OpenAI family coverage register

This register uses one post per family, retaining the source identifiers even where their numbering has gaps. Written means a substantive explanatory article exists; it does not mean that the research theorem has been independently verified. Pending means an eligible article has not yet been written.

There are 277 included families, all written. A further 95 families are excluded. The four excluded catalogue sections account for 74 families; the additional 21 exclusions are listed below. The combined algebraic-and-complex-geometry section is omitted as a group. Operator algebras remain included as analysis.

🏷️ Number theory

Family	Topic	Article
003	The quasi-Riemann hypothesis	Written
005	Irrationality of Catalan’s constant	Written
007	Two-point Chowla and the corrected binary Elliott conjecture	Written
011	The Ford–Konyagin–Luca conjecture on prime predecessors	Written
012	Independent largest prime factors of consecutive integers	Written
013	Ostmann’s inverse Goldbach conjecture	Written
015	Torus-packet equidistribution in prime, quartic, and sextic degrees	Written
017	The irrationality exponent of $\pi$ is $2$	Written
020	Squarefree quartics and power-free polynomial values	Written
021	A quadratic bound for Jacobsthal’s function	Written
022	The weak inhomogeneous Duffin–Schaeffer conjecture	Written
023	Patterson’s first moment for cubic Gauss sums	Written
024	An asymptotic formula for the number of totients	Written
025	Erdős’s short Egyptian-fraction conjecture	Written
026	Positive lower density of large prime gaps	Written
028	The Gaussian moat conjecture	Written
029	Artin’s primitive root conjecture: infinitude for every base	Written

🏷️ Real and complex analysis

Family	Topic	Article
071	Koebe’s circle-domain conjecture and circle-domain rigidity	Written
072	Brennan’s conjecture and a counterexample to Kraetzer’s prediction	Written
073	The Falconer distance conjecture	Written
074	Kakeya in three and four dimensions	Written
075	The $L\log L$ Fourier-convergence conjecture	Written
076	Ultraflat real Littlewood polynomials	Written
077	Fourier restriction for positively curved surfaces	Written
078	The three-dimensional Bochner–Riesz conjecture	Written
079	Sogge’s local smoothing conjecture in dimension three	Written
080	The Sobolev endpoint in Carleson’s Schrödinger convergence problem	Written
081	The David–Semmes Riesz-transform problem in higher codimension	Written
082	Maximal and variational bounds for the triangular Hilbert transform	Written
083	Stein’s conjecture for Hilbert transforms along Lipschitz directions	Written
084	The geometric case of the Erdős similarity conjecture	Written
085	Endpoint regularity of the planar centered maximal function	Written
086	An $L^3$ bound for the trilinear Hilbert transform	Written

🏷️ Convex and metric geometry

Family	Topic	Article
087	The Mahler conjectures and symplectic width	Written
088	Petty’s projection-volume conjecture and simplex counterexamples	Written
089	Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs	Written
090	Universal optimality of the triangular lattice	Written
091	The logarithmic Brunn–Minkowski conjecture	Written
092	The optimal order of convex-body covering density	Written
093	Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures	Written
094	Subpolynomial dimension reduction in $L_p$	Written
095	Hyperbolicity cones without semidefinite lifts	Written
096	The Gaussian propeller conjecture	Written
097	The Euclidean Steinitz–Bergström conjecture	Written
098	A negative answer to the Lang–Plaut problem	Written
099	The sharp distortion of edit distance into ${\ell }_1$	Written
100	A counterexample to Bang’s cylinder-covering bound	Written
101	The sharp simplex conjecture for isotropic constants	Written

🏷️ Theoretical computer science

Family	Topic	Article
102	The Unique Games Conjecture and optimal approximation thresholds	Written
103	Derandomization of logarithmic space: $\mathsf{L}=\mathsf{RL}=\mathsf{BPL}$	Written
104	Quasipolynomial algorithms for mean-payoff, stochastic and parity games	Written
105	The 2-to-1 Games Conjecture with perfect completeness	Written
106	Hardness of coloring three-colorable graphs	Written
107	Matrix multiplication with exponent at most $9/4$	Written
108	A cubic permanent–determinant lower bound	Written
109	Integer multiplication below $n\log n$	Written
110	Optimal-order randomized $k$-server on arbitrary metrics	Written
111	One-sample matroid prophet inequalities against an almighty adversary	Written
112	Beyond the square-root exponent for depth-three circuits	Written
113	Approximate counting and the perfect-matching entropy conjecture	Written
114	Approximate counting of common integer polymatroid bases	Written
115	Sampling and counting contingency tables with arbitrary margins	Written
117	Uniform sparsest cut: hardness and semidefinite gaps	Written
118	Unbounded bin-packing gaps and the modified integer round-up conjecture	Written
119	The Courtade–Kumar and Hellinger conjectures	Written
120	Almost-linear-time exact matching in general graphs	Written
121	Almost-linear expected-time approximation of edit distance	Written
122	Superpolynomial lower bounds and quasipolynomial reconstruction from deletion traces	Written
124	Polynomial-time scheduling on three identical machines	Written
125	The approximation threshold for metric $k$-median	Written
126	Exponential semidefinite complexity of perfect matching	Written
127	The asymptotic Gotsman–Linial conjecture	Written
128	A factor-two approximation for shortest common superstring	Written
129	Exponential state costs for two-way automata	Written
130	Fourier transforms below $n\log n$	Written
131	Polynomial mixing of graph switches with prescribed degrees	Written
132	A counterexample to the quadratic sensitivity conjecture	Written
133	The complexity of Weisfeiler–Leman refinement	Written
134	Generalized star height at most three	Written
135	Sharp homogeneous depth-five complexity of matrix products	Written
136	The quasilinear PCP-for-PPAD conjecture	Written
137	One-tape time simulation in two-fifths-power space	Written
138	Subset Sum in $O(2^{0.49n})$ time	Written
139	Subpolynomial queries for log-concave sampling	Written
140	Memory–sample lower bounds for noiseless Gaussian regression	Written

🏷️ Dynamical systems and ergodic theory

Family	Topic	Article
143	Uniform limit-cycle bounds in Hilbert’s sixteenth problem	Written
144	Banach’s simple Lebesgue-spectrum problem	Written
145	Rokhlin’s multiple-mixing problem	Written
146	Sinai’s positive-entropy conjecture for the standard map	Written
147	The near-boundary Birkhoff conjecture	Written
148	The dimension formula for self-similar measures on the line	Written
149	Permanence for weakly reversible reaction networks	Written
150	Weak mixing of irrational triangular billiards	Written
151	A $C^1$ counterexample to Shub’s entropy conjecture	Written
152	Zero entropy does not guarantee a smooth positive-volume model	Written
153	Arithmetic classification of Bernoulli convolutions	Written
154	Pointwise multiple ergodic averages for mixing transformations	Written

🏷️ Combinatorics

Family	Topic	Article
155	A counterexample to periodic tiling in dimension three	Written
156	Borsuk’s conjecture fails in dimension nine	Written
157	Counterexamples to the Hadwiger and Colin de Verdière conjectures	Written
158	The Euclidean plane cannot be colored with five colors	Written
159	Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi bounds	Written
160	Superexponential van der Waerden numbers	Written
161	Counterexamples to Sidorenko’s conjecture and the forcing conjecture	Written
162	Counterexamples to Ryser’s covering and Gyárfás’s tree-cover conjectures	Written
164	Hindman’s finite sums and products conjecture	Written
165	Exact crossing numbers of complete and complete bipartite graphs	Written
166	The higher-dimensional Erdős distinct-distances conjecture	Written
167	Pinned distances and a power saving for planar unit distances	Written
170	Sharp logarithmic exponents for off-diagonal Ramsey numbers	Written
171	The hypercube Ramsey conjecture	Written
172	Classification of finite Euclidean Ramsey configurations	Written
173	Seymour’s second-neighborhood conjecture	Written
174	Deterministic construction of strong thin spanning trees	Written
175	Talagrand’s conjectures and graph decompositions at expectation thresholds	Written
176	The second Kahn–Kalai conjecture	Written
177	Bounded-degree coboundary expanders in every dimension	Written
178	Deterministic nonbipartite Ramanujan graphs in every fixed degree	Written
179	The circulant Hadamard conjecture	Written
180	Barnette’s Hamiltonian-cycle conjecture	Written
181	The Erdős–Gallai cycle-decomposition conjecture	Written
182	Power savings for polynomial-difference-free sets	Written
183	Power savings for planar halving lines and $k$-sets	Written
184	Coloring and independence in graphs with forbidden subgraphs	Written
185	Counterexamples to infinite matroid intersection and packing/covering	Written
186	The Friedgut–Kalai graph and hypergraph threshold conjectures	Written
187	Snaky in 21 Maker moves	Written
188	The sharp constant in random triangle removal	Written
189	Exact cycle–clique Ramsey numbers	Written
190	Polynomial removal fails for ordered binary matrices	Written
191	A power improvement in the Heilbronn triangle problem	Written
192	A counterexample to the Gopalan–Servedio conjecture	Written

🏷️ Probability and statistical mechanics

Family	Topic	Article
211	Geometry, diffusion, and spectra of random planar maps	Written
212	No bigeodesics and smooth limit shapes in planar first-passage percolation	Written
213	No infinite critical clusters on quasi-transitive graphs	Written
214	The Benjamini–Schramm nonuniqueness conjecture	Written
215	Massive continuum limits and exact mass asymptotics for planar $O(n)$ models	Written
216	Critical logarithmic corrections and BKT scaling for the planar XY model	Written
217	The low-temperature Sherrington–Kirkpatrick fluctuation law	Written
218	Conformal universality for weakly interacting and disordered Ising models	Written
219	GOE universality for random regular graphs with weak disorder	Written
220	Directional zero–one laws and ballisticity in random environments	Written
221	The Mézard–Parisi formula for diluted spin glasses	Written
222	Perceptron free energies and microscopic jamming	Written
223	Conformal limits of square-lattice random-cluster interfaces	Written
224	Critical and near-critical universality for Voronoi percolation	Written
225	Gaussian free field limits for the balanced six-vertex model	Written
226	The double-dimer ${\mathrm{CLE}}_4$ conjecture in the half-plane	Written
227	The dynamical phase transition in the Sherrington–Kirkpatrick model	Written
228	Continuum phase transitions for radial pair potentials	Written
229	Sharp three- and four-state reconstruction thresholds	Written
230	Exact Hausdorff measure for SLE	Written
231	The free uniform spanning forest is a factor of IID	Written
232	Gaussian fields and SLE interfaces for Lipschitz heights	Written
233	The joint critical Ashkin–Teller scaling limit	Written
234	All-temperature pressure for orthogonally invariant Ising spin glasses	Written
235	Random-SAT thresholds, sharp variance and computability	Written
236	The factor-of-IID threshold for free Ising states on trees	Written
237	The three-quarter diameter exponent for honeycomb walks	Written
238	Optimal logarithmic mixing of the Thorp shuffle	Written
239	Sharp singularity rates for symmetric sign matrices	Written

🏷️ Mathematical physics

Family	Topic	Article
260	Spacetime Penrose inequalities and rigidity	Written
261	Localization and delocalization in the Anderson model	Written
262	Sharp one-dimensional Lieb–Thirring inequalities	Written
263	The ionization and generalized ionization conjectures	Written
264	Strong cosmic censorship near two-ended Kerr data	Written
265	The two-dimensional gapped area law	Written
266	Exactly three mutually unbiased bases in dimension six	Written
267	Positive-temperature Bose–Einstein condensation and quantum depletion	Written
268	The spin-one Haldane gap	Written
269	The Laughlin gap and stability under scalar disorder	Written
270	Threshold and positive-energy bound states of the BFSS model	Written
271	Bloch’s law and spontaneous ferromagnetic order	Written
272	Entanglement without secret key and the PPT-square conjecture	Written
273	The entropy photon-number inequality	Written
274	Moore’s parity conjecture for ${\mathrm{QAC}}^0$	Written
275	QMA-hardness of continuum Coulomb energy	Written
276	The classical capacity of generalized amplitude damping	Written
277	Threshold repetition for entangled games	Written
278	Failure of Kohn–Sham ensemble representation	Written
279	Exact quantum factoring over a fixed finite gate set	Written
281	QAOA optimality for the SK model	Written
282	Scale-to-conformal enhancement in four-dimensional QFT	Written
283	Polynomial-time, constant-error unitary synthesis from a Boolean oracle	Written
284	The optimal randomized–quantum query exponent	Written

🏷️ Operator algebras

Family	Topic	Article
285	Counterexamples to Baum–Connes and Kadison–Kaplansky	Written
286	Arithmetic rigidity of lattice von Neumann algebras	Written
287	All nonabelian free group factors are isomorphic	Written
288	Kadison’s similarity conjecture	Written
289	The strong Kadison–Kastler conjecture	Written
290	Connes’ bicentralizer conjecture and relative bicentralizers	Written
291	Toms–Winter and equivariant Jiang–Su stability	Written
292	A counterexample to Kirchberg’s norm-ultrapower embedding problem	Written
293	A counterexample to the hyperinvariant-subspace problem	Written
294	A counterexample to Kaplansky’s quasitrace conjecture	Written
295	The Kadison–Ringrose cohomology conjecture	Written
296	The generator problem for finite factors	Written
297	A ZFC counterexample to Naimark’s problem	Written
298	A counterexample to Voiculescu’s free-entropy equality conjecture	Written
299	The Kirchberg–Rørdam character criterion	Written
300	The Popa–Vaes quadratic strong-operator paving conjecture	Written
301	Classification by trace cones after Razak–Jacelon stabilization	Written
302	The Phillips–Toms formula for minimal integer actions	Written
303	From ordinary to strong pure infiniteness	Written

🏷️ Topology

Family	Topic	Article
304	The Hilbert–Smith conjecture in every dimension	Written
305	Counterexamples to disk embedding and Wall’s manifold conjecture	Written
306	The purely cosmetic surgery conjecture for knots in $S^3$	Written
307	Failure of rational injectivity for maximal coarse assembly	Written
308	Smith–Toda complexes at every height with varying primes	Written
309	The Kervaire invariant problem at the prime three	Written
310	Quillen’s conjecture in rational homology	Written
311	Chai’s invariant-ideal conjecture	Written
312	The Grothendieck homotopy hypothesis	Written
313	Finite generation for the $K(n)$-local sphere	Written
314	The chromatic Smith fixed-point problem for finite $p$-groups	Written
315	The four-dimensional Singer conjecture	Written
316	Curtis’s conjecture	Written
317	Thomason model structures in every strict higher dimension	Written
318	Chromatic splitting: counterexamples and filtrations	Written
319	Counterexamples to the Hahn–Wilson conjecture at height two	Written
320	A four-dimensional counterexample to Borel rigidity	Written
321	A counterexample to Wall’s finite D(2) conjecture	Written

🏷️ Functional analysis

Family	Topic	Article
322	Tingley’s sphere-isometry problem	Written
324	Lipschitz equivalence without linear isomorphism	Written
325	The complete Crouzeix conjecture	Written
326	The cotype–cotype conjecture under the approximation property	Written
327	Markov type characterizes superreflexivity	Written
328	Fixed points of nonexpansive maps in reflexive Banach spaces	Written
329	A counterexample to Pietsch’s metric-entropy duality conjecture	Written
330	A negative answer to Kalton’s Lipschitz-free approximation question	Written
331	Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming	Written
332	Metric Markov cotype two for ${\ell }_1$	Written

🏷️ Differential geometry

Family	Topic	Article
333	Smooth isometric immersions of surfaces into ${\mathbb{R}}^4$	Written
334	A smooth surface metric with no local immersion in ${\mathbb{R}}^3$	Written
335	Gromov’s integral scalar-curvature inequality	Written
336	Spectral scalar curvature and codimension-two width	Written
337	Cartan–Hadamard isoperimetry and CAT$(0)$ fillings	Written
338	Yau’s uniformization conjecture	Written
339	Katok’s entropy rigidity conjecture	Written
340	A counterexample to the nearby Lagrangian conjecture	Written
341	Donaldson’s hypersymplectic deformation conjecture	Written
342	Donaldson’s tamed-to-compatible conjecture	Written
343	Sharp symplectic ball-packing criteria in higher dimensions	Written
344	The metric Blaschke conjecture	Written
345	Infinitely many closed geodesics on spheres and three-manifolds	Written
346	Sharp singular-set bounds for stationary integral varifolds	Written
347	Counterexamples to strong forms of Arnold’s fixed-point conjecture	Written
348	Nonnegatively curved Einstein four-manifolds and a topological gap	Written
349	The Solomon–Yau least-volume conjecture	Written
350	Yau’s nodal conjecture: surfaces and counterexamples	Written
351	Scalar curvature detects four-dimensional Ricci-flow singularities	Written
352	Finite-time singularity of Calabi flow	Written
353	The sharp dimension threshold for affine Bernstein rigidity	Written
354	Isoperimetric regions in the cubic three-torus	Written
355	Unique tangent flows at the first surface singularity	Written
356	Gigli’s characterization of Alexandrov curvature	Written
357	Bi-Lipschitz coordinates at every regular RCD point	Written
358	A three-manifold with no conjugate points and no nonpositively curved metric	Written
359	Negative Kähler curvature without bounded holomorphic coordinates	Written
360	Villani’s convexity conjecture and regular optimal transport	Written
361	Counterexamples to Yau’s harmonic dimension bound	Written

🏷️ Partial differential equations

Family	Topic	Article
362	Global smoothness for relativistic Vlasov–Maxwell	Written
363	Boltzmann nonuniqueness with exact local conservation	Written
364	Kinetic limits and fluctuations over the Boltzmann lifespan	Written
365	Joint metric and connection recovery from one boundary patch	Written
366	The planar Mumford–Shah regularity conjecture	Written
367	The critical dimension for the one-phase Bernoulli problem	Written
368	The three-dimensional Ball–Evans approximation problem	Written
369	The hot spots conjecture for simply connected planar domains	Written
370	The subcritical Lane–Emden and Hénon–Lane–Emden conjectures	Written
371	Stable blowup for a defocusing Schrödinger equation	Written
372	Global uniqueness in smooth isotropic elasticity	Written
373	Nonattainment in three-marginal Coulomb transport	Written
374	Sharp one-third stability of optimal transport maps	Written
375	De Giorgi’s conjecture in dimension eight	Written
376	Universal computation in forced Navier–Stokes flows	Written
377	Interior $C^{1,\alpha }$ regularity for infinity-harmonic functions	Written

🏷️ Excluded families

These exclusions apply the requested subject scope, including families catalogued under another heading. They do not assess the importance or validity of a manuscript.

Family	Topic	Reason
001	Milne’s rationality conjecture	Algebra, algebraic geometry, group theory, or logic is central
002	The full Birch–Swinnerton-Dyer formula in Selmer coranks zero and one	Algebra, algebraic geometry, group theory, or logic is central
004	Hilbert’s tenth problem over $\mathbb{Q}$	Algebra, algebraic geometry, group theory, or logic is central
006	Goldfeld’s conjecture	Algebra, algebraic geometry, group theory, or logic is central
008	The Deligne–Drinfeld conjecture	Algebra, algebraic geometry, group theory, or logic is central
009	Bogomolov–Pop and Milnor $K$-theoretic reconstruction	Algebra, algebraic geometry, group theory, or logic is central
010	Fontaine–Mazur modularity at the prime $2$ and $2$-adic pro-modularity	Algebra, algebraic geometry, group theory, or logic is central
014	Restricted geometric Langlands, generic Ramanujan and Arthur parameters	Algebra, algebraic geometry, group theory, or logic is central
016	Zilber–Pink in abelian varieties and the Siegel threefold	Algebra, algebraic geometry, group theory, or logic is central
018	The Margulis–Platonov conjecture over global fields	Algebra, algebraic geometry, group theory, or logic is central
019	The $p$-adic section conjecture	Algebra, algebraic geometry, group theory, or logic is central
027	Integral density on curve character varieties	Algebra, algebraic geometry, group theory, or logic is central
030	Modularity over imaginary quadratic fields	Algebra, algebraic geometry, group theory, or logic is central
031	Uchida’s conjecture for open Galois homomorphisms	Algebra, algebraic geometry, group theory, or logic is central
032	The rational Hodge conjecture for CM abelian varieties and products of K3 surfaces	Algebraic and complex geometry
033	Campana’s orbifold Iitaka conjecture and logarithmic subadditivity	Algebraic and complex geometry
034	Log abundance and effective Iitaka fibrations	Algebraic and complex geometry
035	Threefold log abundance in numerical dimension one in characteristic $p>3$	Algebraic and complex geometry
036	Numerical semiampleness and generalized minimal models	Algebraic and complex geometry
037	The sharp ordinary-double-point volume gap	Algebraic and complex geometry
038	Fujita’s freeness conjecture	Algebraic and complex geometry
039	Nagata’s conjecture and maximal Seshadri constants	Algebraic and complex geometry
040	Bloch’s conjecture for complex surfaces	Algebraic and complex geometry
041	Hyperkähler SYZ and projective-space bases	Algebraic and complex geometry
042	Oka classification for K3 surfaces and other compact complex surfaces	Algebraic and complex geometry
043	$P=W$ for fixed-determinant moduli spaces	Algebraic and complex geometry
044	The equivariant cohomological Hikita conjecture for quivers	Algebraic and complex geometry
046	Counterexamples to Shafarevich holomorphic convexity	Algebraic and complex geometry
047	Complex counterexamples to cancellation and affine fibrations	Algebraic and complex geometry
048	A characteristic-zero counterexample to Lipman–Zariski	Algebraic and complex geometry
049	A stable-coordinate counterexample in four variables	Algebraic and complex geometry
050	A counterexample to Griffiths’ positivity conjecture	Algebraic and complex geometry
051	Kobayashi’s canonical-ampleness conjecture	Algebraic and complex geometry
052	Tangent-bundle splittings and universal covers	Algebraic and complex geometry
053	A counterexample to Pixton’s original completeness conjecture	Algebraic and complex geometry
054	Counterexamples to Kuznetsov’s rationality conjecture	Algebraic and complex geometry
055	Toda’s Gepner conjecture and large-volume stability	Algebraic and complex geometry
056	Termination of fourfold minimal model programs	Algebraic and complex geometry
057	Campana’s abelianity conjecture and special varieties	Algebraic and complex geometry
058	The Kollár–Pardon universal-cover conjecture	Algebraic and complex geometry
059	Counterexamples to Zariski’s multiplicity conjecture	Algebraic and complex geometry
060	The Global Spherical Shell conjecture	Algebraic and complex geometry
062	The LeBrun–Salamon conjecture and projective contact classification	Algebraic and complex geometry
063	The generalized Mukai conjecture	Algebraic and complex geometry
064	The $\mu$-constant problem for surface singularities	Algebraic and complex geometry
065	Virasoro constraints for complete intersections and projective bundles	Algebraic and complex geometry
066	Bounded klt complements for Fano contractions	Algebraic and complex geometry
067	The Campana–Peternell conjecture in dimension six	Algebraic and complex geometry
068	Anticanonical nonvanishing under smooth semipositivity	Algebraic and complex geometry
069	Quantum geometric Langlands at irrational level	Algebraic and complex geometry
116	Uniform identity testing for noncommutative formulas	Algebra, algebraic geometry, group theory, or logic is central
141	The existential theory of the reals and existential–universal sentences in the counting hierarchy	Algebra, algebraic geometry, group theory, or logic is central
142	Deterministic polynomial factorization over prime fields	Algebra, algebraic geometry, group theory, or logic is central
168	Combinatorial invariance of Kazhdan–Lusztig polynomials	Algebra, algebraic geometry, group theory, or logic is central
169	The Shareshian–Wachs $e$-positivity conjecture	Algebra, algebraic geometry, group theory, or logic is central
193	Serre’s intersection-multiplicity conjecture	Algebra
194	Lech’s multiplicity conjecture	Algebra
195	A counterexample to the small Cohen–Macaulay module conjecture	Algebra
196	A counterexample to Kaplansky’s zero-divisor conjecture	Algebra
197	Nonsofic groups and group-ring counterexamples	Algebra
198	A counterexample to the little finitistic-dimension conjecture	Algebra
199	Counterexamples to conjectures of Auslander–Reiten, Tachikawa, and Nakayama	Algebra
200	Eisenbud–Green–Harris and lex-plus-powers in characteristic zero	Algebra
201	A counterexample to Kurosh’s division-ring problem	Algebra
202	The blockwise Alperin weight conjecture	Algebra
203	Donovan’s conjecture over fields and discrete valuation rings	Algebra
204	Tensor saturation for even spin groups	Algebra
205	Saxl’s conjecture and universal tensor squares	Algebra
206	Finite lattice representation: counterexamples and undecidability	Algebra
207	The ${\ell }^1$-Bass and complex Bass trace conjectures	Algebra
208	The finite Benson–Etingof–Ostrik conjecture	Algebra
209	Integral counterexamples to Gersten’s conjecture	Algebra
210	Foulkes’ conjecture for sixth powers and quadratic stabilization	Algebra
240	Shelah’s eventual categoricity conjecture	Mathematical logic
241	Rigidity of the Turing degrees	Mathematical logic
242	Single-fold Diophantine representations	Mathematical logic
243	Choiceless counting does not capture polynomial time	Mathematical logic
244	The partition principle does not imply choice	Mathematical logic
245	The $\beta$-Barendregt–Geuvers–Klop conjecture	Mathematical logic
246	Cannon’s conjecture	Group theory
247	An infinite finitely presented residually finite $2$-group	Group theory
248	Thompson’s group $F$ is nonamenable	Group theory
249	A finitely generated counterexample to Eilenberg–Ganea	Group theory
250	The Boone–Higman conjecture and higher finiteness	Group theory
251	Amenability, unitarizability, and Ulam stability	Group theory
252	A non-residually-finite torsion-free hyperbolic group	Group theory
253	An infinite finitely presented simple amenable group	Group theory
254	Classifying spaces and geometric obstructions for Artin groups	Group theory
255	Quasi-isometric rigidity of virtually polycyclic groups	Group theory
256	Howie’s conjecture on equations over groups	Group theory
257	A hyperbolic group with no geometric CAT(0) action	Group theory
258	Gersten’s conjecture for one-relator groups	Group theory
259	A group without fixed price	Group theory
280	Strong locality for strongly rational unitary vertex operator algebras	Algebra, algebraic geometry, group theory, or logic is central
323	Relative independence of the separable quotient problem	Algebra, algebraic geometry, group theory, or logic is central

See Also

• OpenAI collection explains the prerequisites, reading sequence, and verification policy.