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Edition 2026-10-09-v14. Every one of the 372 active result families has its own source subdirectory and individual first-pass application assessment. All 719 catalog manuscripts are inventoried; they have not all received individual main-paper or proof review. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

Use the product catalog for 41 developed software/business hypotheses and the commercial priorities for the initial implementation shortlist. A family without a developed dossier still has an assessment explaining its possible use, material limit and next verification action. Academic reference uses are not presented as demonstrated lucrative businesses.

Discipline coverage

Discipline Assessed families
Algebra 18
Algebraic and complex geometry 36
Combinatorics 37
Convex and metric geometry 15
Differential geometry 29
Dynamical systems and ergodic theory 12
Functional analysis 11
Group theory 14
Mathematical logic 6
Mathematical physics 25
Number theory 31
Operator algebras 19
Partial differential equations 16
Probability and statistical mechanics 29
Real and complex analysis 16
Theoretical computer science 40
Topology 18

Algebra

Family Result and source directory Latest application assessment Dossier IDs
193 Serre’s intersection-multiplicity conjecture Intersection multiplicity consistency library First-pass assessment only
194 Lech’s multiplicity conjecture Multiplicity monotonicity formal adapter First-pass assessment only
195 A counterexample to the small Cohen–Macaulay module conjecture Cohen–Macaulay approximation limitation ledger First-pass assessment only
196 A counterexample to Kaplansky’s zero-divisor conjecture Group-algebra zero-divisor counterexample fixture First-pass assessment only
197 A torsion-free group algebra that is not directly finite Algebraic inverse and cellular-automaton scope audit First-pass assessment only
198 A counterexample to finitistic-dimension finiteness Homological dimension counterexample library First-pass assessment only
199 Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures Homological conjecture dependency and counterexample graph First-pass assessment only
200 Eisenbud–Green–Harris and lex-plus-powers Hilbert function and Betti bound research adapter First-pass assessment only
201 A counterexample to Kurosh’s division-ring problem Division-ring local-finiteness limitation reference First-pass assessment only
202 The blockwise Alperin weight conjecture Brauer character and weight counting cross-check First-pass assessment only
203 Donovan's conjecture over fields and complete mixed-characteristic DVRs Block classification finiteness provenance First-pass assessment only
204 Tensor saturation for even spin groups Spin-group tensor invariant scale reduction First-pass assessment only
205 Saxl’s conjecture and universal tensor squares Symmetric representation tensor-square reference First-pass assessment only
206 Finite lattice representation and undecidability Finite algebra representation solver completeness contract First-pass assessment only
207 The ℓ¹-Bass conjecture for all discrete groups Idempotent trace support and coefficient-regime audit First-pass assessment only
208 Finite symmetric tensor categories and the Verlinde tower Finite symmetric tensor category fiber-functor adapter First-pass assessment only
209 Integral counterexamples to Gersten’s conjecture K-theory localization information-loss fixture First-pass assessment only
210 Foulkes' conjecture for sixth powers and quadratic stabilization Symmetric power map stabilization benchmark First-pass assessment only

Algebraic and complex geometry

Family Result and source directory Latest application assessment Dossier IDs
032 The rational Hodge conjecture for CM abelian varieties Hodge–Tate proof dependency adapter 002
033 Iitaka subadditivity, variation, and logarithmic additivity Orbifold subadditivity hypothesis ledger First-pass assessment only
034 Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity Abundance and Iitaka dependency evidence First-pass assessment only
035 Log-canonical threefold abundance in numerical dimension one Positive-characteristic threefold adjoint contract First-pass assessment only
036 Numerical semiampleness and generalized minimal models Numerical semiampleness model contract First-pass assessment only
037 The ordinary-double-point volume gap Normalized-volume singularity reference First-pass assessment only
038 Fujita’s freeness conjecture Adjoint linear-system generation contract First-pass assessment only
039 Nagata’s conjecture and maximal Seshadri constants Very-general-point interpolation boundary First-pass assessment only
040 Bloch’s conjecture for complex surfaces Surface cycle-class assumption reference First-pass assessment only
041 Hyperkähler SYZ and projective-space bases Hyperkähler fibration existence ledger First-pass assessment only
042 Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII Complex-manifold Oka classification reference First-pass assessment only
043 <i>P</i> = <i>W</i> for fixed-determinant SL<sub><i>n</i></sub> moduli spaces P=W cohomology computation cross-check First-pass assessment only
044 The equivariant cohomological Hikita conjecture Quiver cohomology correspondence adapter First-pass assessment only
046 Shafarevich counterexamples in dimension two and with large fundamental group Universal-cover convexity counterexample library First-pass assessment only
047 Zariski cancellation and affine fibrations over the complex numbers Algebraic cancellation counterexample fixture First-pass assessment only
048 A characteristic-zero counterexample to Lipman–Zariski Tangent-sheaf smoothness contract counterexample First-pass assessment only
049 A stable-coordinate counterexample in four variables Stable polynomial coordinate counterexample First-pass assessment only
050 A counterexample to Griffiths’ positivity conjecture Bundle positivity assumption audit First-pass assessment only
051 Kobayashi’s canonical-ampleness conjecture Hyperbolicity-to-projectivity evidence ledger First-pass assessment only
052 Tangent splittings and product decompositions Holomorphic splitting integrability contract First-pass assessment only
053 A counterexample to Pixton completeness in Chow Tautological relation completeness counterexample First-pass assessment only
054 Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations Cubic-fourfold rationality scope audit First-pass assessment only
055 Gepner symmetry and large-volume stability on threefolds Stability-condition research adapter First-pass assessment only
056 Termination of projective and Kähler fourfold minimal model programs Termination-versus-runtime solver contract First-pass assessment only
057 Fundamental groups of special complex varieties and root orbifolds Special-manifold group implication ledger First-pass assessment only
058 Semialgebraic universal covers and bounded domains Semialgebraic universal-cover classification reference First-pass assessment only
059 Counterexamples to Zariski’s multiplicity conjecture Topology-versus-multiplicity counterexample First-pass assessment only
060 The Global Spherical Shell conjecture Class-VII surface classification evidence First-pass assessment only
062 Projective contact classification and the LeBrun–Salamon conjecture Quaternionic and contact classification ledger First-pass assessment only
063 The generalized Mukai conjecture Fano invariant inequality reference First-pass assessment only
064 Topological triviality of <i>μ</i>-constant surface singularities Singularity-family topological triviality contract First-pass assessment only
065 Virasoro constraints for complete intersections and projective-bundle towers Projectivization transfer is a conditional research computation lead First-pass assessment only
066 Bounded klt complements for Fano contractions Complement-index boundedness contract First-pass assessment only
067 The Campana–Peternell conjecture in dimension six Six-dimensional Fano classification reference First-pass assessment only
068 Anticanonical nonvanishing in every dimension Semipositive anticanonical section contract First-pass assessment only
069 Global quantum geometric Langlands at irrational level Geometric Langlands correspondence provenance First-pass assessment only

Combinatorics

Family Result and source directory Latest application assessment Dossier IDs
155 A counterexample to periodic tiling in dimension three Three-dimensional tiling feasibility and periodicity audit First-pass assessment only
156 Borsuk's conjecture fails in dimension nine Diameter partition counterexample library First-pass assessment only
157 Graph coloring, clique minors, and Colin de Verdière invariants Graph coloring bound assumption auditor First-pass assessment only
158 The Euclidean plane cannot be colored with five colors Plane-coloring boundary and finite certificate audit First-pass assessment only
159 Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi bounds Arithmetic progression density reference First-pass assessment only
160 Superexponential van der Waerden numbers Ramsey forcing-scale reference First-pass assessment only
161 Counterexamples to Sidorenko’s conjecture and the forcing conjecture Graph null-model motif counterexample audit First-pass assessment only
162 Counterexamples to Ryser’s covering conjecture Hypergraph cover relaxation limitation audit First-pass assessment only
164 Hindman’s finite sums and products conjecture Finite sums/products Ramsey research explorer First-pass assessment only
165 The Harary–Hill and Zarankiewicz crossing-number formulas Complete-graph drawing crossing reference First-pass assessment only
166 The higher-dimensional Erdős distinct-distances conjecture Distinct-distance point-set reference First-pass assessment only
167 Planar distinct distances and unit-distance bounds Planar geometric incidence benchmark First-pass assessment only
168 Combinatorial invariance of Kazhdan–Lusztig polynomials Bruhat interval polynomial caching library First-pass assessment only
169 Shareshian–Wachs elementary positivity Elementary-basis witness and algebra audit 039
170 Sharp logarithmic exponents for off-diagonal Ramsey numbers Off-diagonal Ramsey exponent reference First-pass assessment only
171 The hypercube Ramsey conjecture Hypercube Ramsey forcing reference First-pass assessment only
172 Classification of finite Euclidean Ramsey configurations Euclidean Ramsey configuration classifier research First-pass assessment only
173 Seymour’s second-neighborhood conjecture Oriented graph two-hop reach benchmark First-pass assessment only
174 Deterministic construction of strong thin spanning trees Thin trees: all-cut checking and conservative signing constants 024, 036
175 Talagrand’s expectation thresholds, discrete convexity, and graph decompositions Expectation-threshold and decomposition reference First-pass assessment only
176 The second Kahn–Kalai conjecture with an edge-count bound Random-graph motif appearance planner First-pass assessment only
177 Bounded-degree coboundary expanders High-dimensional expander research generator First-pass assessment only
178 Deterministic nonbipartite Ramanujan graphs in every fixed degree Spectral construction: millions of tracked parameters and uninstantiated thresholds 036
179 The circulant Hadamard and Barker-sequence conjectures Binary waveform constraint feasibility audit 035
180 Barnette’s Hamiltonian-cycle conjecture Hamiltonian graph-class feasibility reference First-pass assessment only
181 The Erdős–Gallai cycle-decomposition conjecture Graph cycle decomposition research toolkit First-pass assessment only
182 Power savings for intersective polynomial differences and prime arguments Polynomial-difference avoidance reference First-pass assessment only
183 Power savings for planar halving lines and <i>k</i>-sets Geometric split-count research benchmark First-pass assessment only
184 Correspondence coloring with a fixed forbidden subgraph Conflict coloring class assumption audit First-pass assessment only
185 Counterexamples to infinite matroid intersection and packing/covering Infinite matroid guarantee limitation map First-pass assessment only
186 Uniform influence and sharp thresholds for graph and hypergraph properties Relabeling-invariant threshold research reference First-pass assessment only
187 Snaky in 21 Maker moves Finite strategy certificate teaching engine First-pass assessment only
188 The sharp terminal leave in random triangle removal Random triangle-removal process reference First-pass assessment only
189 Cycle–clique Ramsey numbers Cycle–clique Ramsey exact reference library First-pass assessment only
190 Polynomial removal fails for ordered binary matrices Ordered matrix pattern-sampling limitation audit First-pass assessment only
191 A power improvement in the Heilbronn triangle lower bound Nondegenerate planar point-set research design First-pass assessment only
192 Boolean functions violate the square-root degree bound by arbitrary factors Boolean Fourier degree limitation reference First-pass assessment only

Convex and metric geometry

Family Result and source directory Latest application assessment Dossier IDs
087 The Mahler conjectures, functional inequalities and polar-product symplectic width Convex geometry inequality and equality-case workbench First-pass assessment only
088 Sharp projection-body inequalities and a counterexample to simplex maximization Projection volume model validation toolkit First-pass assessment only
089 Bounded-distortion <i>L</i><sub>1</sub> embeddings of planar and bounded-treewidth graphs Planar metric embedding and flow-cut review 024
090 Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energy Triangular lattice energy benchmark First-pass assessment only
091 Logarithmic and <i>L</i><sub><i>p</i></sub> Brunn–Minkowski inequalities and the B-conjecture Symmetric convex-body interpolation audit First-pass assessment only
092 The optimal order of convex-body covering density Covering-density research planner First-pass assessment only
093 Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures Log-concave sampling assumption audit First-pass assessment only
094 Subpolynomial dimension reduction in <i>L</i><sub><i>p</i></sub> Finite Lp embedding contract audit 025
095 Hyperbolicity cones without semidefinite lifts Conic formulation scope checker First-pass assessment only
096 The Gaussian propeller conjecture in every dimension Kernel clustering hardness and Gaussian partition benchmark First-pass assessment only
097 The Euclidean Steinitz–Bergström bound Vector prefix balancing research simulator First-pass assessment only
098 Compact counterexamples to bi-Lipschitz dimension reduction Metric compression impossibility demonstrator First-pass assessment only
099 The sharp exponential scale of edit-distance distortion Edit metric embedding limits audit 008, 025
100 Cylinder coverings below the half-area bound Cylinder covering counterexample visualizer First-pass assessment only
101 The sharp simplex conjecture for isotropic constants Log-concave entropy and isotropic geometry benchmark First-pass assessment only

Differential geometry

Family Result and source directory Latest application assessment Dossier IDs
333 Smooth isometric immersions of surfaces into ℝ<sup>4</sup> Metric surface realization research library First-pass assessment only
334 A smooth surface metric with no local isometric immersion in ℝ<sup>3</sup> Surface realization limitation audit First-pass assessment only
335 Gromov’s integral scalar-curvature bound for simplicial volume Scalar curvature and topology assumption ledger First-pass assessment only
336 Spectral scalar curvature, Urysohn width, and macroscopic dimension Spectral geometry width research planner First-pass assessment only
337 Sharp Cartan–Hadamard isoperimetry and rigidity Curved-space isoperimetric and filling reference First-pass assessment only
338 Yau's uniformization conjecture Kähler uniformization provenance module First-pass assessment only
339 Katok's entropy rigidity conjecture Geodesic entropy rigidity research reference First-pass assessment only
340 A counterexample to the nearby Lagrangian conjecture Lagrangian equivalence limitation ledger First-pass assessment only
341 Donaldson's hypersymplectic deformation conjecture Hypersymplectic deformation research toolkit First-pass assessment only
342 Donaldson's tamed-to-compatible conjecture Almost-complex compatibility assumption map First-pass assessment only
343 Symplectic ball packing in higher dimensions Symplectic capacity packing research calculator First-pass assessment only
344 The metric Blaschke conjecture Injectivity-radius rigidity research reference First-pass assessment only
345 Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds Closed geodesic research benchmark library First-pass assessment only
346 Sharp singular-set bounds for stationary integral varifolds Varifold regularity class audit First-pass assessment only
347 Counterexamples to stable-Morse and strong Arnold fixed-point bounds Hamiltonian fixed-point lower-bound limitation library First-pass assessment only
348 Nonnegative-curvature Einstein classification and an <i>L</i><sup>2</sup> topological gap Einstein four-manifold classification reference First-pass assessment only
349 The Solomon–Yau least-volume conjecture Spherical minimal-surface volume reference First-pass assessment only
350 Yau’s nodal bounds: surfaces and higher dimensions Spectral nodal-set scope and mesh benchmark First-pass assessment only
351 Scalar curvature and finite-time Ricci-flow singularities Ricci flow singularity evidence audit First-pass assessment only
352 A finite-time singularity of Calabi flow Calabi flow failure reference First-pass assessment only
353 Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexample Affine maximal graph rigidity reference First-pass assessment only
354 The isoperimetric profile of the cubic three-torus Periodic microstructure interface reference calculator 037
355 Unique tangent flows at the first surface singularity Mean curvature first-singularity comparison reference First-pass assessment only
356 Gigli’s characterization of Alexandrov curvature Metric-measure curvature definition audit First-pass assessment only
357 Bi-Lipschitz coordinates at every regular RCD point RCD local coordinate research toolkit First-pass assessment only
358 A three-manifold without conjugate points or nonpositive curvature Metric existence implication limitation map First-pass assessment only
359 Negative Kähler curvature without bounded holomorphic coordinates Holomorphic coordinate limitation reference First-pass assessment only
360 Weak MTW curvature gives convexity and regular optimal transport Curved optimal-transport regularity contract First-pass assessment only
361 Failure of integer-degree harmonic dimension comparison Harmonic growth dimension comparison limitation First-pass assessment only

Dynamical systems and ergodic theory

Family Result and source directory Latest application assessment Dossier IDs
143 Hilbert's sixteenth problem: uniform bounds for limit cycles Planar oscillator cycle-count assurance First-pass assessment only
144 Banach’s simple Lebesgue-spectrum problem Smooth dynamics spectral-model research library First-pass assessment only
145 Rokhlin’s multiple-mixing problem Single-action mixing claim contract First-pass assessment only
146 Positive metric entropy for the standard map Standard-map chaos research benchmark First-pass assessment only
147 The near-boundary Birkhoff conjecture Billiard integrability assumption audit First-pass assessment only
148 The entropy-rate dimension formula for self-similar measures Self-similar measure dimension workbench First-pass assessment only
149 Classwise permanence for weakly reversible mass-action systems Reaction network model assurance plugin 002, 003, 013
150 Weak mixing of triangular billiards with an irrational angle Triangular billiard mixing reference First-pass assessment only
151 A <i>C</i><sup>1</sup> counterexample to the entropy conjecture Dynamical entropy counterexample provenance First-pass assessment only
152 Zero entropy does not guarantee a smooth positive-volume model Smooth-model representation limitation ledger First-pass assessment only
153 Arithmetic classification and non-Pisot singularity for Bernoulli convolutions Bernoulli convolution parameter classification research First-pass assessment only
154 Pointwise multiple ergodic averages for mixing transformations Multiple ergodic average convergence reference First-pass assessment only

Functional analysis

Family Result and source directory Latest application assessment Dossier IDs
322 Tingley’s sphere-isometry problem Banach sphere isometry teaching and formalization module First-pass assessment only
323 Independence of the separable quotient problem Set-theoretic assumption provenance viewer First-pass assessment only
324 Lipschitz equivalent Banach spaces need not be linearly isomorphic Metric versus linear representation counterexample explorer First-pass assessment only
325 The complete Crouzeix conjecture Complete polynomial inequality and bounded nonnormal-matrix evidence 001, 014
326 The cotype–cotype conjecture under the approximation property Banach geometry property implication map First-pass assessment only
327 Markov type characterizes superreflexivity Metric Markov type renorming research explorer First-pass assessment only
328 Nonexpansive fixed points in reflexive Banach spaces Fixed-point existence assumption checker First-pass assessment only
329 A counterexample to metric-entropy duality Covering-number duality counterexample benchmark First-pass assessment only
330 A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces Approximation property distinction library First-pass assessment only
331 Reflexive midpoint convexity and diamond distortion Convexity and diamond embedding benchmark First-pass assessment only
332 Metric Markov cotype of <i>ℓ</i><sub>1</sub> and Hilbert-space Lipschitz extension Lipschitz extension research toolkit First-pass assessment only

Group theory

Family Result and source directory Latest application assessment Dossier IDs
246 Cannon's conjecture Hyperbolic boundary recognition research contract First-pass assessment only
247 An infinite finitely presented residually finite 2-group and a finitely presented nil algebra Residual-finiteness versus torsion fixture First-pass assessment only
248 Thompson's group <i>F</i> is nonamenable Amenability assumption evidence First-pass assessment only
249 A finitely generated Eilenberg–Ganea counterexample Cohomological versus geometric dimension fixture First-pass assessment only
250 Boone–Higman embeddings with higher finiteness Decidable word-problem embedding contract First-pass assessment only
251 Amenability, unitarizability, and strong Ulam stability Representation stability hypothesis adapter First-pass assessment only
252 A torsion-free hyperbolic group that is neither residually finite nor linear over any field Finite-representation separation counterexample First-pass assessment only
253 An infinite finitely presented simple amenable group Simple amenable group research fixture First-pass assessment only
254 Classifying spaces and geometric obstructions for Artin groups Artin membership is effective but has no claimed cost bound First-pass assessment only
255 Quasi-isometric recognition of virtually polycyclic groups Coarse-group recognition contract First-pass assessment only
256 Nonsingular systems of equations over arbitrary groups Overgroup equation solvability contract First-pass assessment only
257 A hyperbolic group without a geometric CAT(0) action CAT(0) action counterexample library First-pass assessment only
258 Gersten’s conjecture and virtual compact specialness of one-relator groups One-relator hyperbolicity conditional adapter First-pass assessment only
259 A group without fixed price Measured-action cost comparison reference First-pass assessment only

Mathematical logic

Family Result and source directory Latest application assessment Dossier IDs
240 Shelah's eventual categoricity and the prescribed-threshold obstruction Model-theory threshold and axiom provenance First-pass assessment only
241 Rigidity of the Turing degrees Computability-degree rigidity reference First-pass assessment only
242 Single-fold Diophantine representations and undecidability under an at-most-one-solution promise Unique-solution promise solver limitation audit First-pass assessment only
243 Separating choiceless counting from polynomial time and witnessed choice Symmetry-preserving query language expressiveness audit First-pass assessment only
244 The Partition Principle does not imply Choice Set-theoretic assumption dependency viewer First-pass assessment only
245 Weak normalization implies strong normalization in pure type systems Pure-beta normalization assurance has a global premise 038

Mathematical physics

Family Result and source directory Latest application assessment Dossier IDs
260 Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions Relativistic initial-data inequality audit First-pass assessment only
261 Localization and delocalization in the Anderson model Disordered spectral model benchmark First-pass assessment only
262 Sharp finite-matrix Lieb–Thirring inequalities and all equality cases Matrix-valued spectral bound library First-pass assessment only
263 The ionization and generalized ionization conjectures Atomic binding and asymptotic plausibility checks First-pass assessment only
264 Strong cosmic censorship near two-ended Kerr data Relativity extension-class evidence map First-pass assessment only
265 Area laws and tensor networks for two-dimensional gapped systems Tensor-network representation feasibility audit 030
266 Exactly three mutually unbiased bases in dimension six Certified computation reproducibility workbench 034
267 Positive-temperature Bose–Einstein condensation and exact quantum depletion Dilute Bose gas reference regime planner First-pass assessment only
268 The spin-one Haldane gap Spin-chain gap reference suite First-pass assessment only
269 Uniform Laughlin gap and stability under bounded scalar disorder Laughlin model disorder robustness audit First-pass assessment only
270 Threshold and positive-energy bound states of the BFSS matrix model BFSS spectral conjecture provenance library First-pass assessment only
271 Bloch's law, its lattice correction, and the spherical magnetization law Ferromagnet asymptotic reference fitter First-pass assessment only
272 Entanglement without distillable secret key Quantum security resource assumption audit First-pass assessment only
273 The entropy photon-number inequality Bosonic entropy and channel-bound calculator First-pass assessment only
274 Parity is not in QAC<sup>0</sup> Quantum circuit architecture impossibility ledger First-pass assessment only
275 QMA-hardness of continuum Coulomb energy Electronic-structure complexity scope audit First-pass assessment only
276 Classical capacity of generalized amplitude damping Thermal qubit channel capacity calculator 003, 019
277 Threshold repetition for entangled games Entangled-game soundness planning reference First-pass assessment only
278 Failure of Kohn–Sham ensemble representation Density-functional representation limitation audit First-pass assessment only
279 Exact quantum factoring over a fixed finite gate set Exact quantum factoring excludes a practical resource-improvement claim First-pass assessment only
280 Unitary vertex operator algebras and conformal nets VOA-to-conformal-net theorem and structure bridge First-pass assessment only
281 QAOA attains the SK optimum in the thermodynamic-first limit Quantum optimization regime and resource audit 031
282 From scale symmetry to local conformal symmetry in four-dimensional QFT Quantum-field assumption provenance map First-pass assessment only
283 Polynomial-time unitary synthesis from a Boolean oracle Oracle construction and unitary-synthesis cost audit 031
284 The optimal quartic separation between randomized and quantum queries Quantum-query complexity comparison ledger 031

Number theory

Family Result and source directory Latest application assessment Dossier IDs
001 Milne’s rationality conjecture and algebraic specialization Arithmetic cycle specialization provenance First-pass assessment only
002 The full BSD formula from low Selmer corank Elliptic-curve BSD evidence ledger First-pass assessment only
003 The quasi-Riemann hypothesis L-function assumption and algorithm dependency audit 016
004 Hilbert’s tenth problem over ℚ Rational constraint solver completeness contract First-pass assessment only
005 Irrationality of Catalan’s constant Exact constant provenance teaching module First-pass assessment only
006 Goldfeld’s conjecture: densities and mean analytic rank Quadratic twist rank distribution reference First-pass assessment only
007 Ordinary two-point correlations and the corrected Elliott conjecture Multiplicative sequence correlation benchmark First-pass assessment only
008 The Deligne–Drinfeld conjecture Grothendieck–Teichmüller graded algebra reference First-pass assessment only
009 Function-field reconstruction from Milnor K-theory and Galois data Function-field reconstruction formal adapter First-pass assessment only
010 Unrestricted pro-modularity at the prime two Dyadic modularity assumption ledger First-pass assessment only
011 Prime-factor statistics of $p-1$ Prime-minus-one factor statistics reference First-pass assessment only
012 Independent largest prime factors of consecutive integers Consecutive integer factor statistics benchmark First-pass assessment only
013 Ostmann’s inverse Goldbach conjecture Additive prime decomposition limitation reference First-pass assessment only
014 Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan Langlands characteristic and assumption coverage graph First-pass assessment only
015 Torus-packet equidistribution in prime, quartic, and sextic degrees Arithmetic packet equidistribution research benchmark First-pass assessment only
016 Zilber–Pink in abelian varieties and the Siegel threefold Atypical subvariety provenance library First-pass assessment only
017 The irrationality exponent of <i>π</i> is 2 Constant approximation and Flint–Hills reference First-pass assessment only
018 The Margulis–Platonov conjecture over global fields Arithmetic group normal-subgroup classification adapter First-pass assessment only
019 The local <i>p</i>-adic section conjecture and global consequences Rational point/Galois section correspondence ledger First-pass assessment only
020 Squarefree quartics and power-free polynomial values Polynomial value density reference First-pass assessment only
021 A quadratic bound for Jacobsthal’s function Coprime search interval budget research First-pass assessment only
022 The weak inhomogeneous Duffin–Schaeffer conjecture Inhomogeneous approximation assumption reference First-pass assessment only
023 Patterson's first moment for cubic Gauss sums Cubic Gauss sum exact reference library First-pass assessment only
024 An asymptotic formula for the number of totients Totient counting asymptotic reference First-pass assessment only
025 Short Egyptian fractions Egyptian fraction construction research library First-pass assessment only
026 Positive lower density of large prime gaps Prime-gap distribution reference First-pass assessment only
027 Potential integral density on curve character varieties Character variety integral-point provenance First-pass assessment only
028 Uniformly bounded components of Gaussian-prime graphs Gaussian prime graph component research explorer First-pass assessment only
029 Primitive roots for every admissible integer base Primitive-root prime generation assumption audit 016
030 Modularity of elliptic curves over imaginary quadratic fields Imaginary-quadratic elliptic curve modularity adapter First-pass assessment only
031 Uchida’s conjecture for open homomorphisms of Galois groups Galois homomorphism reconstruction reference First-pass assessment only

Operator algebras

Family Result and source directory Latest application assessment Dossier IDs
285 Counterexamples to Baum–Connes and Kadison–Kaplansky Assembly and projection counterexample ledger First-pass assessment only
286 Rigidity and arithmetic of lattice von Neumann algebras Rigid lattice bimodule classification reference First-pass assessment only
287 Isomorphism of the free group factors Free-group-factor equivalence evidence First-pass assessment only
288 Kadison's similarity conjecture C-star similarity hypothesis contract First-pass assessment only
289 Strong Kadison–Kastler stability and its spatial boundaries Operator-algebra perturbation scope audit First-pass assessment only
290 Relative bicentralizers and modular spectral recovery Bicentralizer inclusion evidence ledger First-pass assessment only
291 Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stability Nuclear C-star regularity equivalence adapter First-pass assessment only
292 Kirchberg's $\mathcal O_2$ norm-ultrapower embedding problem Nuclear ultrapower embedding counterexample First-pass assessment only
293 Invariant projections, hyperinvariant subspaces, and transitive algebras Infinite-operator invariant-subspace fixture First-pass assessment only
294 Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness Quasitrace and tensor-finiteness counterexample First-pass assessment only
295 The Kadison–Ringrose cohomology conjecture Bounded cohomology primitive contract First-pass assessment only
296 The generator problem for finite factors Single-generator representation research adapter First-pass assessment only
297 A ZFC counterexample to Naimark's problem Nonseparable representation contract First-pass assessment only
298 Two notions of free entropy differ even when both are finite Free entropy notion separation reference First-pass assessment only
299 The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability Central-sequence regularity contract First-pass assessment only
300 Approximation and quadratic strong-operator paving Compressed strong paving scope audit First-pass assessment only
301 Trace cones and Razak–Jacelon stabilization Stabilized trace-cone classification reference First-pass assessment only
302 Radius of comparison equals half the mean dimension Mean-dimension comparison evidence First-pass assessment only
303 Weak pure infiniteness and Cuntz-algebra absorption Pure infiniteness and absorption contract First-pass assessment only

Partial differential equations

Family Result and source directory Latest application assessment Dossier IDs
362 Global smoothness for relativistic Vlasov–Maxwell Relativistic plasma model assumption and solver benchmark library 029
363 Nonuniqueness with local conservation for the hard-sphere Boltzmann equation Kinetic solution selection and conservation audit 029
364 Kinetic limits and fluctuations over the Boltzmann lifespan Molecular-to-kinetic simulation validity planner First-pass assessment only
365 Joint metric and connection recovery from one boundary patch Inverse boundary measurement evidence workbench 026
366 The planar Mumford–Shah regularity conjecture and local weak-<i>L</i><sup>4</sup> gradient bounds Variational segmentation structure diagnostic 028
367 The critical dimension for the one-phase Bernoulli problem Free boundary critical-dimension research benchmark 028
368 The three-dimensional Ball–Evans approximation problem Diffeomorphic deformation feasibility research toolkit First-pass assessment only
369 The hot spots conjecture for simply connected planar domains Neumann eigenmode extrema validation First-pass assessment only
370 The Lane–Emden and Hénon–Lane–Emden conjectures Nonlinear elliptic model nonexistence assumption map First-pass assessment only
371 Stable blowup for the defocusing Schrödinger equation Scientific Fourier discretization audit 029
372 Global uniqueness in smooth isotropic elasticity Elastic material identifiability experiment workbench 027
373 Nonattainment of the three-marginal Coulomb Monge problem Multi-marginal transport representation audit First-pass assessment only
374 Sharp one-third stability of Brenier maps Transport sharpness benchmark and source-domain audit 015, 020
375 De Giorgi's conjecture in dimension eight Allen–Cahn classification and phase-field research reference First-pass assessment only
376 Universal computation in forced Navier–Stokes flows Scientific prediction claim and computational-limit audit 002, 029
377 Interior $C^{1,\alpha}$ regularity for infinity-harmonic functions Infinity-harmonic interpolation regularity reference 029

Probability and statistical mechanics

Family Result and source directory Latest application assessment Dossier IDs
211 The geometric phase diagram, diffusion, and spectra of random planar maps Random-map geometry and diffusion research benchmark First-pass assessment only
212 Planar first-passage geometry and the absence of bigeodesics First-passage routing model asymptotic audit First-pass assessment only
213 Critical percolation on every quasi-transitive graph Percolation criticality research simulator First-pass assessment only
214 The Benjamini–Schramm nonuniqueness conjecture Nonamenable network phase reference First-pass assessment only
215 Canonical $O(3)$ continuum limit and exact $O(4)$ mass asymptotics Spin-model continuum and mass reference calculator First-pass assessment only
216 Critical and near-critical XY scaling and BKT universality BKT model scaling analysis workbench First-pass assessment only
217 The low-temperature Sherrington–Kirkpatrick fluctuation law Low-temperature SK fluctuation normalization benchmark First-pass assessment only
218 Conformal universality for weakly interacting and random-bond Ising models Ising perturbation universality benchmark First-pass assessment only
219 GOE bulk universality for regular graphs with weak Anderson disorder Random regular graph spectral calibration First-pass assessment only
220 Directional zero–one laws beyond iid environments and iid ballisticity Random-environment transport assumption audit First-pass assessment only
221 The Mézard–Parisi formula for diluted spin glasses Diluted spin-glass variational model library First-pass assessment only
222 Perceptron free energies and microscopic jamming exponents Perceptron capacity and jamming regime planner First-pass assessment only
223 Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling Random-cluster interface reference library First-pass assessment only
224 Critical and quenched near-critical universality for Poisson–Voronoi percolation Voronoi critical crossing calibration First-pass assessment only
225 Gaussian free field limits throughout the balanced six-vertex regime Six-vertex height variance reference First-pass assessment only
226 The double-dimer loop ensemble converges to CLE<sub>4</sub> Double-dimer loop scaling research suite First-pass assessment only
227 Critical SK autocorrelation processes and dynamics across the temperature transition Spin sampler clock and regime audit First-pass assessment only
228 Continuum phase transitions for radial pair potentials Continuum phase-transition model reference First-pass assessment only
229 Exact three- and four-state reconstruction thresholds and four-state tree capacity Graph reconstruction feasibility audit 032
230 Exact Hausdorff gauges for SLE SLE fractal-measure normalization reference First-pass assessment only
231 The free uniform spanning forest is a factor of IID Root-free randomized graph construction research First-pass assessment only
232 Gaussian fields and interfaces for triangular-lattice Lipschitz heights Lipschitz random-height reference suite First-pass assessment only
233 The joint critical Ashkin–Teller current limit Ashkin–Teller joint structure benchmark First-pass assessment only
234 All-temperature pressure of orthogonally invariant Ising spin glasses Invariant spin-glass pressure reference First-pass assessment only
235 Limiting random SAT thresholds, sharp variance and computability Random SAT benchmark regime calibration 033
236 The exact factor-of-IID threshold for free Ising spins on trees Tree Ising distributed-sampling feasibility map First-pass assessment only
237 The three-quarter exponent for honeycomb self-avoiding walk Self-avoiding polymer scaling reference First-pass assessment only
238 Optimal logarithmic mixing of the Thorp shuffle Queryable permutation framework and randomness bridge 040
239 Sharp singularity rates for symmetric random sign matrices Random symmetric matrix singularity reference First-pass assessment only

Real and complex analysis

Family Result and source directory Latest application assessment Dossier IDs
071 Koebe’s circle-domain conjecture Conformal domain representation research toolkit First-pass assessment only
072 Brennan's conjecture and the integral-means spectrum Conformal derivative and boundary spectrum audit First-pass assessment only
073 The Falconer distance conjecture Fractal distance-set research explorer First-pass assessment only
074 Kakeya in three and four dimensions Directional tube analysis reference First-pass assessment only
075 The $L\log L$ Fourier-convergence conjecture Fourier convergence assumption reference First-pass assessment only
076 Real ultraflat Littlewood polynomials and unbounded binary merit factors Binary waveform spectrum and correlation contract audit 035
077 Fourier restriction for positively curved surfaces Curved-surface Fourier extension reference First-pass assessment only
078 The three-dimensional Bochner–Riesz conjecture Spectral filter boundedness reference First-pass assessment only
079 Local smoothing in three dimensions Wave propagation regularity assumption ledger First-pass assessment only
080 The exact Sobolev endpoint for Schrödinger convergence Schrödinger initial-data convergence reference First-pass assessment only
081 Riesz transforms and rectifiability in higher codimension Geometric measure regularity evidence map First-pass assessment only
082 Annular variation and dyadic absolute bounds for the triangular Hilbert transform Multilinear singular-integral reference suite First-pass assessment only
083 Hilbert transforms along Lipschitz directions Directional filtering scale contract First-pass assessment only
084 The geometric case of the Erdős similarity conjecture Geometric-pattern avoidance research construction First-pass assessment only
085 Endpoint Sobolev regularity of centered disk averages Scale-space maximal filter regularity audit First-pass assessment only
086 An <i>L</i><sup>3</sup> bound for the trilinear Hilbert transform Trilinear Hilbert transform research benchmark First-pass assessment only

Theoretical computer science

Family Result and source directory Latest application assessment Dossier IDs
102 The Unique Games Conjecture and optimal approximation thresholds Approximation hardness review service First-pass assessment only
103 Exact derandomization of logarithmic space: $\mathsf L=\mathsf{RL}=\mathsf{BPL}$ Small-space decision and compiler readiness audit 020
104 Quasipolynomial algorithms for mean-payoff, stochastic and parity games Mean payoff strategy synthesis plugin 003, 018
105 Perfect completeness for 2-to-1 games Perfect-completeness reduction benchmark library First-pass assessment only
106 Hardness of coloring three-colorable graphs Graph-coloring solver stress suite First-pass assessment only
107 Matrix multiplication with exponent at most 9/4 Matrix tensor construction research toolkit 003, 020, 022
108 A cubic permanent–determinant lower bound Symbolic representation complexity audit First-pass assessment only
109 Integer multiplication below $n\log n$ Big integer asymptotic feasibility worksheet 020
110 Optimal-order randomized <i>k</i>-server on arbitrary metrics Metric movement and activation audit 010, 020
111 One-sample matroid prophet inequalities against an almighty adversary Matroid allocation research simulator 020, 021
112 Beyond the square-root exponent for depth-three circuits Depth-three circuit lower-bound teaching and benchmark module First-pass assessment only
113 Approximate counting and entropy of perfect matchings Matching counts: literal schedule exclusion and bounded fragility reference 001, 006
114 Approximate counting of common integer polymatroid bases Constraint allocation space counter First-pass assessment only
115 Sampling and counting contingency tables with arbitrary margins Fixed-margin tables: law distinction and literal schedule exclusion 001, 004, 041
116 Uniform black-box noncommutative identity testing across characteristics Noncommutative identity testing library 012
117 Uniform sparsest cut: hardness and semidefinite gaps Cut relaxation calibration suite First-pass assessment only
118 Bin packing and unbounded configuration-LP gaps Bin packing approximation claim auditor First-pass assessment only
119 The Courtade–Kumar and Hellinger conjectures Noisy binary summary information benchmark First-pass assessment only
120 Almost-linear-time exact matching and prescribed-degree factors in general graphs General matching: literal backend prerequisite prevents a practical speedup claim 007
121 Almost-linear approximation of edit distance Approximate long-document edit comparison 008
122 Quantitative trace-reconstruction bounds with a uniform decoder Deletion-channel reconstruction validation suite First-pass assessment only
124 Polynomial-time scheduling on three identical machines Three-machine scheduling: source model and practical boundary 001, 009, 020
125 The metric <i>k</i>-median approximation threshold and recovery Metric facility placement planner 011
126 Exponential semidefinite complexity of perfect matching Matching formulation complexity audit First-pass assessment only
127 Average sensitivity of polynomial threshold functions Polynomial threshold sensitivity benchmark First-pass assessment only
128 A factor-two approximation for shortest common superstring Superstring construction, byte objectives and practical packaging 023
129 Exponential state costs for two-way automata Automata transformation resource estimator First-pass assessment only
130 Exact Fourier transforms below $n\log n$ Exact Fourier algorithm feasibility worksheet 020
131 Rapid mixing of graph switches for every degree sequence Graph switching: host, event-time and exactness boundaries 003, 005
132 A superquadratic separation of sensitivity and block sensitivity Sensitivity counterexample generator First-pass assessment only
133 The computational complexity of Weisfeiler–Leman refinement Graph refinement cost and capability evaluator First-pass assessment only
134 Generalized star height at most three Generalized regular expression research compiler First-pass assessment only
135 Homogeneous depth-five lower bounds for iterated matrix multiplication Arithmetic circuit restriction benchmark First-pass assessment only
136 A quasilinear PCP theorem for PPAD Robust local verification research toolkit First-pass assessment only
137 One-tape time simulation in two-fifths-power space Memory-constrained simulation explorer First-pass assessment only
138 Subset Sum in $O(2^{0.49n})$ time Subset-sum decisions: resource, identity and assurance boundary 017
139 Subpolynomial query complexity for log-concave sampling Oracle sampling cost audit 020
140 Memory–sample lower bounds for noiseless Gaussian regression Streaming inference precision budget model First-pass assessment only
141 Existential–universal real sentences in the counting hierarchy Real constraint complexity scope explorer First-pass assessment only
142 Deterministic polynomial factorization over prime fields Deterministic finite-field factorization backend 016

Topology

Family Result and source directory Latest application assessment Dossier IDs
304 The Hilbert–Smith conjecture in every dimension Continuous symmetry classification contract First-pass assessment only
305 Four-dimensional disk embedding and Wall's conjecture Four-dimensional embedding obstruction fixture First-pass assessment only
306 The purely cosmetic surgery conjecture Knot surgery distinctness research contract First-pass assessment only
307 Failure of rational injectivity for maximal coarse assembly Coarse assembly counterexample ledger First-pass assessment only
308 Finite Smith–Toda complexes at every height Chromatic finite-complex existence catalog First-pass assessment only
309 The Kervaire invariant problem at the prime three Odd-primary Kervaire witness registry First-pass assessment only
310 Quillen's conjecture in rational homology Finite-group poset homology contract First-pass assessment only
311 The Hovey–Strickland and Chai conjectures Chromatic tensor-ideal classification ledger First-pass assessment only
312 The Grothendieck homotopy hypothesis Infinity-groupoid model correspondence evidence First-pass assessment only
313 Finite generation for the $K(n)$-local sphere Localized homotopy finite-generation contract First-pass assessment only
314 Cyclic length and chromatic fixed-point loss Cyclic-chain length is computable for bounded finite examples First-pass assessment only
315 The four-dimensional Singer conjecture Four-dimensional L2 homology contract First-pass assessment only
316 Curtis’s conjecture Stable Hurewicz image reference First-pass assessment only
317 Thomason model structures in all strict higher dimensions Categorical homotopy model interoperability First-pass assessment only
318 Chromatic splitting: filtrations and counterexamples Chromatic splitting regime audit First-pass assessment only
319 Counterexamples to finite generation at chromatic height two Finite-building assumption counterexample First-pass assessment only
320 Nonhomeomorphic closed aspherical four-manifolds Homotopy-to-homeomorphism inference fixture First-pass assessment only
321 A counterexample to Wall's finite D(2) problem Cell-dimension simplification contract First-pass assessment only