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690 source-grounded records. Verification labels remain separate from source authentication and publication status.
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VibeMathed recorded: Grothendieck's Finite Flat Group Scheme Order Question. Consult the linked registry entry for the original report and scope.
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.
VibeMathed recorded: The Mihail-Vazirani Conjecture. Consult the linked registry entry for the original report and scope.
Settles subspace dimensions 2 and 3; the generalized problem stays open for larger m.
Bellman's problem for general regions remains open
asymptotic form only; Kotzig's conjecture itself remains far from solved
Priority: the result was first obtained by Max Grinsztajn with GPT-5.5 Pro assistance, published 26 May 2026 and recorded as the current best bound on Tao's optimization-problems ledger. The same construction was found again independently in August 2026 by Nicholas Konz working with Claude, with a different derivation and a fuller AI disclosure; the two efforts were evidently unaware of each other, and the submitter…
Constructed an explicit class of smooth random, time-dependent incompressible velocity fields on T^3, obtained by alternating smooth shear flows with iid random phases on finite time blocks. For every fixed sufficiently small resistivity, the magnetic field has an almost-sure exponential growth rate at least 1/2, together with a time-uniform lower bound whose random prefactor has a resistivity-uniform inverse-moment…
Talagrand's Conjecture 11.7.5 is resolved affirmatively for the critical Ising Sherrington-Kirkpatrick model: converges to a positive finite constant. The paper proves substantially more, showing that the entire quenched distribution of converges to an explicit random probability measure defined from the reflected point process. The same…
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…
VibeMathed recorded: Maxwell's Conjecture on Point-Charge Equilibria. Consult the linked registry entry for the original report and scope.
A dense case, not the conjecture: it remains open in general. The concrete gain is on the size of any counterexample - combined with the known minimum-outdegree results, this raises the best known lower bound on the order of a counterexample from 16 to 17, and to 19 conditional on the 2026 preprint of Sadhukhan, Sandeep and Sen. The novelty against the earlier dense-case work is that no structure is prescribed on th…
VibeMathed recorded: A Five-Variable Counterexample to the Hessian Conjecture. Consult the linked registry entry for the original report and scope.
VibeMathed recorded: Babai's Minimal Cayley Graph Problem. Consult the linked registry entry for the original report and scope.
For every , the paper constructs a bounded map , smooth on but discontinuous at the origin, together with an antisymmetric potential such that Moreover, the potential satisfies the sh…
Closes both gaps left open by Bandeira and Maillard: exact fitting, and removal of the operator-norm constraint. The threshold turns out to be governed by the statistical dimension d(d+1)/4 of the PSD cone.
One variant case of Arnold's 1994 fast-dynamo problem, not the problem itself. Arnold asks for a single velocity field on T^3 that is smooth, divergence-free, autonomous and deterministic, fixed independently of the magnetic diffusivity, and that grows the magnetic field exponentially at every small enough diffusivity. The field constructed here is all of that except smooth: it is Lipschitz, not C^1. The sibling ent…
VibeMathed recorded: Kannan–Tetali–Vempala conjecture (bipartite/binary-matrix case). Consult the linked registry entry for the original report and scope.
Settles 9 and 10 runners only; the general conjecture remains open.
the group case; the full Matrix Spencer conjecture remains open
VibeMathed recorded: Ben Green's Open Problem 90. Consult the linked registry entry for the original report and scope.
Explicit construction of a Hadamard matrix of order 668, the smallest previously unresolved order, verified exactly by this site from the announcement plus its decoder reply. The same post encodes matrices for all twelve previously-open admissible orders below 2000 (668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948, 1964), and this site verified every one of them. The entry records the order-668 existenc…
Refuting log-concavity of the flat counts is weaker than refuting their unimodality, since log-concavity is the stronger property. A counterexample to unimodality followed three weeks later and is tracked separately as Rota's Unimodality Conjecture for Matroid Flats; this paper came first.
VibeMathed recorded: Universal Multiplicative FDR Bound for Benjamini-Hochberg. Consult the linked registry entry for the original report and scope.
For fixed and all sufficiently large depending only on , Glauber dynamics for proper -colorings mixes rapidly on every graph of girth at least whenever : spectral gap and . An analogous theorem holds for the anti-ferromagnetic Potts model at…
a structured special case, proved the same week as the independent group version
Proves the divisible rank-three case: rank exactly three and ground-set size a multiple of three, with no restriction to simple, paving, representable or graphic matroids. The part not previously in the literature is the non-simple sub-case, since McGuinness had settled all paving matroids and a rank-three matroid is paving exactly when it has no parallel pairs. Combined with the coprime-case theorem of van den Heuv…
For every , Bondarenko and Seip construct a nonzero real-valued continuous even function such that and They normalize the construction by requiring , so the function is genuinely nontrivial. For , this gives…
The repository gives a Lean proof of Conway's 1976 refinement conjecture for omnific integers: whenever with , there exist satisfying The proof is formalized twice: once using CombinatorialGames' surreal-number implementation and once with the required surreal definitions inlined over Mathlib. The development also…
VibeMathed recorded: Counting Linear Extensions Below the Barrier. Consult the linked registry entry for the original report and scope.
VibeMathed recorded: The Kára–Pór–Wood Big-Line-Big-Clique Conjecture: Four Collinear Points or a Six-Clique. Consult the linked registry entry for the original report and scope.
For the Ising pure -spin glass where , it was predicted by Gardner that there exists critical inverse temperatures such that: (1) When , the Parisi measure is replica symmetric (RS); (2) When , the Parisi measure is one-step replica symmetry breaking (1-RSB); (3) When , the Parisi measure is full rep…
VibeMathed recorded: The Optimal Approximation Ratio for Permanents of PSD Matrices. Consult the linked registry entry for the original report and scope.
If a bilinear form admits an -sparse bound, its coordinate-wise extension to -valued functions admits an -convex body sparse bound, for with . It holds both in a fixed dyadic lattice (Theorem 2.6, constants independent of the ambient dimension) and for arbitrary cubes (Theorem 3.4), via a randomization of the good part of the form. On scope, two thin…
The paper constructs a simple theory in which forking cannot always be witnessed by a stable formula. Precisely, what fails is: in a simple theory, if then there is forking over whose parameter-free form is stable. The counterexample is an infinite-dimensional vector space over the division ring of fractions of the quantum graph alg…
Let be convex. Williams proves the stronger statement that for every , where denotes poset width. Taking gives which is exactly the Daykin-Frankl conjecture. The proof proceeds by induction on , reducing the step to a structural lemma for a convex subset of and…