p-Group Extensions →
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algebraJul 20, 2026Significance 13/100Registry: lean verified

Kourovka Problem 21.24 - Cograph Power Graphs Are Chordal

Prior state unknown→proved

If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four - that is, is every cograph power graph chordal?

Source authenticatedKourovka Problem 21.24 - Cograph Power Graphs Are Chordal →
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number-theoryJul 29, 2026Significance 13/100Registry: unreviewed

Improved Bounds for Distinct Multiples in Intervals

Prior state unknown→disproved

For the Erdős–Pomerance functions F(n)F(n) and hP(n)h_{\mathbb{P}}(n) counting how many consecutive integers are needed to contain a distinct multiple of each integer, respectively prime, up to nn, the paper proves F(n)≥hP(n)≥nexp⁡((log⁡22−o(1))log⁡nlog⁡log⁡n)F(n) \ge h_{\mathbb{P}}(n) \ge n\exp\left(\left(\frac{\log 2}{2} - o(1)\right)\frac{\log n}{\log\log n}\right), disproving Kominers' conjecture that F(n)≪nlog⁡nF(n) \ll n\log n. The paper also significantly improve…

Source authenticatedImproved Bounds for Distinct Multiples in Intervals →
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combinatoricsJul 23, 2026Significance 13/100Registry: lean verified

Erdős Problem #593

Prior state unknown→proved

Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.

Source authenticatedErdős Problem #593 →
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algorithms-optimizationAug 10, 2026Significance 12/100Registry: unreviewed

Bounded Oracle Error in Nonconvex Stochastic Optimization

Prior state unknown→proved

Arjevani et al. asked whether almost-surely bounded oracle error permits a better rate than bounded variance for smooth nonconvex stochastic optimization. It does not: every randomized adaptive algorithm still needs Omega(dL/eps^2 + dL sigma^2/eps^4) queries, matching the standard upper bound.

Source authenticatedBounded Oracle Error in Nonconvex Stochastic Optimization →
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analysisJun 22, 2026Significance 12/100Registry: lean verified

Erdős Problem #671

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

Source authenticatedErdős Problem #671 →
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combinatoricsFeb 17, 2026Significance 12/100Registry: unreviewed

The Leading Constant for Large-Order Davenport-Schinzel Sequences

Prior state unknown→proved

Wellman and Pettie noted that the true leading constant for large-order Davenport-Schinzel sequences was known only to lie in an interval. The paper improves the Roselle-Stanton lower bound to match the pigeonhole upper bound in the leading term, resolving the constant to exactly 1/2.

Source authenticatedThe Leading Constant for Large-Order Davenport-Schinzel Sequences →
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probability-statisticsApr 5, 2026Significance 12/100Registry: unreviewed

Equality in Fill's Spectral Gap Problem

Prior state unknown→proved

For the adjacent-transposition chain on Sn\mathfrak{S}_n with a regular parameter vector, Fill's spectral gap conjecture (recently resolved) leaves open the characterization of the equality cases. The paper settles them, constructing the additional eigenfunctions in the exceptional regime.

Source authenticatedEquality in Fill's Spectral Gap Problem →
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theoretical-computer-scienceJul 24, 2026Significance 12/100Registry: unreviewed

Ghasemi-Kopparty Problem on Sparse SS-Decoding Polynomials

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

Source authenticatedGhasemi-Kopparty Problem on Sparse SS-Decoding Polynomials →
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probability-statisticsMar 31, 2026Significance 12/100Registry: unreviewed

Counting Partial Hadamard Matrices in the Cubic Regime

Prior state unknown→proved

A precise asymptotic formula for the number of n×4tn \times 4t partial Hadamard matrices in the regimes t/n3→∞t/n^3 \to \infty and t/n3→Θt/n^3 \to \Theta, reaching the cubic regime that previous approaches (de Launey-Levin and successors) could not.

Source authenticatedCounting Partial Hadamard Matrices in the Cubic Regime →
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geometry-topologyAug 7, 2026Significance 12/100Registry: unreviewed

Log-Submodularity of Zonoid Volume

Prior state unknown→disproved

The paper also proves the conjecture in the unimodular case and characterizes equality there, so the boundary between true and false is drawn rather than just crossed.

Source authenticatedLog-Submodularity of Zonoid Volume →
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combinatoricsAug 4, 2026Significance 12/100Registry: expert verified

The Middle Stair of Parallel Chip-Firing

Prior state unknown→proved

Ji, Li and Wang conjectured in 2024 that every parallel chip-firing game on a finite connected graph whose chip count lies strictly between 2∣E∣−∣V∣2|E|-|V| and 2∣E∣2|E| has period exactly 2, generalizing the middle rung of Levine's devil's staircase from complete graphs to all graphs. Known before only for trees, cycles, complete and complete bipartite graphs.

Source authenticatedThe Middle Stair of Parallel Chip-Firing →
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combinatoricsAug 13, 2026Significance 12/100Registry: unreviewed

The Foregger–Sinkhorn Tie-Point Conjecture

Prior state unknown→disproved

The Foregger–Sinkhorn tie-point conjecture, Conjecture 41 in Minc's survey, asserts that if a nearly decomposable doubly stochastic matrix minimizes the permanent on a face and the permanental cofactor at a prescribed zero exceeds its permanent, then that zero is a tie point. False: an explicit 8×88 \times 8 counterexample exists, built on the unique root β\beta of 7t3−13t2+12t−47t^3 - 13t^2 + 12t - 4 in (59/100,3/5)(59/100, 3/5).

Source authenticatedThe Foregger–Sinkhorn Tie-Point Conjecture →
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quantum-information-computingAug 6, 2026Significance 12/100Registry: site confirmed

Absolutely Maximally Entangled States in Five Open Cases

Prior state unknown→proved

Five existence statements, all by explicit construction: AME(12,5)\mathrm{AME}(12,5), AME(17,11)\mathrm{AME}(17,11), AME(18,11)\mathrm{AME}(18,11), AME(17,13)\mathrm{AME}(17,13) and AME(18,13)\mathrm{AME}(18,13). The [12,6,7]25[12,6,7]_{25} code came from a direct search with no symmetry imposed; its automorphism group turned out to have a regular Z32\mathbb{Z}_3^2 coordinate orbit, and imposing that translation symmetry on two nine-coordinate orbits collapses an…

Source authenticatedAbsolutely Maximally Entangled States in Five Open Cases →
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number-theoryMay 21, 2026Significance 12/100Registry: lean verified

Erdős Problem #12

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

Source authenticatedErdős Problem #12 →
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number-theoryAug 22, 2026Significance 12/100Registry: unreviewed

Transcendence in the affine case of Erdős Problem 270

Prior state unknown→proved

The manuscript claims Ca,bC_{a,b} is transcendental for every a≥1a\ge1 and b≥1−ab\ge1-a, settling the positive integer-valued affine subclass of Erdős Problem 270. Two pieces of context matter. Problem 270 as Erdős and Graham posed it, for every f(n)→∞f(n)\to\infty, was already answered no by Crmarić and Kovač in 2025: for any α>0\alpha>0 some such ff makes the series sum to α\alpha. What survives is the non-decreasing case,…

Source authenticatedTranscendence in the affine case of Erdős Problem 270 →
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number-theoryApr 23, 2026Significance 12/100Registry: lean verified

Erdős Problem #202

Prior state unknown→proved

VibeMathed records this result as “Erdős Problem #202.” The registry entry and named primary source contain the available statement and scope.

Source authenticatedErdős Problem #202 →
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