Mathematical FrontierNetworkSubmit movement

Open registry federation

Mathematical findings

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

All 690unreviewed 432lean verified 144site confirmed 66lean checked 33expert verified 13contested 2

Editorial data from VibeMathed is CC BY 4.0 licensed. Linked papers and authors’ text retain their own rights. Each record links to its registry entry and primary source. Verification labels are attributed to the registry.

geometry-topologyAug 13, 2026Significance 38/100Registry: unreviewed

Universal volume growth bounds from positive intermediate curvature

Prior state unknown→proved

Gromov's 1986 question drew three independent proofs within about 24 hours, two with AI in the loop. Ge's non-AI proof (heat-kernel Fisher metric, Nash entropy) came first, 13 August. Antonelli's proof here (14 August, GPT-5.6 Sol) takes a different route, Hodge obstruction and rank improvement, and its headline addition is the general family: for every 0≤m≤n−20\le m\le n-2, nonnegative Ricci plus positive (m+1)(m{+}1)-inte…

Source authenticatedUniversal volume growth bounds from positive intermediate curvature →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
combinatoricsAug 4, 2026Significance 38/100Registry: lean verified

Asymptotically attaining the Moore bound

Prior state unknown→proved

Settles two conjectures. Theorem 1.1 proves Bollobas's asymptotic degree-diameter conjecture, in the stronger liminf form rather than the conjectured limsup. Corollary 1.2 proves Conjecture 3 of Cambie, Cames van Batenburg, de Joannis de Verclos and Kang on the edge variant, again in the stronger liminf form, and is tight for bipartite graphs.

Source authenticatedAsymptotically attaining the Moore bound →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
probability-statisticsAug 16, 2026Significance 37/100Registry: unreviewed

Talagrand’s convolution conjecture

Prior state unknown→proved

The claim is the exact conjectured decay: ψμa(u)≤Ca/log⁡u\psi_{\mu_a}(u) \le C_a/\sqrt{\log u} for every u>1u > 1 and every nn, with CaC_a dimension-free - concretely ≲κa2(log⁡κaκa−1)1/2\lesssim \kappa_a^2(\log\frac{\kappa_a}{\kappa_a-1})^{1/2} where κa=(1+a)/(1−a)\kappa_a = (1+a)/(1-a). What is new is one step in a three-paper chain rather than a proof from scratch, and the paper is explicit about it. Chen's reverse-heat and Boolean-bridge framework and X…

Source authenticatedTalagrand’s convolution conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
probability-statisticsMay 11, 2026Significance 37/100Registry: unreviewed

Talagrand's Convexity Problem

Prior state unknown→proved

VibeMathed recorded: Talagrand's Convexity Problem. Consult the linked registry entry for the original report and scope.

Source authenticatedTalagrand's Convexity Problem →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
quantum-information-computingSep 2, 2026Significance 36/100Registry: unreviewed

A Quantum Oracle Separation Between QMA(2)\mathsf{QMA}(2) and QMA\mathsf{QMA}

Prior state unknown→proved

The authors construct a unitary oracle UU such that QMAU≠QMA(2)U. \mathsf{QMA}^{U}\neq\mathsf{QMA}(2)^{U}. Their black-box problem is solvable by a QMA(2)\mathsf{QMA}(2) verifier with one oracle query and linear-size unentangled proofs, whereas any QMA\mathsf{QMA} verifier must use either exponentially many queries or an exponentially large witness. As a non-oracle consequence, they prove that for every fixed…

Source authenticatedA Quantum Oracle Separation Between QMA(2)\mathsf{QMA}(2) and QMA\mathsf{QMA} →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theoryAug 28, 2026Significance 35/100Registry: lean verified

Erdős Problem #126: prime divisors of pairwise sums

Prior state unknown→proved

For f(n)=min⁡∣A∣=n∣{p prime:p∣a+b for some distinct a,b∈A}∣, f(n)=\min_{|A|=n}\left|\left\{p\text{ prime}:p\mid a+b\text{ for some distinct }a,b\in A\right\}\right|, Astra formally proves f(n)log⁡n→∞. \frac{f(n)}{\log n}\to\infty. The repository contains substantially stronger proofs. In particular, one verified alternate resolution establishes n≤3r2, n\le 3r^2, where rr is the number of supporting primes, yielding f(n)≫n1/2. f(n)\gg n^{1/2}. Other independent resolutions give…

Source authenticatedErdős Problem #126: prime divisors of pairwise sums →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
algebraJul 22, 2026Significance 35/100Registry: unreviewed

An Explicit Counterexample to the Rank-Two Poisson Conjecture

Prior state unknown→disproved

The paper constructs explicit R,T,D,S∈Q[x,q,p,z]R,T,D,S\in\mathbb Q[x,q,p,z] defining a Poisson endomorphism of the canonical rank-two Poisson algebra P2\mathcal P_2 that is not an automorphism. Its associated polynomial map preserves the canonical symplectic form, has Jacobian determinant 11, and has an explicit fiber of exactly three points. Thus PC(2)\mathrm{PC}(2) is false, and stabilization gives failure of PC(n)\mathrm{PC}(n) for…

Source authenticatedAn Explicit Counterexample to the Rank-Two Poisson Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
theoretical-computer-scienceAug 1, 2026Significance 35/100Registry: lean verified

Polynomial-Factor Hardness for the Closest Vector Problem

Prior state unknown→proved

VibeMathed recorded: Polynomial-Factor Hardness for the Closest Vector Problem. Consult the linked registry entry for the original report and scope.

Source authenticatedPolynomial-Factor Hardness for the Closest Vector Problem →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
mathematical-physicsJul 20, 2026Significance 35/100Registry: unreviewed

Full-RSB in the Sherrington–Kirkpatrick spin glass

Prior state unknown→proved

For the Sherrington-Kirkpatrick model with no external field, at zero temperature β=∞\beta=\infty, the paper proves that the zero-temperature Parisi minimizer is absolutely continuous with a smooth density and has support [0,1)[0,1) - full replica symmetry breaking, confirming the Parisi picture at the ground state. It also shows qβ→1q_\beta\to1 as β→∞\beta\to\infty. The positive-temperature input is Lopatto's: for every…

Source authenticatedFull-RSB in the Sherrington–Kirkpatrick spin glass →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisAug 12, 2026Significance 35/100Registry: unreviewed

Gamow liquid-drop minimizer conjecture

Prior state unknown→proved

The complete fixed-volume picture, closing a gap that partial results had narrowed from both ends without meeting: balls uniquely minimize for every volume up to V_* = 3.51..., and above it no minimizer exists at all. Before this the best minimality range was V <= 1 (Chodosh-Ruohoniemi, 2025) and the best nonexistence bound V >= 7.5 (Schulz, posted two days earlier), so the open middle ran from 1 to 7.5. Frank-Nam h…

Source authenticatedGamow liquid-drop minimizer conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisJul 31, 2026Significance 35/100Registry: unreviewed

Pólya's Conjecture for Neumann Balls in Dimensions Three and Higher

Prior state unknown→proved

The ball case. For arbitrary domains Pólya's conjecture remains open; this continues the authors' programme after the planar disk, circular sectors, and the Dirichlet case in arbitrary dimensions.

Source authenticatedPólya's Conjecture for Neumann Balls in Dimensions Three and Higher →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theoryMay 20, 2026Significance 35/100Registry: unreviewed

Erdős Problem #387

Prior state unknown→disproved

false in general; the positive direction holds for k large relative to n

Source authenticatedErdős Problem #387 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
logic-foundationsAug 13, 2026Significance 35/100Registry: unreviewed

SOP2=SOP3SOP_2 = SOP_3

Prior state unknown→proved

The new content is SOP2⇒SOP3SOP_2 \Rightarrow SOP_3; the converse implication was known from the start. Dzamonja and Shelah asked whether either implication in SOP3⇒SOP2⇒SOP1SOP_3 \Rightarrow SOP_2 \Rightarrow SOP_1 reverses: Mutchnik answered the second (SOP1=SOP2SOP_1 = SOP_2), and this answers the first, collapsing the bottom of the hierarchy to SOP1=SOP2=SOP3SOP_1 = SOP_2 = SOP_3. The SOPnSOP_n hierarchy for n≥3n \ge 3 remains, as does everything above…

Source authenticatedSOP2=SOP3SOP_2 = SOP_3 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
probability-statisticsJul 27, 2026Significance 35/100Registry: lean verified

Feige's Conjecture

Prior state unknown→proved

VibeMathed recorded: Feige's Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedFeige's Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
theoretical-computer-scienceJul 20, 2026Significance 35/100Registry: unreviewed

Optimality of Greedy for Single-Pass Semi-Streaming Matching

Prior state unknown→proved

VibeMathed recorded: Optimality of Greedy for Single-Pass Semi-Streaming Matching. Consult the linked registry entry for the original report and scope.

Source authenticatedOptimality of Greedy for Single-Pass Semi-Streaming Matching →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
quantum-information-computingJul 23, 2026Significance 35/100Registry: unreviewed

Two-Copy Distillability of Werner States

Prior state unknown→disproved

Two-copy distillable if and only if already one-copy distillable. Four independent papers settled this within five days of each other, and no single one of them is the account of record. Fu, Gao and Park posted first on 23 July (arXiv:2607.21367), followed by Song and Chen on 26 July (arXiv:2607.23416), then on 27 July both Fraser, Huber, Pozsgay and Vona (arXiv:2607.24309) and Bharti, Gajjala and Haug (arXiv:2607.…

Source authenticatedTwo-Copy Distillability of Werner States →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisJul 27, 2026Significance 35/100Registry: expert verified

Crouzeix's Conjecture

Prior state unknown→proved

Two independent proofs within eight days, both with AI in the loop. Jin's (posted 27 July, preprints.org, submitted to Annals) is the first: its decisive theorem came out of an autonomous GPT-5.6 Sol run, and it is the proof Townsend, Greenbaum and Crouzeix have checked. Lorist and Schwenninger's five-page argument (arXiv, 4 August) is a genuinely different route - double-layer potentials plus a perturbation lemma f…

Source authenticatedCrouzeix's Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisAug 5, 2026Significance 33/100Registry: unreviewed

HRT Conjecture

Prior state unknown→disproved

VibeMathed recorded: HRT Conjecture. Consult the linked registry entry for the original report and scope.

Source authenticatedHRT Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
combinatoricsAug 29, 2026Significance 32/100Registry: site confirmed

Dean's conjecture for k=5k=5

Prior state unknown→proved

Claims the last open case of Dean's conjecture: every finite simple graph with minimum degree at least five contains a cycle of length divisible by five. Verified independently against Luo, Ma and Zhao (arXiv:2601.13552), whose abstract confirms the landscape - the conjecture was known for k∈{3,4}k\in\{3,4\} and they proved every k≥6k\ge6, leaving k=5k=5 open. If this proof stands, Dean's conjecture holds for all k≥3k\ge3.…

Source authenticatedDean's conjecture for k=5k=5 →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
algorithms-optimizationOct 27, 2025Significance 32/100Registry: unreviewed

Point Convergence of Nesterov's Accelerated Gradient Method

Prior state unknown→proved

VibeMathed recorded: Point Convergence of Nesterov's Accelerated Gradient Method. Consult the linked registry entry for the original report and scope.

Source authenticatedPoint Convergence of Nesterov's Accelerated Gradient Method →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
probability-statisticsAug 6, 2026Significance 32/100Registry: unreviewed

Central limit theorem for the random assignment problem

Prior state unknown→proved

Claims the central limit theorem for the bipartite random assignment problem with bounded uniform costs: n (Cn−ζ(2))⇒N(0, 4ζ(2)−4ζ(3))\sqrt{n}\,(C_n-\zeta(2)) \Rightarrow \mathcal{N}(0,\,4\zeta(2)-4\zeta(3)). The limiting constant is not itself new - Wästlund had computed exactly 4ζ(2)−4ζ(3)4\zeta(2)-4\zeta(3) for the mean-one exponential model, and Malatesta, Parisi and Sicuro derived the non-bipartite analogue by replicas - but neither is a proof fo…

Source authenticatedCentral limit theorem for the random assignment problem →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
differential-equationsSep 2, 2026Significance 30/100Registry: unreviewed

Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

Prior state unknown→proved

For every n≥3n\geq3, let u∈C∞(B2)u\in C^\infty(B_2) be an admissible solution of κ[u]∈Γ2,σ2(κ[u])=1, \kappa[u]\in\Gamma_2,\qquad \sigma_2(\kappa[u])=1, with ∥u∥L∞(B2)+∥Du∥L∞(B2)≤K. \|u\|_{L^\infty(B_2)}+\|Du\|_{L^\infty(B_2)}\le K. Then sup⁡B1/2∣κ[u]∣≤C(n,K). \sup_{B_{1/2}}|\kappa[u]|\le C(n,K). Thus an admissible graph of constant scalar curvature with bounded height and slope cannot develop unbounded interior curvature, in any dimension n≥3n\ge3. Prior unrestricted qua…

Source authenticatedInterior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
analysisAug 12, 2026Significance 30/100Registry: lean verified

Phelps–Rodriguez Conjecture

Prior state unknown→proved

Phelps-Rodriguez implies Sendov, so this entry records the stronger of the pair; the companion Sendov entry records the weaker statement and Mazur's original formalization, which proved Sendov but never stated the equality classification. The exceptional family is genuinely attained rather than an artefact of the proof: for p = z^n - 1 and a = 1 the only critical point is the origin, at distance exactly 1. Both conj…

Source authenticatedPhelps–Rodriguez Conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
geometry-topologyAug 14, 2026Significance 30/100Registry: unreviewed

Kusner's Conjecture on Equilateral Sets in ℓpn\ell_p^n

Prior state unknown→disproved

VibeMathed recorded: Kusner's Conjecture on Equilateral Sets in ℓpn\ell_p^n. Consult the linked registry entry for the original report and scope.

Source authenticatedKusner's Conjecture on Equilateral Sets in ℓpn\ell_p^n →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
mathematical-physicsAug 9, 2026Significance 30/100Registry: unreviewed

Talagrand's critical Sherrington-Kirkpatrick overlap conjecture

Prior state unknown→proved

Talagrand's Conjecture 11.7.5 is resolved affirmatively for the critical Ising Sherrington-Kirkpatrick model: N2/3E⟨R1,22⟩N^{2/3}\mathbb{E}\langle R_{1,2}^2\rangle converges to a positive finite constant. The paper proves substantially more, showing that the entire quenched distribution of N1/3R1,2N^{1/3}R_{1,2} converges to an explicit random probability measure defined from the reflected Airy1\mathrm{Airy}_1 point process. The same…

Source authenticatedTalagrand's critical Sherrington-Kirkpatrick overlap conjecture →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
quantum-information-computingAug 9, 2026Significance 30/100Registry: unreviewed

Finite-Copy Distillability of NPT States in the DiVincenzo Family

Prior state unknown→disproved

Partial deliberately: the NPT bound entanglement problem itself is untouched. What falls is the conjecture about the canonical family, and the paper is explicit that a substantial neighbouring region remains unresolved while another is known two-copy undistillable.

Source authenticatedFinite-Copy Distillability of NPT States in the DiVincenzo Family →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review