# Complete family assessment directory

Edition 2026-10-09-v17. 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](opportunities/CATALOG-2026-10-09-v22.md) for 41 developed software/business hypotheses and the [commercial priorities](COMMERCIAL-PRIORITIES-2026-10-09-v19.md) 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](snapshots/2026-10-08-baseline/families/193/source.json) | [Intersection multiplicity consistency library](snapshots/2026-10-08-baseline/families/193/review-2026-10-09-v1.md) | First-pass assessment only |
| 194 | [Lech’s multiplicity conjecture](snapshots/2026-10-08-baseline/families/194/source.json) | [Multiplicity monotonicity formal adapter](snapshots/2026-10-08-baseline/families/194/review-2026-10-09-v1.md) | First-pass assessment only |
| 195 | [A counterexample to the small Cohen–Macaulay module conjecture](snapshots/2026-10-08-baseline/families/195/source.json) | [Cohen–Macaulay approximation limitation ledger](snapshots/2026-10-08-baseline/families/195/review-2026-10-09-v1.md) | First-pass assessment only |
| 196 | [A counterexample to Kaplansky’s zero-divisor conjecture](snapshots/2026-10-08-baseline/families/196/source.json) | [Group-algebra zero-divisor counterexample fixture](snapshots/2026-10-08-baseline/families/196/review-2026-10-09-v1.md) | First-pass assessment only |
| 197 | [A torsion-free group algebra that is not directly finite](snapshots/2026-10-08-baseline/families/197/source.json) | [Algebraic inverse and cellular-automaton scope audit](snapshots/2026-10-08-baseline/families/197/review-2026-10-09-v1.md) | First-pass assessment only |
| 198 | [A counterexample to finitistic-dimension finiteness](snapshots/2026-10-08-baseline/families/198/source.json) | [Homological dimension counterexample library](snapshots/2026-10-08-baseline/families/198/review-2026-10-09-v1.md) | First-pass assessment only |
| 199 | [Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures](snapshots/2026-10-08-baseline/families/199/source.json) | [Homological conjecture dependency and counterexample graph](snapshots/2026-10-08-baseline/families/199/review-2026-10-09-v1.md) | First-pass assessment only |
| 200 | [Eisenbud–Green–Harris and lex-plus-powers](snapshots/2026-10-08-baseline/families/200/source.json) | [Hilbert function and Betti bound research adapter](snapshots/2026-10-08-baseline/families/200/review-2026-10-09-v1.md) | First-pass assessment only |
| 201 | [A counterexample to Kurosh’s division-ring problem](snapshots/2026-10-08-baseline/families/201/source.json) | [Division-ring local-finiteness limitation reference](snapshots/2026-10-08-baseline/families/201/review-2026-10-09-v1.md) | First-pass assessment only |
| 202 | [The blockwise Alperin weight conjecture](snapshots/2026-10-08-baseline/families/202/source.json) | [Brauer character and weight counting cross-check](snapshots/2026-10-08-baseline/families/202/review-2026-10-09-v1.md) | First-pass assessment only |
| 203 | [Donovan's conjecture over fields and complete mixed-characteristic DVRs](snapshots/2026-10-08-baseline/families/203/source.json) | [Block classification finiteness provenance](snapshots/2026-10-08-baseline/families/203/review-2026-10-09-v1.md) | First-pass assessment only |
| 204 | [Tensor saturation for even spin groups](snapshots/2026-10-08-baseline/families/204/source.json) | [Spin-group tensor invariant scale reduction](snapshots/2026-10-08-baseline/families/204/review-2026-10-09-v1.md) | First-pass assessment only |
| 205 | [Saxl’s conjecture and universal tensor squares](snapshots/2026-10-08-baseline/families/205/source.json) | [Symmetric representation tensor-square reference](snapshots/2026-10-08-baseline/families/205/review-2026-10-09-v1.md) | First-pass assessment only |
| 206 | [Finite lattice representation and undecidability](snapshots/2026-10-08-baseline/families/206/source.json) | [Finite algebra representation solver completeness contract](snapshots/2026-10-08-baseline/families/206/review-2026-10-09-v1.md) | First-pass assessment only |
| 207 | [The ℓ¹-Bass conjecture for all discrete groups](snapshots/2026-10-08-baseline/families/207/source.json) | [Idempotent trace support and coefficient-regime audit](snapshots/2026-10-08-baseline/families/207/review-2026-10-09-v1.md) | First-pass assessment only |
| 208 | [Finite symmetric tensor categories and the Verlinde tower](snapshots/2026-10-08-baseline/families/208/source.json) | [Finite symmetric tensor category fiber-functor adapter](snapshots/2026-10-08-baseline/families/208/review-2026-10-09-v1.md) | First-pass assessment only |
| 209 | [Integral counterexamples to Gersten’s conjecture](snapshots/2026-10-08-baseline/families/209/source.json) | [K-theory localization information-loss fixture](snapshots/2026-10-08-baseline/families/209/review-2026-10-09-v1.md) | First-pass assessment only |
| 210 | [Foulkes' conjecture for sixth powers and quadratic stabilization](snapshots/2026-10-08-baseline/families/210/source.json) | [Symmetric power map stabilization benchmark](snapshots/2026-10-08-baseline/families/210/review-2026-10-09-v1.md) | 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](snapshots/2026-10-08-baseline/families/032/source.json) | [Hodge–Tate proof dependency adapter](snapshots/2026-10-08-baseline/families/032/review-2026-10-09-v1.md) | 002 |
| 033 | [Iitaka subadditivity, variation, and logarithmic additivity](snapshots/2026-10-08-baseline/families/033/source.json) | [Orbifold subadditivity hypothesis ledger](snapshots/2026-10-08-baseline/families/033/review-2026-10-09-v1.md) | First-pass assessment only |
| 034 | [Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity](snapshots/2026-10-08-baseline/families/034/source.json) | [Abundance and Iitaka dependency evidence](snapshots/2026-10-08-baseline/families/034/review-2026-10-09-v1.md) | First-pass assessment only |
| 035 | [Log-canonical threefold abundance in numerical dimension one](snapshots/2026-10-08-baseline/families/035/source.json) | [Positive-characteristic threefold adjoint contract](snapshots/2026-10-08-baseline/families/035/review-2026-10-09-v1.md) | First-pass assessment only |
| 036 | [Numerical semiampleness and generalized minimal models](snapshots/2026-10-08-baseline/families/036/source.json) | [Numerical semiampleness model contract](snapshots/2026-10-08-baseline/families/036/review-2026-10-09-v1.md) | First-pass assessment only |
| 037 | [The ordinary-double-point volume gap](snapshots/2026-10-08-baseline/families/037/source.json) | [Normalized-volume singularity reference](snapshots/2026-10-08-baseline/families/037/review-2026-10-09-v1.md) | First-pass assessment only |
| 038 | [Fujita’s freeness conjecture](snapshots/2026-10-08-baseline/families/038/source.json) | [Adjoint linear-system generation contract](snapshots/2026-10-08-baseline/families/038/review-2026-10-09-v1.md) | First-pass assessment only |
| 039 | [Nagata’s conjecture and maximal Seshadri constants](snapshots/2026-10-08-baseline/families/039/source.json) | [Very-general-point interpolation boundary](snapshots/2026-10-08-baseline/families/039/review-2026-10-09-v1.md) | First-pass assessment only |
| 040 | [Bloch’s conjecture for complex surfaces](snapshots/2026-10-08-baseline/families/040/source.json) | [Surface cycle-class assumption reference](snapshots/2026-10-08-baseline/families/040/review-2026-10-09-v1.md) | First-pass assessment only |
| 041 | [Hyperkähler SYZ and projective-space bases](snapshots/2026-10-08-baseline/families/041/source.json) | [Hyperkähler fibration existence ledger](snapshots/2026-10-08-baseline/families/041/review-2026-10-09-v1.md) | First-pass assessment only |
| 042 | [Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII](snapshots/2026-10-08-baseline/families/042/source.json) | [Complex-manifold Oka classification reference](snapshots/2026-10-08-baseline/families/042/review-2026-10-09-v1.md) | First-pass assessment only |
| 043 | [<i>P</i> = <i>W</i> for fixed-determinant SL<sub><i>n</i></sub> moduli spaces](snapshots/2026-10-08-baseline/families/043/source.json) | [P=W cohomology computation cross-check](snapshots/2026-10-08-baseline/families/043/review-2026-10-09-v1.md) | First-pass assessment only |
| 044 | [The equivariant cohomological Hikita conjecture](snapshots/2026-10-08-baseline/families/044/source.json) | [Quiver cohomology correspondence adapter](snapshots/2026-10-08-baseline/families/044/review-2026-10-09-v1.md) | First-pass assessment only |
| 046 | [Shafarevich counterexamples in dimension two and with large fundamental group](snapshots/2026-10-08-baseline/families/046/source.json) | [Universal-cover convexity counterexample library](snapshots/2026-10-08-baseline/families/046/review-2026-10-09-v1.md) | First-pass assessment only |
| 047 | [Zariski cancellation and affine fibrations over the complex numbers](snapshots/2026-10-08-baseline/families/047/source.json) | [Algebraic cancellation counterexample fixture](snapshots/2026-10-08-baseline/families/047/review-2026-10-09-v1.md) | First-pass assessment only |
| 048 | [A characteristic-zero counterexample to Lipman–Zariski](snapshots/2026-10-08-baseline/families/048/source.json) | [Tangent-sheaf smoothness contract counterexample](snapshots/2026-10-08-baseline/families/048/review-2026-10-09-v1.md) | First-pass assessment only |
| 049 | [A stable-coordinate counterexample in four variables](snapshots/2026-10-08-baseline/families/049/source.json) | [Stable polynomial coordinate counterexample](snapshots/2026-10-08-baseline/families/049/review-2026-10-09-v1.md) | First-pass assessment only |
| 050 | [A counterexample to Griffiths’ positivity conjecture](snapshots/2026-10-08-baseline/families/050/source.json) | [Bundle positivity assumption audit](snapshots/2026-10-08-baseline/families/050/review-2026-10-09-v1.md) | First-pass assessment only |
| 051 | [Kobayashi’s canonical-ampleness conjecture](snapshots/2026-10-08-baseline/families/051/source.json) | [Hyperbolicity-to-projectivity evidence ledger](snapshots/2026-10-08-baseline/families/051/review-2026-10-09-v1.md) | First-pass assessment only |
| 052 | [Tangent splittings and product decompositions](snapshots/2026-10-08-baseline/families/052/source.json) | [Holomorphic splitting integrability contract](snapshots/2026-10-08-baseline/families/052/review-2026-10-09-v1.md) | First-pass assessment only |
| 053 | [A counterexample to Pixton completeness in Chow](snapshots/2026-10-08-baseline/families/053/source.json) | [Tautological relation completeness counterexample](snapshots/2026-10-08-baseline/families/053/review-2026-10-09-v1.md) | First-pass assessment only |
| 054 | [Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations](snapshots/2026-10-08-baseline/families/054/source.json) | [Cubic-fourfold rationality scope audit](snapshots/2026-10-08-baseline/families/054/review-2026-10-09-v1.md) | First-pass assessment only |
| 055 | [Gepner symmetry and large-volume stability on threefolds](snapshots/2026-10-08-baseline/families/055/source.json) | [Stability-condition research adapter](snapshots/2026-10-08-baseline/families/055/review-2026-10-09-v1.md) | First-pass assessment only |
| 056 | [Termination of projective and Kähler fourfold minimal model programs](snapshots/2026-10-08-baseline/families/056/source.json) | [Termination-versus-runtime solver contract](snapshots/2026-10-08-baseline/families/056/review-2026-10-09-v1.md) | First-pass assessment only |
| 057 | [Fundamental groups of special complex varieties and root orbifolds](snapshots/2026-10-08-baseline/families/057/source.json) | [Special-manifold group implication ledger](snapshots/2026-10-08-baseline/families/057/review-2026-10-09-v1.md) | First-pass assessment only |
| 058 | [Semialgebraic universal covers and bounded domains](snapshots/2026-10-08-baseline/families/058/source.json) | [Semialgebraic universal-cover classification reference](snapshots/2026-10-08-baseline/families/058/review-2026-10-09-v1.md) | First-pass assessment only |
| 059 | [Counterexamples to Zariski’s multiplicity conjecture](snapshots/2026-10-08-baseline/families/059/source.json) | [Topology-versus-multiplicity counterexample](snapshots/2026-10-08-baseline/families/059/review-2026-10-09-v1.md) | First-pass assessment only |
| 060 | [The Global Spherical Shell conjecture](snapshots/2026-10-08-baseline/families/060/source.json) | [Class-VII surface classification evidence](snapshots/2026-10-08-baseline/families/060/review-2026-10-09-v1.md) | First-pass assessment only |
| 062 | [Projective contact classification and the LeBrun–Salamon conjecture](snapshots/2026-10-08-baseline/families/062/source.json) | [Quaternionic and contact classification ledger](snapshots/2026-10-08-baseline/families/062/review-2026-10-09-v1.md) | First-pass assessment only |
| 063 | [The generalized Mukai conjecture](snapshots/2026-10-08-baseline/families/063/source.json) | [Fano invariant inequality reference](snapshots/2026-10-08-baseline/families/063/review-2026-10-09-v1.md) | First-pass assessment only |
| 064 | [Topological triviality of <i>μ</i>-constant surface singularities](snapshots/2026-10-08-baseline/families/064/source.json) | [Singularity-family topological triviality contract](snapshots/2026-10-08-baseline/families/064/review-2026-10-09-v1.md) | First-pass assessment only |
| 065 | [Virasoro constraints for complete intersections and projective-bundle towers](snapshots/2026-10-08-baseline/families/065/source.json) | [Projectivization transfer is a conditional research computation lead](snapshots/2026-10-08-baseline/families/065/review-2026-10-09-v2.md) | First-pass assessment only |
| 066 | [Bounded klt complements for Fano contractions](snapshots/2026-10-08-baseline/families/066/source.json) | [Complement-index boundedness contract](snapshots/2026-10-08-baseline/families/066/review-2026-10-09-v1.md) | First-pass assessment only |
| 067 | [The Campana–Peternell conjecture in dimension six](snapshots/2026-10-08-baseline/families/067/source.json) | [Six-dimensional Fano classification reference](snapshots/2026-10-08-baseline/families/067/review-2026-10-09-v1.md) | First-pass assessment only |
| 068 | [Anticanonical nonvanishing in every dimension](snapshots/2026-10-08-baseline/families/068/source.json) | [Semipositive anticanonical section contract](snapshots/2026-10-08-baseline/families/068/review-2026-10-09-v1.md) | First-pass assessment only |
| 069 | [Global quantum geometric Langlands at irrational level](snapshots/2026-10-08-baseline/families/069/source.json) | [Geometric Langlands correspondence provenance](snapshots/2026-10-08-baseline/families/069/review-2026-10-09-v1.md) | First-pass assessment only |

## Combinatorics

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 155 | [A counterexample to periodic tiling in dimension three](snapshots/2026-10-08-baseline/families/155/source.json) | [Three-dimensional tiling feasibility and periodicity audit](snapshots/2026-10-08-baseline/families/155/review-2026-10-09-v1.md) | First-pass assessment only |
| 156 | [Borsuk's conjecture fails in dimension nine](snapshots/2026-10-08-baseline/families/156/source.json) | [Diameter partition counterexample library](snapshots/2026-10-08-baseline/families/156/review-2026-10-09-v1.md) | First-pass assessment only |
| 157 | [Graph coloring, clique minors, and Colin de Verdière invariants](snapshots/2026-10-08-baseline/families/157/source.json) | [Graph coloring bound assumption auditor](snapshots/2026-10-08-baseline/families/157/review-2026-10-09-v1.md) | First-pass assessment only |
| 158 | [The Euclidean plane cannot be colored with five colors](snapshots/2026-10-08-baseline/families/158/source.json) | [Plane-coloring boundary and finite certificate audit](snapshots/2026-10-08-baseline/families/158/review-2026-10-09-v2.md) | First-pass assessment only |
| 159 | [Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi bounds](snapshots/2026-10-08-baseline/families/159/source.json) | [Arithmetic progression density reference](snapshots/2026-10-08-baseline/families/159/review-2026-10-09-v1.md) | First-pass assessment only |
| 160 | [Superexponential van der Waerden numbers](snapshots/2026-10-08-baseline/families/160/source.json) | [Ramsey forcing-scale reference](snapshots/2026-10-08-baseline/families/160/review-2026-10-09-v1.md) | First-pass assessment only |
| 161 | [Counterexamples to Sidorenko’s conjecture and the forcing conjecture](snapshots/2026-10-08-baseline/families/161/source.json) | [Graph null-model motif counterexample audit](snapshots/2026-10-08-baseline/families/161/review-2026-10-09-v1.md) | First-pass assessment only |
| 162 | [Counterexamples to Ryser’s covering conjecture](snapshots/2026-10-08-baseline/families/162/source.json) | [Hypergraph cover relaxation limitation audit](snapshots/2026-10-08-baseline/families/162/review-2026-10-09-v1.md) | First-pass assessment only |
| 164 | [Hindman’s finite sums and products conjecture](snapshots/2026-10-08-baseline/families/164/source.json) | [Finite sums/products Ramsey research explorer](snapshots/2026-10-08-baseline/families/164/review-2026-10-09-v1.md) | First-pass assessment only |
| 165 | [The Harary–Hill and Zarankiewicz crossing-number formulas](snapshots/2026-10-08-baseline/families/165/source.json) | [Complete-graph drawing crossing reference](snapshots/2026-10-08-baseline/families/165/review-2026-10-09-v1.md) | First-pass assessment only |
| 166 | [The higher-dimensional Erdős distinct-distances conjecture](snapshots/2026-10-08-baseline/families/166/source.json) | [Distinct-distance point-set reference](snapshots/2026-10-08-baseline/families/166/review-2026-10-09-v1.md) | First-pass assessment only |
| 167 | [Planar distinct distances and unit-distance bounds](snapshots/2026-10-08-baseline/families/167/source.json) | [Planar geometric incidence benchmark](snapshots/2026-10-08-baseline/families/167/review-2026-10-09-v1.md) | First-pass assessment only |
| 168 | [Combinatorial invariance of Kazhdan–Lusztig polynomials](snapshots/2026-10-08-baseline/families/168/source.json) | [Bruhat interval polynomial caching library](snapshots/2026-10-08-baseline/families/168/review-2026-10-09-v1.md) | First-pass assessment only |
| 169 | [Shareshian–Wachs elementary positivity](snapshots/2026-10-08-baseline/families/169/source.json) | [Elementary-basis witness and algebra audit](snapshots/2026-10-08-baseline/families/169/review-2026-10-09-v2.md) | 039 |
| 170 | [Sharp logarithmic exponents for off-diagonal Ramsey numbers](snapshots/2026-10-08-baseline/families/170/source.json) | [Off-diagonal Ramsey exponent reference](snapshots/2026-10-08-baseline/families/170/review-2026-10-09-v1.md) | First-pass assessment only |
| 171 | [The hypercube Ramsey conjecture](snapshots/2026-10-08-baseline/families/171/source.json) | [Hypercube Ramsey forcing reference](snapshots/2026-10-08-baseline/families/171/review-2026-10-09-v1.md) | First-pass assessment only |
| 172 | [Classification of finite Euclidean Ramsey configurations](snapshots/2026-10-08-baseline/families/172/source.json) | [Euclidean Ramsey configuration classifier research](snapshots/2026-10-08-baseline/families/172/review-2026-10-09-v1.md) | First-pass assessment only |
| 173 | [Seymour’s second-neighborhood conjecture](snapshots/2026-10-08-baseline/families/173/source.json) | [Oriented graph two-hop reach benchmark](snapshots/2026-10-08-baseline/families/173/review-2026-10-09-v1.md) | First-pass assessment only |
| 174 | [Deterministic construction of strong thin spanning trees](snapshots/2026-10-08-baseline/families/174/source.json) | [Thin trees: all-cut checking and conservative signing constants](snapshots/2026-10-08-baseline/families/174/review-2026-10-09-v2.md) | 024, 036 |
| 175 | [Talagrand’s expectation thresholds, discrete convexity, and graph decompositions](snapshots/2026-10-08-baseline/families/175/source.json) | [Expectation-threshold and decomposition reference](snapshots/2026-10-08-baseline/families/175/review-2026-10-09-v1.md) | First-pass assessment only |
| 176 | [The second Kahn–Kalai conjecture with an edge-count bound](snapshots/2026-10-08-baseline/families/176/source.json) | [Random-graph motif appearance planner](snapshots/2026-10-08-baseline/families/176/review-2026-10-09-v1.md) | First-pass assessment only |
| 177 | [Bounded-degree coboundary expanders](snapshots/2026-10-08-baseline/families/177/source.json) | [High-dimensional expander research generator](snapshots/2026-10-08-baseline/families/177/review-2026-10-09-v1.md) | First-pass assessment only |
| 178 | [Deterministic nonbipartite Ramanujan graphs in every fixed degree](snapshots/2026-10-08-baseline/families/178/source.json) | [Spectral construction: millions of tracked parameters and uninstantiated thresholds](snapshots/2026-10-08-baseline/families/178/review-2026-10-09-v2.md) | 036 |
| 179 | [The circulant Hadamard and Barker-sequence conjectures](snapshots/2026-10-08-baseline/families/179/source.json) | [Binary waveform constraint feasibility audit](snapshots/2026-10-08-baseline/families/179/review-2026-10-09-v1.md) | 035 |
| 180 | [Barnette’s Hamiltonian-cycle conjecture](snapshots/2026-10-08-baseline/families/180/source.json) | [Hamiltonian graph-class feasibility reference](snapshots/2026-10-08-baseline/families/180/review-2026-10-09-v1.md) | First-pass assessment only |
| 181 | [The Erdős–Gallai cycle-decomposition conjecture](snapshots/2026-10-08-baseline/families/181/source.json) | [Graph cycle decomposition research toolkit](snapshots/2026-10-08-baseline/families/181/review-2026-10-09-v1.md) | First-pass assessment only |
| 182 | [Power savings for intersective polynomial differences and prime arguments](snapshots/2026-10-08-baseline/families/182/source.json) | [Polynomial-difference avoidance reference](snapshots/2026-10-08-baseline/families/182/review-2026-10-09-v1.md) | First-pass assessment only |
| 183 | [Power savings for planar halving lines and <i>k</i>-sets](snapshots/2026-10-08-baseline/families/183/source.json) | [Geometric split-count research benchmark](snapshots/2026-10-08-baseline/families/183/review-2026-10-09-v1.md) | First-pass assessment only |
| 184 | [Correspondence coloring with a fixed forbidden subgraph](snapshots/2026-10-08-baseline/families/184/source.json) | [Conflict coloring class assumption audit](snapshots/2026-10-08-baseline/families/184/review-2026-10-09-v1.md) | First-pass assessment only |
| 185 | [Counterexamples to infinite matroid intersection and packing/covering](snapshots/2026-10-08-baseline/families/185/source.json) | [Infinite matroid guarantee limitation map](snapshots/2026-10-08-baseline/families/185/review-2026-10-09-v1.md) | First-pass assessment only |
| 186 | [Uniform influence and sharp thresholds for graph and hypergraph properties](snapshots/2026-10-08-baseline/families/186/source.json) | [Relabeling-invariant threshold research reference](snapshots/2026-10-08-baseline/families/186/review-2026-10-09-v1.md) | First-pass assessment only |
| 187 | [Snaky in 21 Maker moves](snapshots/2026-10-08-baseline/families/187/source.json) | [Finite strategy certificate teaching engine](snapshots/2026-10-08-baseline/families/187/review-2026-10-09-v1.md) | First-pass assessment only |
| 188 | [The sharp terminal leave in random triangle removal](snapshots/2026-10-08-baseline/families/188/source.json) | [Random triangle-removal process reference](snapshots/2026-10-08-baseline/families/188/review-2026-10-09-v1.md) | First-pass assessment only |
| 189 | [Cycle–clique Ramsey numbers](snapshots/2026-10-08-baseline/families/189/source.json) | [Cycle–clique Ramsey exact reference library](snapshots/2026-10-08-baseline/families/189/review-2026-10-09-v1.md) | First-pass assessment only |
| 190 | [Polynomial removal fails for ordered binary matrices](snapshots/2026-10-08-baseline/families/190/source.json) | [Ordered matrix pattern-sampling limitation audit](snapshots/2026-10-08-baseline/families/190/review-2026-10-09-v1.md) | First-pass assessment only |
| 191 | [A power improvement in the Heilbronn triangle lower bound](snapshots/2026-10-08-baseline/families/191/source.json) | [Nondegenerate planar point-set research design](snapshots/2026-10-08-baseline/families/191/review-2026-10-09-v1.md) | First-pass assessment only |
| 192 | [Boolean functions violate the square-root degree bound by arbitrary factors](snapshots/2026-10-08-baseline/families/192/source.json) | [Boolean Fourier degree limitation reference](snapshots/2026-10-08-baseline/families/192/review-2026-10-09-v1.md) | 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](snapshots/2026-10-08-baseline/families/087/source.json) | [Convex geometry inequality and equality-case workbench](snapshots/2026-10-08-baseline/families/087/review-2026-10-09-v1.md) | First-pass assessment only |
| 088 | [Sharp projection-body inequalities and a counterexample to simplex maximization](snapshots/2026-10-08-baseline/families/088/source.json) | [Projection volume model validation toolkit](snapshots/2026-10-08-baseline/families/088/review-2026-10-09-v1.md) | First-pass assessment only |
| 089 | [Bounded-distortion <i>L</i><sub>1</sub> embeddings of planar and bounded-treewidth graphs](snapshots/2026-10-08-baseline/families/089/source.json) | [Planar metric embedding and flow-cut review](snapshots/2026-10-08-baseline/families/089/review-2026-10-09-v1.md) | 024 |
| 090 | [Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energy](snapshots/2026-10-08-baseline/families/090/source.json) | [Triangular lattice energy benchmark](snapshots/2026-10-08-baseline/families/090/review-2026-10-09-v1.md) | First-pass assessment only |
| 091 | [Logarithmic and <i>L</i><sub><i>p</i></sub> Brunn–Minkowski inequalities and the B-conjecture](snapshots/2026-10-08-baseline/families/091/source.json) | [Symmetric convex-body interpolation audit](snapshots/2026-10-08-baseline/families/091/review-2026-10-09-v1.md) | First-pass assessment only |
| 092 | [The optimal order of convex-body covering density](snapshots/2026-10-08-baseline/families/092/source.json) | [Covering-density research planner](snapshots/2026-10-08-baseline/families/092/review-2026-10-09-v1.md) | First-pass assessment only |
| 093 | [Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures](snapshots/2026-10-08-baseline/families/093/source.json) | [Log-concave sampling assumption audit](snapshots/2026-10-08-baseline/families/093/review-2026-10-09-v1.md) | First-pass assessment only |
| 094 | [Subpolynomial dimension reduction in <i>L</i><sub><i>p</i></sub>](snapshots/2026-10-08-baseline/families/094/source.json) | [Finite Lp embedding contract audit](snapshots/2026-10-08-baseline/families/094/review-2026-10-09-v1.md) | 025 |
| 095 | [Hyperbolicity cones without semidefinite lifts](snapshots/2026-10-08-baseline/families/095/source.json) | [Conic formulation scope checker](snapshots/2026-10-08-baseline/families/095/review-2026-10-09-v1.md) | First-pass assessment only |
| 096 | [The Gaussian propeller conjecture in every dimension](snapshots/2026-10-08-baseline/families/096/source.json) | [Kernel clustering hardness and Gaussian partition benchmark](snapshots/2026-10-08-baseline/families/096/review-2026-10-09-v1.md) | First-pass assessment only |
| 097 | [The Euclidean Steinitz–Bergström bound](snapshots/2026-10-08-baseline/families/097/source.json) | [Vector prefix balancing research simulator](snapshots/2026-10-08-baseline/families/097/review-2026-10-09-v1.md) | First-pass assessment only |
| 098 | [Compact counterexamples to bi-Lipschitz dimension reduction](snapshots/2026-10-08-baseline/families/098/source.json) | [Metric compression impossibility demonstrator](snapshots/2026-10-08-baseline/families/098/review-2026-10-09-v1.md) | First-pass assessment only |
| 099 | [The sharp exponential scale of edit-distance distortion](snapshots/2026-10-08-baseline/families/099/source.json) | [Edit metric embedding limits audit](snapshots/2026-10-08-baseline/families/099/review-2026-10-09-v1.md) | 008, 025 |
| 100 | [Cylinder coverings below the half-area bound](snapshots/2026-10-08-baseline/families/100/source.json) | [Cylinder covering counterexample visualizer](snapshots/2026-10-08-baseline/families/100/review-2026-10-09-v1.md) | First-pass assessment only |
| 101 | [The sharp simplex conjecture for isotropic constants](snapshots/2026-10-08-baseline/families/101/source.json) | [Log-concave entropy and isotropic geometry benchmark](snapshots/2026-10-08-baseline/families/101/review-2026-10-09-v1.md) | 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>](snapshots/2026-10-08-baseline/families/333/source.json) | [Metric surface realization research library](snapshots/2026-10-08-baseline/families/333/review-2026-10-09-v1.md) | First-pass assessment only |
| 334 | [A smooth surface metric with no local isometric immersion in ℝ<sup>3</sup>](snapshots/2026-10-08-baseline/families/334/source.json) | [Surface realization limitation audit](snapshots/2026-10-08-baseline/families/334/review-2026-10-09-v1.md) | First-pass assessment only |
| 335 | [Gromov’s integral scalar-curvature bound for simplicial volume](snapshots/2026-10-08-baseline/families/335/source.json) | [Scalar curvature and topology assumption ledger](snapshots/2026-10-08-baseline/families/335/review-2026-10-09-v1.md) | First-pass assessment only |
| 336 | [Spectral scalar curvature, Urysohn width, and macroscopic dimension](snapshots/2026-10-08-baseline/families/336/source.json) | [Spectral geometry width research planner](snapshots/2026-10-08-baseline/families/336/review-2026-10-09-v1.md) | First-pass assessment only |
| 337 | [Sharp Cartan–Hadamard isoperimetry and rigidity](snapshots/2026-10-08-baseline/families/337/source.json) | [Curved-space isoperimetric and filling reference](snapshots/2026-10-08-baseline/families/337/review-2026-10-09-v1.md) | First-pass assessment only |
| 338 | [Yau's uniformization conjecture](snapshots/2026-10-08-baseline/families/338/source.json) | [Kähler uniformization provenance module](snapshots/2026-10-08-baseline/families/338/review-2026-10-09-v1.md) | First-pass assessment only |
| 339 | [Katok's entropy rigidity conjecture](snapshots/2026-10-08-baseline/families/339/source.json) | [Geodesic entropy rigidity research reference](snapshots/2026-10-08-baseline/families/339/review-2026-10-09-v1.md) | First-pass assessment only |
| 340 | [A counterexample to the nearby Lagrangian conjecture](snapshots/2026-10-08-baseline/families/340/source.json) | [Lagrangian equivalence limitation ledger](snapshots/2026-10-08-baseline/families/340/review-2026-10-09-v1.md) | First-pass assessment only |
| 341 | [Donaldson's hypersymplectic deformation conjecture](snapshots/2026-10-08-baseline/families/341/source.json) | [Hypersymplectic deformation research toolkit](snapshots/2026-10-08-baseline/families/341/review-2026-10-09-v1.md) | First-pass assessment only |
| 342 | [Donaldson's tamed-to-compatible conjecture](snapshots/2026-10-08-baseline/families/342/source.json) | [Almost-complex compatibility assumption map](snapshots/2026-10-08-baseline/families/342/review-2026-10-09-v1.md) | First-pass assessment only |
| 343 | [Symplectic ball packing in higher dimensions](snapshots/2026-10-08-baseline/families/343/source.json) | [Symplectic capacity packing research calculator](snapshots/2026-10-08-baseline/families/343/review-2026-10-09-v1.md) | First-pass assessment only |
| 344 | [The metric Blaschke conjecture](snapshots/2026-10-08-baseline/families/344/source.json) | [Injectivity-radius rigidity research reference](snapshots/2026-10-08-baseline/families/344/review-2026-10-09-v1.md) | First-pass assessment only |
| 345 | [Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds](snapshots/2026-10-08-baseline/families/345/source.json) | [Closed geodesic research benchmark library](snapshots/2026-10-08-baseline/families/345/review-2026-10-09-v1.md) | First-pass assessment only |
| 346 | [Sharp singular-set bounds for stationary integral varifolds](snapshots/2026-10-08-baseline/families/346/source.json) | [Varifold regularity class audit](snapshots/2026-10-08-baseline/families/346/review-2026-10-09-v1.md) | First-pass assessment only |
| 347 | [Counterexamples to stable-Morse and strong Arnold fixed-point bounds](snapshots/2026-10-08-baseline/families/347/source.json) | [Hamiltonian fixed-point lower-bound limitation library](snapshots/2026-10-08-baseline/families/347/review-2026-10-09-v1.md) | First-pass assessment only |
| 348 | [Nonnegative-curvature Einstein classification and an <i>L</i><sup>2</sup> topological gap](snapshots/2026-10-08-baseline/families/348/source.json) | [Einstein four-manifold classification reference](snapshots/2026-10-08-baseline/families/348/review-2026-10-09-v1.md) | First-pass assessment only |
| 349 | [The Solomon–Yau least-volume conjecture](snapshots/2026-10-08-baseline/families/349/source.json) | [Spherical minimal-surface volume reference](snapshots/2026-10-08-baseline/families/349/review-2026-10-09-v1.md) | First-pass assessment only |
| 350 | [Yau’s nodal bounds: surfaces and higher dimensions](snapshots/2026-10-08-baseline/families/350/source.json) | [Spectral nodal-set scope and mesh benchmark](snapshots/2026-10-08-baseline/families/350/review-2026-10-09-v1.md) | First-pass assessment only |
| 351 | [Scalar curvature and finite-time Ricci-flow singularities](snapshots/2026-10-08-baseline/families/351/source.json) | [Ricci flow singularity evidence audit](snapshots/2026-10-08-baseline/families/351/review-2026-10-09-v1.md) | First-pass assessment only |
| 352 | [A finite-time singularity of Calabi flow](snapshots/2026-10-08-baseline/families/352/source.json) | [Calabi flow failure reference](snapshots/2026-10-08-baseline/families/352/review-2026-10-09-v1.md) | First-pass assessment only |
| 353 | [Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexample](snapshots/2026-10-08-baseline/families/353/source.json) | [Affine maximal graph rigidity reference](snapshots/2026-10-08-baseline/families/353/review-2026-10-09-v1.md) | First-pass assessment only |
| 354 | [The isoperimetric profile of the cubic three-torus](snapshots/2026-10-08-baseline/families/354/source.json) | [Periodic microstructure interface reference calculator](snapshots/2026-10-08-baseline/families/354/review-2026-10-09-v1.md) | 037 |
| 355 | [Unique tangent flows at the first surface singularity](snapshots/2026-10-08-baseline/families/355/source.json) | [Mean curvature first-singularity comparison reference](snapshots/2026-10-08-baseline/families/355/review-2026-10-09-v1.md) | First-pass assessment only |
| 356 | [Gigli’s characterization of Alexandrov curvature](snapshots/2026-10-08-baseline/families/356/source.json) | [Metric-measure curvature definition audit](snapshots/2026-10-08-baseline/families/356/review-2026-10-09-v1.md) | First-pass assessment only |
| 357 | [Bi-Lipschitz coordinates at every regular RCD point](snapshots/2026-10-08-baseline/families/357/source.json) | [RCD local coordinate research toolkit](snapshots/2026-10-08-baseline/families/357/review-2026-10-09-v1.md) | First-pass assessment only |
| 358 | [A three-manifold without conjugate points or nonpositive curvature](snapshots/2026-10-08-baseline/families/358/source.json) | [Metric existence implication limitation map](snapshots/2026-10-08-baseline/families/358/review-2026-10-09-v1.md) | First-pass assessment only |
| 359 | [Negative Kähler curvature without bounded holomorphic coordinates](snapshots/2026-10-08-baseline/families/359/source.json) | [Holomorphic coordinate limitation reference](snapshots/2026-10-08-baseline/families/359/review-2026-10-09-v1.md) | First-pass assessment only |
| 360 | [Weak MTW curvature gives convexity and regular optimal transport](snapshots/2026-10-08-baseline/families/360/source.json) | [Curved optimal-transport regularity contract](snapshots/2026-10-08-baseline/families/360/review-2026-10-09-v1.md) | First-pass assessment only |
| 361 | [Failure of integer-degree harmonic dimension comparison](snapshots/2026-10-08-baseline/families/361/source.json) | [Harmonic growth dimension comparison limitation](snapshots/2026-10-08-baseline/families/361/review-2026-10-09-v1.md) | 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](snapshots/2026-10-08-baseline/families/143/source.json) | [Planar oscillator cycle-count assurance](snapshots/2026-10-08-baseline/families/143/review-2026-10-09-v1.md) | First-pass assessment only |
| 144 | [Banach’s simple Lebesgue-spectrum problem](snapshots/2026-10-08-baseline/families/144/source.json) | [Smooth dynamics spectral-model research library](snapshots/2026-10-08-baseline/families/144/review-2026-10-09-v1.md) | First-pass assessment only |
| 145 | [Rokhlin’s multiple-mixing problem](snapshots/2026-10-08-baseline/families/145/source.json) | [Single-action mixing claim contract](snapshots/2026-10-08-baseline/families/145/review-2026-10-09-v2.md) | First-pass assessment only |
| 146 | [Positive metric entropy for the standard map](snapshots/2026-10-08-baseline/families/146/source.json) | [Standard-map chaos research benchmark](snapshots/2026-10-08-baseline/families/146/review-2026-10-09-v1.md) | First-pass assessment only |
| 147 | [The near-boundary Birkhoff conjecture](snapshots/2026-10-08-baseline/families/147/source.json) | [Billiard integrability assumption audit](snapshots/2026-10-08-baseline/families/147/review-2026-10-09-v1.md) | First-pass assessment only |
| 148 | [The entropy-rate dimension formula for self-similar measures](snapshots/2026-10-08-baseline/families/148/source.json) | [Self-similar measure dimension workbench](snapshots/2026-10-08-baseline/families/148/review-2026-10-09-v1.md) | First-pass assessment only |
| 149 | [Classwise permanence for weakly reversible mass-action systems](snapshots/2026-10-08-baseline/families/149/source.json) | [Reaction network model assurance plugin](snapshots/2026-10-08-baseline/families/149/review-2026-10-09-v1.md) | 002, 003, 013 |
| 150 | [Weak mixing of triangular billiards with an irrational angle](snapshots/2026-10-08-baseline/families/150/source.json) | [Triangular billiard mixing reference](snapshots/2026-10-08-baseline/families/150/review-2026-10-09-v1.md) | First-pass assessment only |
| 151 | [A <i>C</i><sup>1</sup> counterexample to the entropy conjecture](snapshots/2026-10-08-baseline/families/151/source.json) | [Dynamical entropy counterexample provenance](snapshots/2026-10-08-baseline/families/151/review-2026-10-09-v1.md) | First-pass assessment only |
| 152 | [Zero entropy does not guarantee a smooth positive-volume model](snapshots/2026-10-08-baseline/families/152/source.json) | [Smooth-model representation limitation ledger](snapshots/2026-10-08-baseline/families/152/review-2026-10-09-v1.md) | First-pass assessment only |
| 153 | [Arithmetic classification and non-Pisot singularity for Bernoulli convolutions](snapshots/2026-10-08-baseline/families/153/source.json) | [Bernoulli convolution parameter classification research](snapshots/2026-10-08-baseline/families/153/review-2026-10-09-v1.md) | First-pass assessment only |
| 154 | [Pointwise multiple ergodic averages for mixing transformations](snapshots/2026-10-08-baseline/families/154/source.json) | [Multiple ergodic average convergence reference](snapshots/2026-10-08-baseline/families/154/review-2026-10-09-v1.md) | First-pass assessment only |

## Functional analysis

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 322 | [Tingley’s sphere-isometry problem](snapshots/2026-10-08-baseline/families/322/source.json) | [Banach sphere isometry teaching and formalization module](snapshots/2026-10-08-baseline/families/322/review-2026-10-09-v1.md) | First-pass assessment only |
| 323 | [Independence of the separable quotient problem](snapshots/2026-10-08-baseline/families/323/source.json) | [Set-theoretic assumption provenance viewer](snapshots/2026-10-08-baseline/families/323/review-2026-10-09-v1.md) | First-pass assessment only |
| 324 | [Lipschitz equivalent Banach spaces need not be linearly isomorphic](snapshots/2026-10-08-baseline/families/324/source.json) | [Metric versus linear representation counterexample explorer](snapshots/2026-10-08-baseline/families/324/review-2026-10-09-v1.md) | First-pass assessment only |
| 325 | [The complete Crouzeix conjecture](snapshots/2026-10-08-baseline/families/325/source.json) | [Complete polynomial inequality and bounded nonnormal-matrix evidence](snapshots/2026-10-08-baseline/families/325/review-2026-10-09-v2.md) | 001, 014 |
| 326 | [The cotype–cotype conjecture under the approximation property](snapshots/2026-10-08-baseline/families/326/source.json) | [Banach geometry property implication map](snapshots/2026-10-08-baseline/families/326/review-2026-10-09-v1.md) | First-pass assessment only |
| 327 | [Markov type characterizes superreflexivity](snapshots/2026-10-08-baseline/families/327/source.json) | [Metric Markov type renorming research explorer](snapshots/2026-10-08-baseline/families/327/review-2026-10-09-v1.md) | First-pass assessment only |
| 328 | [Nonexpansive fixed points in reflexive Banach spaces](snapshots/2026-10-08-baseline/families/328/source.json) | [Fixed-point existence assumption checker](snapshots/2026-10-08-baseline/families/328/review-2026-10-09-v1.md) | First-pass assessment only |
| 329 | [A counterexample to metric-entropy duality](snapshots/2026-10-08-baseline/families/329/source.json) | [Covering-number duality counterexample benchmark](snapshots/2026-10-08-baseline/families/329/review-2026-10-09-v1.md) | First-pass assessment only |
| 330 | [A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces](snapshots/2026-10-08-baseline/families/330/source.json) | [Approximation property distinction library](snapshots/2026-10-08-baseline/families/330/review-2026-10-09-v1.md) | First-pass assessment only |
| 331 | [Reflexive midpoint convexity and diamond distortion](snapshots/2026-10-08-baseline/families/331/source.json) | [Convexity and diamond embedding benchmark](snapshots/2026-10-08-baseline/families/331/review-2026-10-09-v1.md) | First-pass assessment only |
| 332 | [Metric Markov cotype of <i>ℓ</i><sub>1</sub> and Hilbert-space Lipschitz extension](snapshots/2026-10-08-baseline/families/332/source.json) | [Lipschitz extension research toolkit](snapshots/2026-10-08-baseline/families/332/review-2026-10-09-v1.md) | First-pass assessment only |

## Group theory

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 246 | [Cannon's conjecture](snapshots/2026-10-08-baseline/families/246/source.json) | [Hyperbolic boundary recognition research contract](snapshots/2026-10-08-baseline/families/246/review-2026-10-09-v1.md) | First-pass assessment only |
| 247 | [An infinite finitely presented residually finite 2-group and a finitely presented nil algebra](snapshots/2026-10-08-baseline/families/247/source.json) | [Residual-finiteness versus torsion fixture](snapshots/2026-10-08-baseline/families/247/review-2026-10-09-v1.md) | First-pass assessment only |
| 248 | [Thompson's group <i>F</i> is nonamenable](snapshots/2026-10-08-baseline/families/248/source.json) | [Amenability assumption evidence](snapshots/2026-10-08-baseline/families/248/review-2026-10-09-v1.md) | First-pass assessment only |
| 249 | [A finitely generated Eilenberg–Ganea counterexample](snapshots/2026-10-08-baseline/families/249/source.json) | [Cohomological versus geometric dimension fixture](snapshots/2026-10-08-baseline/families/249/review-2026-10-09-v1.md) | First-pass assessment only |
| 250 | [Boone–Higman embeddings with higher finiteness](snapshots/2026-10-08-baseline/families/250/source.json) | [Decidable word-problem embedding contract](snapshots/2026-10-08-baseline/families/250/review-2026-10-09-v1.md) | First-pass assessment only |
| 251 | [Amenability, unitarizability, and strong Ulam stability](snapshots/2026-10-08-baseline/families/251/source.json) | [Representation stability hypothesis adapter](snapshots/2026-10-08-baseline/families/251/review-2026-10-09-v1.md) | First-pass assessment only |
| 252 | [A torsion-free hyperbolic group that is neither residually finite nor linear over any field](snapshots/2026-10-08-baseline/families/252/source.json) | [Finite-representation separation counterexample](snapshots/2026-10-08-baseline/families/252/review-2026-10-09-v1.md) | First-pass assessment only |
| 253 | [An infinite finitely presented simple amenable group](snapshots/2026-10-08-baseline/families/253/source.json) | [Simple amenable group research fixture](snapshots/2026-10-08-baseline/families/253/review-2026-10-09-v1.md) | First-pass assessment only |
| 254 | [Classifying spaces and geometric obstructions for Artin groups](snapshots/2026-10-08-baseline/families/254/source.json) | [Artin membership is effective but has no claimed cost bound](snapshots/2026-10-08-baseline/families/254/review-2026-10-09-v2.md) | First-pass assessment only |
| 255 | [Quasi-isometric recognition of virtually polycyclic groups](snapshots/2026-10-08-baseline/families/255/source.json) | [Coarse-group recognition contract](snapshots/2026-10-08-baseline/families/255/review-2026-10-09-v1.md) | First-pass assessment only |
| 256 | [Nonsingular systems of equations over arbitrary groups](snapshots/2026-10-08-baseline/families/256/source.json) | [Overgroup equation solvability contract](snapshots/2026-10-08-baseline/families/256/review-2026-10-09-v1.md) | First-pass assessment only |
| 257 | [A hyperbolic group without a geometric CAT(0) action](snapshots/2026-10-08-baseline/families/257/source.json) | [CAT(0) action counterexample library](snapshots/2026-10-08-baseline/families/257/review-2026-10-09-v1.md) | First-pass assessment only |
| 258 | [Gersten’s conjecture and virtual compact specialness of one-relator groups](snapshots/2026-10-08-baseline/families/258/source.json) | [One-relator hyperbolicity conditional adapter](snapshots/2026-10-08-baseline/families/258/review-2026-10-09-v1.md) | First-pass assessment only |
| 259 | [A group without fixed price](snapshots/2026-10-08-baseline/families/259/source.json) | [Measured-action cost comparison reference](snapshots/2026-10-08-baseline/families/259/review-2026-10-09-v1.md) | 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](snapshots/2026-10-08-baseline/families/240/source.json) | [Model-theory threshold and axiom provenance](snapshots/2026-10-08-baseline/families/240/review-2026-10-09-v1.md) | First-pass assessment only |
| 241 | [Rigidity of the Turing degrees](snapshots/2026-10-08-baseline/families/241/source.json) | [Computability-degree rigidity reference](snapshots/2026-10-08-baseline/families/241/review-2026-10-09-v1.md) | First-pass assessment only |
| 242 | [Single-fold Diophantine representations and undecidability under an at-most-one-solution promise](snapshots/2026-10-08-baseline/families/242/source.json) | [Unique-solution promise solver limitation audit](snapshots/2026-10-08-baseline/families/242/review-2026-10-09-v1.md) | First-pass assessment only |
| 243 | [Separating choiceless counting from polynomial time and witnessed choice](snapshots/2026-10-08-baseline/families/243/source.json) | [Symmetry-preserving query language expressiveness audit](snapshots/2026-10-08-baseline/families/243/review-2026-10-09-v1.md) | First-pass assessment only |
| 244 | [The Partition Principle does not imply Choice](snapshots/2026-10-08-baseline/families/244/source.json) | [Set-theoretic assumption dependency viewer](snapshots/2026-10-08-baseline/families/244/review-2026-10-09-v1.md) | First-pass assessment only |
| 245 | [Weak normalization implies strong normalization in pure type systems](snapshots/2026-10-08-baseline/families/245/source.json) | [Pure-beta normalization assurance has a global premise](snapshots/2026-10-08-baseline/families/245/review-2026-10-09-v2.md) | 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](snapshots/2026-10-08-baseline/families/260/source.json) | [Relativistic initial-data inequality audit](snapshots/2026-10-08-baseline/families/260/review-2026-10-09-v1.md) | First-pass assessment only |
| 261 | [Localization and delocalization in the Anderson model](snapshots/2026-10-08-baseline/families/261/source.json) | [Disordered spectral model benchmark](snapshots/2026-10-08-baseline/families/261/review-2026-10-09-v1.md) | First-pass assessment only |
| 262 | [Sharp finite-matrix Lieb–Thirring inequalities and all equality cases](snapshots/2026-10-08-baseline/families/262/source.json) | [Matrix-valued spectral bound library](snapshots/2026-10-08-baseline/families/262/review-2026-10-09-v1.md) | First-pass assessment only |
| 263 | [The ionization and generalized ionization conjectures](snapshots/2026-10-08-baseline/families/263/source.json) | [Atomic binding and asymptotic plausibility checks](snapshots/2026-10-08-baseline/families/263/review-2026-10-09-v1.md) | First-pass assessment only |
| 264 | [Strong cosmic censorship near two-ended Kerr data](snapshots/2026-10-08-baseline/families/264/source.json) | [Relativity extension-class evidence map](snapshots/2026-10-08-baseline/families/264/review-2026-10-09-v1.md) | First-pass assessment only |
| 265 | [Area laws and tensor networks for two-dimensional gapped systems](snapshots/2026-10-08-baseline/families/265/source.json) | [Tensor-network representation feasibility audit](snapshots/2026-10-08-baseline/families/265/review-2026-10-09-v1.md) | 030 |
| 266 | [Exactly three mutually unbiased bases in dimension six](snapshots/2026-10-08-baseline/families/266/source.json) | [Certified computation reproducibility workbench](snapshots/2026-10-08-baseline/families/266/review-2026-10-09-v1.md) | 034 |
| 267 | [Positive-temperature Bose–Einstein condensation and exact quantum depletion](snapshots/2026-10-08-baseline/families/267/source.json) | [Dilute Bose gas reference regime planner](snapshots/2026-10-08-baseline/families/267/review-2026-10-09-v1.md) | First-pass assessment only |
| 268 | [The spin-one Haldane gap](snapshots/2026-10-08-baseline/families/268/source.json) | [Spin-chain gap reference suite](snapshots/2026-10-08-baseline/families/268/review-2026-10-09-v1.md) | First-pass assessment only |
| 269 | [Uniform Laughlin gap and stability under bounded scalar disorder](snapshots/2026-10-08-baseline/families/269/source.json) | [Laughlin model disorder robustness audit](snapshots/2026-10-08-baseline/families/269/review-2026-10-09-v1.md) | First-pass assessment only |
| 270 | [Threshold and positive-energy bound states of the BFSS matrix model](snapshots/2026-10-08-baseline/families/270/source.json) | [BFSS spectral conjecture provenance library](snapshots/2026-10-08-baseline/families/270/review-2026-10-09-v1.md) | First-pass assessment only |
| 271 | [Bloch's law, its lattice correction, and the spherical magnetization law](snapshots/2026-10-08-baseline/families/271/source.json) | [Ferromagnet asymptotic reference fitter](snapshots/2026-10-08-baseline/families/271/review-2026-10-09-v1.md) | First-pass assessment only |
| 272 | [Entanglement without distillable secret key](snapshots/2026-10-08-baseline/families/272/source.json) | [Quantum security resource assumption audit](snapshots/2026-10-08-baseline/families/272/review-2026-10-09-v1.md) | First-pass assessment only |
| 273 | [The entropy photon-number inequality](snapshots/2026-10-08-baseline/families/273/source.json) | [Bosonic entropy and channel-bound calculator](snapshots/2026-10-08-baseline/families/273/review-2026-10-09-v1.md) | First-pass assessment only |
| 274 | [Parity is not in QAC<sup>0</sup>](snapshots/2026-10-08-baseline/families/274/source.json) | [Quantum circuit architecture impossibility ledger](snapshots/2026-10-08-baseline/families/274/review-2026-10-09-v1.md) | First-pass assessment only |
| 275 | [QMA-hardness of continuum Coulomb energy](snapshots/2026-10-08-baseline/families/275/source.json) | [Electronic-structure complexity scope audit](snapshots/2026-10-08-baseline/families/275/review-2026-10-09-v1.md) | First-pass assessment only |
| 276 | [Classical capacity of generalized amplitude damping](snapshots/2026-10-08-baseline/families/276/source.json) | [Thermal qubit channel capacity calculator](snapshots/2026-10-08-baseline/families/276/review-2026-10-09-v1.md) | 003, 019 |
| 277 | [Threshold repetition for entangled games](snapshots/2026-10-08-baseline/families/277/source.json) | [Entangled-game soundness planning reference](snapshots/2026-10-08-baseline/families/277/review-2026-10-09-v1.md) | First-pass assessment only |
| 278 | [Failure of Kohn–Sham ensemble representation](snapshots/2026-10-08-baseline/families/278/source.json) | [Density-functional representation limitation audit](snapshots/2026-10-08-baseline/families/278/review-2026-10-09-v1.md) | First-pass assessment only |
| 279 | [Exact quantum factoring over a fixed finite gate set](snapshots/2026-10-08-baseline/families/279/source.json) | [Exact quantum factoring excludes a practical resource-improvement claim](snapshots/2026-10-08-baseline/families/279/review-2026-10-09-v2.md) | First-pass assessment only |
| 280 | [Unitary vertex operator algebras and conformal nets](snapshots/2026-10-08-baseline/families/280/source.json) | [VOA-to-conformal-net theorem and structure bridge](snapshots/2026-10-08-baseline/families/280/review-2026-10-09-v1.md) | First-pass assessment only |
| 281 | [QAOA attains the SK optimum in the thermodynamic-first limit](snapshots/2026-10-08-baseline/families/281/source.json) | [Quantum optimization regime and resource audit](snapshots/2026-10-08-baseline/families/281/review-2026-10-09-v1.md) | 031 |
| 282 | [From scale symmetry to local conformal symmetry in four-dimensional QFT](snapshots/2026-10-08-baseline/families/282/source.json) | [Quantum-field assumption provenance map](snapshots/2026-10-08-baseline/families/282/review-2026-10-09-v1.md) | First-pass assessment only |
| 283 | [Polynomial-time unitary synthesis from a Boolean oracle](snapshots/2026-10-08-baseline/families/283/source.json) | [Oracle construction and unitary-synthesis cost audit](snapshots/2026-10-08-baseline/families/283/review-2026-10-09-v1.md) | 031 |
| 284 | [The optimal quartic separation between randomized and quantum queries](snapshots/2026-10-08-baseline/families/284/source.json) | [Quantum-query complexity comparison ledger](snapshots/2026-10-08-baseline/families/284/review-2026-10-09-v1.md) | 031 |

## Number theory

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 001 | [Milne’s rationality conjecture and algebraic specialization](snapshots/2026-10-08-baseline/families/001/source.json) | [Arithmetic cycle specialization provenance](snapshots/2026-10-08-baseline/families/001/review-2026-10-09-v1.md) | First-pass assessment only |
| 002 | [The full BSD formula from low Selmer corank](snapshots/2026-10-08-baseline/families/002/source.json) | [Elliptic-curve BSD evidence ledger](snapshots/2026-10-08-baseline/families/002/review-2026-10-09-v1.md) | First-pass assessment only |
| 003 | [The quasi-Riemann hypothesis](snapshots/2026-10-08-baseline/families/003/source.json) | [L-function assumption and algorithm dependency audit](snapshots/2026-10-08-baseline/families/003/review-2026-10-09-v1.md) | 016 |
| 004 | [Hilbert’s tenth problem over ℚ](snapshots/2026-10-08-baseline/families/004/source.json) | [Rational constraint solver completeness contract](snapshots/2026-10-08-baseline/families/004/review-2026-10-09-v1.md) | First-pass assessment only |
| 005 | [Irrationality of Catalan’s constant](snapshots/2026-10-08-baseline/families/005/source.json) | [Exact constant provenance teaching module](snapshots/2026-10-08-baseline/families/005/review-2026-10-09-v1.md) | First-pass assessment only |
| 006 | [Goldfeld’s conjecture: densities and mean analytic rank](snapshots/2026-10-08-baseline/families/006/source.json) | [Quadratic twist rank distribution reference](snapshots/2026-10-08-baseline/families/006/review-2026-10-09-v1.md) | First-pass assessment only |
| 007 | [Ordinary two-point correlations and the corrected Elliott conjecture](snapshots/2026-10-08-baseline/families/007/source.json) | [Multiplicative sequence correlation benchmark](snapshots/2026-10-08-baseline/families/007/review-2026-10-09-v1.md) | First-pass assessment only |
| 008 | [The Deligne–Drinfeld conjecture](snapshots/2026-10-08-baseline/families/008/source.json) | [Grothendieck–Teichmüller graded algebra reference](snapshots/2026-10-08-baseline/families/008/review-2026-10-09-v1.md) | First-pass assessment only |
| 009 | [Function-field reconstruction from Milnor K-theory and Galois data](snapshots/2026-10-08-baseline/families/009/source.json) | [Function-field reconstruction formal adapter](snapshots/2026-10-08-baseline/families/009/review-2026-10-09-v1.md) | First-pass assessment only |
| 010 | [Unrestricted pro-modularity at the prime two](snapshots/2026-10-08-baseline/families/010/source.json) | [Dyadic modularity assumption ledger](snapshots/2026-10-08-baseline/families/010/review-2026-10-09-v1.md) | First-pass assessment only |
| 011 | [Prime-factor statistics of $`p-1`$](snapshots/2026-10-08-baseline/families/011/source.json) | [Prime-minus-one factor statistics reference](snapshots/2026-10-08-baseline/families/011/review-2026-10-09-v1.md) | First-pass assessment only |
| 012 | [Independent largest prime factors of consecutive integers](snapshots/2026-10-08-baseline/families/012/source.json) | [Consecutive integer factor statistics benchmark](snapshots/2026-10-08-baseline/families/012/review-2026-10-09-v1.md) | First-pass assessment only |
| 013 | [Ostmann’s inverse Goldbach conjecture](snapshots/2026-10-08-baseline/families/013/source.json) | [Additive prime decomposition limitation reference](snapshots/2026-10-08-baseline/families/013/review-2026-10-09-v1.md) | First-pass assessment only |
| 014 | [Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan](snapshots/2026-10-08-baseline/families/014/source.json) | [Langlands characteristic and assumption coverage graph](snapshots/2026-10-08-baseline/families/014/review-2026-10-09-v1.md) | First-pass assessment only |
| 015 | [Torus-packet equidistribution in prime, quartic, and sextic degrees](snapshots/2026-10-08-baseline/families/015/source.json) | [Arithmetic packet equidistribution research benchmark](snapshots/2026-10-08-baseline/families/015/review-2026-10-09-v1.md) | First-pass assessment only |
| 016 | [Zilber–Pink in abelian varieties and the Siegel threefold](snapshots/2026-10-08-baseline/families/016/source.json) | [Atypical subvariety provenance library](snapshots/2026-10-08-baseline/families/016/review-2026-10-09-v1.md) | First-pass assessment only |
| 017 | [The irrationality exponent of <i>π</i> is 2](snapshots/2026-10-08-baseline/families/017/source.json) | [Constant approximation and Flint–Hills reference](snapshots/2026-10-08-baseline/families/017/review-2026-10-09-v1.md) | First-pass assessment only |
| 018 | [The Margulis–Platonov conjecture over global fields](snapshots/2026-10-08-baseline/families/018/source.json) | [Arithmetic group normal-subgroup classification adapter](snapshots/2026-10-08-baseline/families/018/review-2026-10-09-v1.md) | First-pass assessment only |
| 019 | [The local <i>p</i>-adic section conjecture and global consequences](snapshots/2026-10-08-baseline/families/019/source.json) | [Rational point/Galois section correspondence ledger](snapshots/2026-10-08-baseline/families/019/review-2026-10-09-v1.md) | First-pass assessment only |
| 020 | [Squarefree quartics and power-free polynomial values](snapshots/2026-10-08-baseline/families/020/source.json) | [Polynomial value density reference](snapshots/2026-10-08-baseline/families/020/review-2026-10-09-v1.md) | First-pass assessment only |
| 021 | [A quadratic bound for Jacobsthal’s function](snapshots/2026-10-08-baseline/families/021/source.json) | [Coprime search interval budget research](snapshots/2026-10-08-baseline/families/021/review-2026-10-09-v1.md) | First-pass assessment only |
| 022 | [The weak inhomogeneous Duffin–Schaeffer conjecture](snapshots/2026-10-08-baseline/families/022/source.json) | [Inhomogeneous approximation assumption reference](snapshots/2026-10-08-baseline/families/022/review-2026-10-09-v1.md) | First-pass assessment only |
| 023 | [Patterson's first moment for cubic Gauss sums](snapshots/2026-10-08-baseline/families/023/source.json) | [Cubic Gauss sum exact reference library](snapshots/2026-10-08-baseline/families/023/review-2026-10-09-v1.md) | First-pass assessment only |
| 024 | [An asymptotic formula for the number of totients](snapshots/2026-10-08-baseline/families/024/source.json) | [Totient counting asymptotic reference](snapshots/2026-10-08-baseline/families/024/review-2026-10-09-v1.md) | First-pass assessment only |
| 025 | [Short Egyptian fractions](snapshots/2026-10-08-baseline/families/025/source.json) | [Egyptian fraction construction research library](snapshots/2026-10-08-baseline/families/025/review-2026-10-09-v1.md) | First-pass assessment only |
| 026 | [Positive lower density of large prime gaps](snapshots/2026-10-08-baseline/families/026/source.json) | [Prime-gap distribution reference](snapshots/2026-10-08-baseline/families/026/review-2026-10-09-v1.md) | First-pass assessment only |
| 027 | [Potential integral density on curve character varieties](snapshots/2026-10-08-baseline/families/027/source.json) | [Character variety integral-point provenance](snapshots/2026-10-08-baseline/families/027/review-2026-10-09-v1.md) | First-pass assessment only |
| 028 | [Uniformly bounded components of Gaussian-prime graphs](snapshots/2026-10-08-baseline/families/028/source.json) | [Gaussian prime graph component research explorer](snapshots/2026-10-08-baseline/families/028/review-2026-10-09-v1.md) | First-pass assessment only |
| 029 | [Primitive roots for every admissible integer base](snapshots/2026-10-08-baseline/families/029/source.json) | [Primitive-root prime generation assumption audit](snapshots/2026-10-08-baseline/families/029/review-2026-10-09-v1.md) | 016 |
| 030 | [Modularity of elliptic curves over imaginary quadratic fields](snapshots/2026-10-08-baseline/families/030/source.json) | [Imaginary-quadratic elliptic curve modularity adapter](snapshots/2026-10-08-baseline/families/030/review-2026-10-09-v1.md) | First-pass assessment only |
| 031 | [Uchida’s conjecture for open homomorphisms of Galois groups](snapshots/2026-10-08-baseline/families/031/source.json) | [Galois homomorphism reconstruction reference](snapshots/2026-10-08-baseline/families/031/review-2026-10-09-v1.md) | First-pass assessment only |

## Operator algebras

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 285 | [Counterexamples to Baum–Connes and Kadison–Kaplansky](snapshots/2026-10-08-baseline/families/285/source.json) | [Assembly and projection counterexample ledger](snapshots/2026-10-08-baseline/families/285/review-2026-10-09-v1.md) | First-pass assessment only |
| 286 | [Rigidity and arithmetic of lattice von Neumann algebras](snapshots/2026-10-08-baseline/families/286/source.json) | [Rigid lattice bimodule classification reference](snapshots/2026-10-08-baseline/families/286/review-2026-10-09-v1.md) | First-pass assessment only |
| 287 | [Isomorphism of the free group factors](snapshots/2026-10-08-baseline/families/287/source.json) | [Free-group-factor equivalence evidence](snapshots/2026-10-08-baseline/families/287/review-2026-10-09-v1.md) | First-pass assessment only |
| 288 | [Kadison's similarity conjecture](snapshots/2026-10-08-baseline/families/288/source.json) | [C-star similarity hypothesis contract](snapshots/2026-10-08-baseline/families/288/review-2026-10-09-v1.md) | First-pass assessment only |
| 289 | [Strong Kadison–Kastler stability and its spatial boundaries](snapshots/2026-10-08-baseline/families/289/source.json) | [Operator-algebra perturbation scope audit](snapshots/2026-10-08-baseline/families/289/review-2026-10-09-v1.md) | First-pass assessment only |
| 290 | [Relative bicentralizers and modular spectral recovery](snapshots/2026-10-08-baseline/families/290/source.json) | [Bicentralizer inclusion evidence ledger](snapshots/2026-10-08-baseline/families/290/review-2026-10-09-v1.md) | First-pass assessment only |
| 291 | [Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stability](snapshots/2026-10-08-baseline/families/291/source.json) | [Nuclear C-star regularity equivalence adapter](snapshots/2026-10-08-baseline/families/291/review-2026-10-09-v1.md) | First-pass assessment only |
| 292 | [Kirchberg's $`\mathcal O_2`$ norm-ultrapower embedding problem](snapshots/2026-10-08-baseline/families/292/source.json) | [Nuclear ultrapower embedding counterexample](snapshots/2026-10-08-baseline/families/292/review-2026-10-09-v1.md) | First-pass assessment only |
| 293 | [Invariant projections, hyperinvariant subspaces, and transitive algebras](snapshots/2026-10-08-baseline/families/293/source.json) | [Infinite-operator invariant-subspace fixture](snapshots/2026-10-08-baseline/families/293/review-2026-10-09-v1.md) | First-pass assessment only |
| 294 | [Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness](snapshots/2026-10-08-baseline/families/294/source.json) | [Quasitrace and tensor-finiteness counterexample](snapshots/2026-10-08-baseline/families/294/review-2026-10-09-v1.md) | First-pass assessment only |
| 295 | [The Kadison–Ringrose cohomology conjecture](snapshots/2026-10-08-baseline/families/295/source.json) | [Bounded cohomology primitive contract](snapshots/2026-10-08-baseline/families/295/review-2026-10-09-v1.md) | First-pass assessment only |
| 296 | [The generator problem for finite factors](snapshots/2026-10-08-baseline/families/296/source.json) | [Single-generator representation research adapter](snapshots/2026-10-08-baseline/families/296/review-2026-10-09-v1.md) | First-pass assessment only |
| 297 | [A ZFC counterexample to Naimark's problem](snapshots/2026-10-08-baseline/families/297/source.json) | [Nonseparable representation contract](snapshots/2026-10-08-baseline/families/297/review-2026-10-09-v2.md) | First-pass assessment only |
| 298 | [Two notions of free entropy differ even when both are finite](snapshots/2026-10-08-baseline/families/298/source.json) | [Free entropy notion separation reference](snapshots/2026-10-08-baseline/families/298/review-2026-10-09-v1.md) | First-pass assessment only |
| 299 | [The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability](snapshots/2026-10-08-baseline/families/299/source.json) | [Central-sequence regularity contract](snapshots/2026-10-08-baseline/families/299/review-2026-10-09-v1.md) | First-pass assessment only |
| 300 | [Approximation and quadratic strong-operator paving](snapshots/2026-10-08-baseline/families/300/source.json) | [Compressed strong paving scope audit](snapshots/2026-10-08-baseline/families/300/review-2026-10-09-v1.md) | First-pass assessment only |
| 301 | [Trace cones and Razak–Jacelon stabilization](snapshots/2026-10-08-baseline/families/301/source.json) | [Stabilized trace-cone classification reference](snapshots/2026-10-08-baseline/families/301/review-2026-10-09-v1.md) | First-pass assessment only |
| 302 | [Radius of comparison equals half the mean dimension](snapshots/2026-10-08-baseline/families/302/source.json) | [Mean-dimension comparison evidence](snapshots/2026-10-08-baseline/families/302/review-2026-10-09-v1.md) | First-pass assessment only |
| 303 | [Weak pure infiniteness and Cuntz-algebra absorption](snapshots/2026-10-08-baseline/families/303/source.json) | [Pure infiniteness and absorption contract](snapshots/2026-10-08-baseline/families/303/review-2026-10-09-v1.md) | First-pass assessment only |

## Partial differential equations

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 362 | [Global smoothness for relativistic Vlasov–Maxwell](snapshots/2026-10-08-baseline/families/362/source.json) | [Relativistic plasma model assumption and solver benchmark library](snapshots/2026-10-08-baseline/families/362/review-2026-10-09-v1.md) | 029 |
| 363 | [Nonuniqueness with local conservation for the hard-sphere Boltzmann equation](snapshots/2026-10-08-baseline/families/363/source.json) | [Kinetic solution selection and conservation audit](snapshots/2026-10-08-baseline/families/363/review-2026-10-09-v1.md) | 029 |
| 364 | [Kinetic limits and fluctuations over the Boltzmann lifespan](snapshots/2026-10-08-baseline/families/364/source.json) | [Molecular-to-kinetic simulation validity planner](snapshots/2026-10-08-baseline/families/364/review-2026-10-09-v1.md) | First-pass assessment only |
| 365 | [Joint metric and connection recovery from one boundary patch](snapshots/2026-10-08-baseline/families/365/source.json) | [Inverse boundary measurement evidence workbench](snapshots/2026-10-08-baseline/families/365/review-2026-10-09-v1.md) | 026 |
| 366 | [The planar Mumford–Shah regularity conjecture and local weak-<i>L</i><sup>4</sup> gradient bounds](snapshots/2026-10-08-baseline/families/366/source.json) | [Variational segmentation structure diagnostic](snapshots/2026-10-08-baseline/families/366/review-2026-10-09-v1.md) | 028 |
| 367 | [The critical dimension for the one-phase Bernoulli problem](snapshots/2026-10-08-baseline/families/367/source.json) | [Free boundary critical-dimension research benchmark](snapshots/2026-10-08-baseline/families/367/review-2026-10-09-v1.md) | 028 |
| 368 | [The three-dimensional Ball–Evans approximation problem](snapshots/2026-10-08-baseline/families/368/source.json) | [Diffeomorphic deformation feasibility research toolkit](snapshots/2026-10-08-baseline/families/368/review-2026-10-09-v1.md) | First-pass assessment only |
| 369 | [The hot spots conjecture for simply connected planar domains](snapshots/2026-10-08-baseline/families/369/source.json) | [Neumann eigenmode extrema validation](snapshots/2026-10-08-baseline/families/369/review-2026-10-09-v1.md) | First-pass assessment only |
| 370 | [The Lane–Emden and Hénon–Lane–Emden conjectures](snapshots/2026-10-08-baseline/families/370/source.json) | [Nonlinear elliptic model nonexistence assumption map](snapshots/2026-10-08-baseline/families/370/review-2026-10-09-v1.md) | First-pass assessment only |
| 371 | [Stable blowup for the defocusing Schrödinger equation](snapshots/2026-10-08-baseline/families/371/source.json) | [Scientific Fourier discretization audit](snapshots/2026-10-08-baseline/families/371/review-2026-10-09-v2.md) | 029 |
| 372 | [Global uniqueness in smooth isotropic elasticity](snapshots/2026-10-08-baseline/families/372/source.json) | [Elastic material identifiability experiment workbench](snapshots/2026-10-08-baseline/families/372/review-2026-10-09-v1.md) | 027 |
| 373 | [Nonattainment of the three-marginal Coulomb Monge problem](snapshots/2026-10-08-baseline/families/373/source.json) | [Multi-marginal transport representation audit](snapshots/2026-10-08-baseline/families/373/review-2026-10-09-v1.md) | First-pass assessment only |
| 374 | [Sharp one-third stability of Brenier maps](snapshots/2026-10-08-baseline/families/374/source.json) | [Transport sharpness benchmark and source-domain audit](snapshots/2026-10-08-baseline/families/374/review-2026-10-09-v2.md) | 015, 020 |
| 375 | [De Giorgi's conjecture in dimension eight](snapshots/2026-10-08-baseline/families/375/source.json) | [Allen–Cahn classification and phase-field research reference](snapshots/2026-10-08-baseline/families/375/review-2026-10-09-v1.md) | First-pass assessment only |
| 376 | [Universal computation in forced Navier–Stokes flows](snapshots/2026-10-08-baseline/families/376/source.json) | [Scientific prediction claim and computational-limit audit](snapshots/2026-10-08-baseline/families/376/review-2026-10-09-v1.md) | 002, 029 |
| 377 | [Interior $`C^{1,\alpha}`$ regularity for infinity-harmonic functions](snapshots/2026-10-08-baseline/families/377/source.json) | [Infinity-harmonic interpolation regularity reference](snapshots/2026-10-08-baseline/families/377/review-2026-10-09-v1.md) | 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](snapshots/2026-10-08-baseline/families/211/source.json) | [Random-map geometry and diffusion research benchmark](snapshots/2026-10-08-baseline/families/211/review-2026-10-09-v1.md) | First-pass assessment only |
| 212 | [Planar first-passage geometry and the absence of bigeodesics](snapshots/2026-10-08-baseline/families/212/source.json) | [First-passage routing model asymptotic audit](snapshots/2026-10-08-baseline/families/212/review-2026-10-09-v1.md) | First-pass assessment only |
| 213 | [Critical percolation on every quasi-transitive graph](snapshots/2026-10-08-baseline/families/213/source.json) | [Percolation criticality research simulator](snapshots/2026-10-08-baseline/families/213/review-2026-10-09-v1.md) | First-pass assessment only |
| 214 | [The Benjamini–Schramm nonuniqueness conjecture](snapshots/2026-10-08-baseline/families/214/source.json) | [Nonamenable network phase reference](snapshots/2026-10-08-baseline/families/214/review-2026-10-09-v1.md) | First-pass assessment only |
| 215 | [Canonical $`O(3)`$ continuum limit and exact $`O(4)`$ mass asymptotics](snapshots/2026-10-08-baseline/families/215/source.json) | [Spin-model continuum and mass reference calculator](snapshots/2026-10-08-baseline/families/215/review-2026-10-09-v1.md) | First-pass assessment only |
| 216 | [Critical and near-critical XY scaling and BKT universality](snapshots/2026-10-08-baseline/families/216/source.json) | [BKT model scaling analysis workbench](snapshots/2026-10-08-baseline/families/216/review-2026-10-09-v1.md) | First-pass assessment only |
| 217 | [The low-temperature Sherrington–Kirkpatrick fluctuation law](snapshots/2026-10-08-baseline/families/217/source.json) | [Low-temperature SK fluctuation normalization benchmark](snapshots/2026-10-08-baseline/families/217/review-2026-10-09-v1.md) | First-pass assessment only |
| 218 | [Conformal universality for weakly interacting and random-bond Ising models](snapshots/2026-10-08-baseline/families/218/source.json) | [Ising perturbation universality benchmark](snapshots/2026-10-08-baseline/families/218/review-2026-10-09-v1.md) | First-pass assessment only |
| 219 | [GOE bulk universality for regular graphs with weak Anderson disorder](snapshots/2026-10-08-baseline/families/219/source.json) | [Random regular graph spectral calibration](snapshots/2026-10-08-baseline/families/219/review-2026-10-09-v1.md) | First-pass assessment only |
| 220 | [Directional zero–one laws beyond iid environments and iid ballisticity](snapshots/2026-10-08-baseline/families/220/source.json) | [Random-environment transport assumption audit](snapshots/2026-10-08-baseline/families/220/review-2026-10-09-v1.md) | First-pass assessment only |
| 221 | [The Mézard–Parisi formula for diluted spin glasses](snapshots/2026-10-08-baseline/families/221/source.json) | [Diluted spin-glass variational model library](snapshots/2026-10-08-baseline/families/221/review-2026-10-09-v1.md) | First-pass assessment only |
| 222 | [Perceptron free energies and microscopic jamming exponents](snapshots/2026-10-08-baseline/families/222/source.json) | [Perceptron capacity and jamming regime planner](snapshots/2026-10-08-baseline/families/222/review-2026-10-09-v1.md) | First-pass assessment only |
| 223 | [Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling](snapshots/2026-10-08-baseline/families/223/source.json) | [Random-cluster interface reference library](snapshots/2026-10-08-baseline/families/223/review-2026-10-09-v1.md) | First-pass assessment only |
| 224 | [Critical and quenched near-critical universality for Poisson–Voronoi percolation](snapshots/2026-10-08-baseline/families/224/source.json) | [Voronoi critical crossing calibration](snapshots/2026-10-08-baseline/families/224/review-2026-10-09-v1.md) | First-pass assessment only |
| 225 | [Gaussian free field limits throughout the balanced six-vertex regime](snapshots/2026-10-08-baseline/families/225/source.json) | [Six-vertex height variance reference](snapshots/2026-10-08-baseline/families/225/review-2026-10-09-v1.md) | First-pass assessment only |
| 226 | [The double-dimer loop ensemble converges to CLE<sub>4</sub>](snapshots/2026-10-08-baseline/families/226/source.json) | [Double-dimer loop scaling research suite](snapshots/2026-10-08-baseline/families/226/review-2026-10-09-v1.md) | First-pass assessment only |
| 227 | [Critical SK autocorrelation processes and dynamics across the temperature transition](snapshots/2026-10-08-baseline/families/227/source.json) | [Spin sampler clock and regime audit](snapshots/2026-10-08-baseline/families/227/review-2026-10-09-v1.md) | First-pass assessment only |
| 228 | [Continuum phase transitions for radial pair potentials](snapshots/2026-10-08-baseline/families/228/source.json) | [Continuum phase-transition model reference](snapshots/2026-10-08-baseline/families/228/review-2026-10-09-v1.md) | First-pass assessment only |
| 229 | [Exact three- and four-state reconstruction thresholds and four-state tree capacity](snapshots/2026-10-08-baseline/families/229/source.json) | [Graph reconstruction feasibility audit](snapshots/2026-10-08-baseline/families/229/review-2026-10-09-v1.md) | 032 |
| 230 | [Exact Hausdorff gauges for SLE](snapshots/2026-10-08-baseline/families/230/source.json) | [SLE fractal-measure normalization reference](snapshots/2026-10-08-baseline/families/230/review-2026-10-09-v1.md) | First-pass assessment only |
| 231 | [The free uniform spanning forest is a factor of IID](snapshots/2026-10-08-baseline/families/231/source.json) | [Root-free randomized graph construction research](snapshots/2026-10-08-baseline/families/231/review-2026-10-09-v1.md) | First-pass assessment only |
| 232 | [Gaussian fields and interfaces for triangular-lattice Lipschitz heights](snapshots/2026-10-08-baseline/families/232/source.json) | [Lipschitz random-height reference suite](snapshots/2026-10-08-baseline/families/232/review-2026-10-09-v1.md) | First-pass assessment only |
| 233 | [The joint critical Ashkin–Teller current limit](snapshots/2026-10-08-baseline/families/233/source.json) | [Ashkin–Teller joint structure benchmark](snapshots/2026-10-08-baseline/families/233/review-2026-10-09-v1.md) | First-pass assessment only |
| 234 | [All-temperature pressure of orthogonally invariant Ising spin glasses](snapshots/2026-10-08-baseline/families/234/source.json) | [Invariant spin-glass pressure reference](snapshots/2026-10-08-baseline/families/234/review-2026-10-09-v1.md) | First-pass assessment only |
| 235 | [Limiting random SAT thresholds, sharp variance and computability](snapshots/2026-10-08-baseline/families/235/source.json) | [Random SAT benchmark regime calibration](snapshots/2026-10-08-baseline/families/235/review-2026-10-09-v1.md) | 033 |
| 236 | [The exact factor-of-IID threshold for free Ising spins on trees](snapshots/2026-10-08-baseline/families/236/source.json) | [Tree Ising distributed-sampling feasibility map](snapshots/2026-10-08-baseline/families/236/review-2026-10-09-v1.md) | First-pass assessment only |
| 237 | [The three-quarter exponent for honeycomb self-avoiding walk](snapshots/2026-10-08-baseline/families/237/source.json) | [Self-avoiding polymer scaling reference](snapshots/2026-10-08-baseline/families/237/review-2026-10-09-v1.md) | First-pass assessment only |
| 238 | [Optimal logarithmic mixing of the Thorp shuffle](snapshots/2026-10-08-baseline/families/238/source.json) | [Queryable permutation framework and randomness bridge](snapshots/2026-10-08-baseline/families/238/review-2026-10-09-v5.md) | 040 |
| 239 | [Sharp singularity rates for symmetric random sign matrices](snapshots/2026-10-08-baseline/families/239/source.json) | [Random symmetric matrix singularity reference](snapshots/2026-10-08-baseline/families/239/review-2026-10-09-v1.md) | First-pass assessment only |

## Real and complex analysis

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 071 | [Koebe’s circle-domain conjecture](snapshots/2026-10-08-baseline/families/071/source.json) | [Conformal domain representation research toolkit](snapshots/2026-10-08-baseline/families/071/review-2026-10-09-v1.md) | First-pass assessment only |
| 072 | [Brennan's conjecture and the integral-means spectrum](snapshots/2026-10-08-baseline/families/072/source.json) | [Conformal derivative and boundary spectrum audit](snapshots/2026-10-08-baseline/families/072/review-2026-10-09-v1.md) | First-pass assessment only |
| 073 | [The Falconer distance conjecture](snapshots/2026-10-08-baseline/families/073/source.json) | [Fractal distance-set research explorer](snapshots/2026-10-08-baseline/families/073/review-2026-10-09-v1.md) | First-pass assessment only |
| 074 | [Kakeya in three and four dimensions](snapshots/2026-10-08-baseline/families/074/source.json) | [Directional tube analysis reference](snapshots/2026-10-08-baseline/families/074/review-2026-10-09-v1.md) | First-pass assessment only |
| 075 | [The $`L\log L`$ Fourier-convergence conjecture](snapshots/2026-10-08-baseline/families/075/source.json) | [Fourier convergence assumption reference](snapshots/2026-10-08-baseline/families/075/review-2026-10-09-v1.md) | First-pass assessment only |
| 076 | [Real ultraflat Littlewood polynomials and unbounded binary merit factors](snapshots/2026-10-08-baseline/families/076/source.json) | [Binary waveform spectrum and correlation contract audit](snapshots/2026-10-08-baseline/families/076/review-2026-10-09-v1.md) | 035 |
| 077 | [Fourier restriction for positively curved surfaces](snapshots/2026-10-08-baseline/families/077/source.json) | [Curved-surface Fourier extension reference](snapshots/2026-10-08-baseline/families/077/review-2026-10-09-v1.md) | First-pass assessment only |
| 078 | [The three-dimensional Bochner–Riesz conjecture](snapshots/2026-10-08-baseline/families/078/source.json) | [Spectral filter boundedness reference](snapshots/2026-10-08-baseline/families/078/review-2026-10-09-v1.md) | First-pass assessment only |
| 079 | [Local smoothing in three dimensions](snapshots/2026-10-08-baseline/families/079/source.json) | [Wave propagation regularity assumption ledger](snapshots/2026-10-08-baseline/families/079/review-2026-10-09-v1.md) | First-pass assessment only |
| 080 | [The exact Sobolev endpoint for Schrödinger convergence](snapshots/2026-10-08-baseline/families/080/source.json) | [Schrödinger initial-data convergence reference](snapshots/2026-10-08-baseline/families/080/review-2026-10-09-v1.md) | First-pass assessment only |
| 081 | [Riesz transforms and rectifiability in higher codimension](snapshots/2026-10-08-baseline/families/081/source.json) | [Geometric measure regularity evidence map](snapshots/2026-10-08-baseline/families/081/review-2026-10-09-v1.md) | First-pass assessment only |
| 082 | [Annular variation and dyadic absolute bounds for the triangular Hilbert transform](snapshots/2026-10-08-baseline/families/082/source.json) | [Multilinear singular-integral reference suite](snapshots/2026-10-08-baseline/families/082/review-2026-10-09-v1.md) | First-pass assessment only |
| 083 | [Hilbert transforms along Lipschitz directions](snapshots/2026-10-08-baseline/families/083/source.json) | [Directional filtering scale contract](snapshots/2026-10-08-baseline/families/083/review-2026-10-09-v1.md) | First-pass assessment only |
| 084 | [The geometric case of the Erdős similarity conjecture](snapshots/2026-10-08-baseline/families/084/source.json) | [Geometric-pattern avoidance research construction](snapshots/2026-10-08-baseline/families/084/review-2026-10-09-v1.md) | First-pass assessment only |
| 085 | [Endpoint Sobolev regularity of centered disk averages](snapshots/2026-10-08-baseline/families/085/source.json) | [Scale-space maximal filter regularity audit](snapshots/2026-10-08-baseline/families/085/review-2026-10-09-v1.md) | First-pass assessment only |
| 086 | [An <i>L</i><sup>3</sup> bound for the trilinear Hilbert transform](snapshots/2026-10-08-baseline/families/086/source.json) | [Trilinear Hilbert transform research benchmark](snapshots/2026-10-08-baseline/families/086/review-2026-10-09-v1.md) | 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](snapshots/2026-10-08-baseline/families/102/source.json) | [Approximation hardness review service](snapshots/2026-10-08-baseline/families/102/review-2026-10-08-v1.md) | First-pass assessment only |
| 103 | [Exact derandomization of logarithmic space: $`\mathsf L=\mathsf{RL}=\mathsf{BPL}`$](snapshots/2026-10-08-baseline/families/103/source.json) | [Small-space decision and compiler readiness audit](snapshots/2026-10-08-baseline/families/103/review-2026-10-09-v2.md) | 020 |
| 104 | [Quasipolynomial algorithms for mean-payoff, stochastic and parity games](snapshots/2026-10-08-baseline/families/104/source.json) | [Mean payoff strategy synthesis plugin](snapshots/2026-10-08-baseline/families/104/review-2026-10-08-v1.md) | 003, 018 |
| 105 | [Perfect completeness for 2-to-1 games](snapshots/2026-10-08-baseline/families/105/source.json) | [Perfect-completeness reduction benchmark library](snapshots/2026-10-08-baseline/families/105/review-2026-10-08-v1.md) | First-pass assessment only |
| 106 | [Hardness of coloring three-colorable graphs](snapshots/2026-10-08-baseline/families/106/source.json) | [Graph-coloring solver stress suite](snapshots/2026-10-08-baseline/families/106/review-2026-10-08-v1.md) | First-pass assessment only |
| 107 | [Matrix multiplication with exponent at most 9/4](snapshots/2026-10-08-baseline/families/107/source.json) | [Matrix tensor construction research toolkit](snapshots/2026-10-08-baseline/families/107/review-2026-10-08-v1.md) | 003, 020, 022 |
| 108 | [A cubic permanent–determinant lower bound](snapshots/2026-10-08-baseline/families/108/source.json) | [Symbolic representation complexity audit](snapshots/2026-10-08-baseline/families/108/review-2026-10-08-v1.md) | First-pass assessment only |
| 109 | [Integer multiplication below $`n\log n`$](snapshots/2026-10-08-baseline/families/109/source.json) | [Big integer asymptotic feasibility worksheet](snapshots/2026-10-08-baseline/families/109/review-2026-10-08-v1.md) | 020 |
| 110 | [Optimal-order randomized <i>k</i>-server on arbitrary metrics](snapshots/2026-10-08-baseline/families/110/source.json) | [Metric movement and activation audit](snapshots/2026-10-08-baseline/families/110/review-2026-10-09-v2.md) | 010, 020 |
| 111 | [One-sample matroid prophet inequalities against an almighty adversary](snapshots/2026-10-08-baseline/families/111/source.json) | [Matroid allocation research simulator](snapshots/2026-10-08-baseline/families/111/review-2026-10-08-v1.md) | 020, 021 |
| 112 | [Beyond the square-root exponent for depth-three circuits](snapshots/2026-10-08-baseline/families/112/source.json) | [Depth-three circuit lower-bound teaching and benchmark module](snapshots/2026-10-08-baseline/families/112/review-2026-10-08-v1.md) | First-pass assessment only |
| 113 | [Approximate counting and entropy of perfect matchings](snapshots/2026-10-08-baseline/families/113/source.json) | [Matching counts: literal schedule exclusion and bounded fragility reference](snapshots/2026-10-08-baseline/families/113/review-2026-10-09-v2.md) | 001, 006 |
| 114 | [Approximate counting of common integer polymatroid bases](snapshots/2026-10-08-baseline/families/114/source.json) | [Constraint allocation space counter](snapshots/2026-10-08-baseline/families/114/review-2026-10-08-v1.md) | First-pass assessment only |
| 115 | [Sampling and counting contingency tables with arbitrary margins](snapshots/2026-10-08-baseline/families/115/source.json) | [Fixed-margin tables: law distinction and literal schedule exclusion](snapshots/2026-10-08-baseline/families/115/review-2026-10-09-v3.md) | 001, 004, 041 |
| 116 | [Uniform black-box noncommutative identity testing across characteristics](snapshots/2026-10-08-baseline/families/116/source.json) | [Family 116: explicit ordered-algebra witnesses and large companion costs](snapshots/2026-10-08-baseline/families/116/review-2026-10-09-v2.md) | 012 |
| 117 | [Uniform sparsest cut: hardness and semidefinite gaps](snapshots/2026-10-08-baseline/families/117/source.json) | [Cut relaxation calibration suite](snapshots/2026-10-08-baseline/families/117/review-2026-10-08-v1.md) | First-pass assessment only |
| 118 | [Bin packing and unbounded configuration-LP gaps](snapshots/2026-10-08-baseline/families/118/source.json) | [Bin packing approximation claim auditor](snapshots/2026-10-08-baseline/families/118/review-2026-10-08-v1.md) | First-pass assessment only |
| 119 | [The Courtade–Kumar and Hellinger conjectures](snapshots/2026-10-08-baseline/families/119/source.json) | [Noisy binary summary information benchmark](snapshots/2026-10-08-baseline/families/119/review-2026-10-08-v1.md) | First-pass assessment only |
| 120 | [Almost-linear-time exact matching and prescribed-degree factors in general graphs](snapshots/2026-10-08-baseline/families/120/source.json) | [General matching: literal backend prerequisite prevents a practical speedup claim](snapshots/2026-10-08-baseline/families/120/review-2026-10-09-v3.md) | 007 |
| 121 | [Almost-linear approximation of edit distance](snapshots/2026-10-08-baseline/families/121/source.json) | [Family 121: practical edit-distance backend deferred](snapshots/2026-10-08-baseline/families/121/review-2026-10-09-v2.md) | 008 |
| 122 | [Quantitative trace-reconstruction bounds with a uniform decoder](snapshots/2026-10-08-baseline/families/122/source.json) | [Deletion-channel reconstruction validation suite](snapshots/2026-10-08-baseline/families/122/review-2026-10-08-v1.md) | First-pass assessment only |
| 124 | [Polynomial-time scheduling on three identical machines](snapshots/2026-10-08-baseline/families/124/source.json) | [Three-machine scheduling: source model and practical boundary](snapshots/2026-10-08-baseline/families/124/review-2026-10-09-v2.md) | 001, 009, 020 |
| 125 | [The metric <i>k</i>-median approximation threshold and recovery](snapshots/2026-10-08-baseline/families/125/source.json) | [Family 125: metric facility threshold and a planning-review product experiment](snapshots/2026-10-08-baseline/families/125/review-2026-10-09-v2.md) | 011 |
| 126 | [Exponential semidefinite complexity of perfect matching](snapshots/2026-10-08-baseline/families/126/source.json) | [Matching formulation complexity audit](snapshots/2026-10-08-baseline/families/126/review-2026-10-08-v1.md) | First-pass assessment only |
| 127 | [Average sensitivity of polynomial threshold functions](snapshots/2026-10-08-baseline/families/127/source.json) | [Polynomial threshold sensitivity benchmark](snapshots/2026-10-08-baseline/families/127/review-2026-10-08-v1.md) | First-pass assessment only |
| 128 | [A factor-two approximation for shortest common superstring](snapshots/2026-10-08-baseline/families/128/source.json) | [Superstring construction, byte objectives and practical packaging](snapshots/2026-10-08-baseline/families/128/review-2026-10-09-v2.md) | 023 |
| 129 | [Exponential state costs for two-way automata](snapshots/2026-10-08-baseline/families/129/source.json) | [Automata transformation resource estimator](snapshots/2026-10-08-baseline/families/129/review-2026-10-08-v1.md) | First-pass assessment only |
| 130 | [Exact Fourier transforms below $`n\log n`$](snapshots/2026-10-08-baseline/families/130/source.json) | [Exact Fourier algorithm feasibility worksheet](snapshots/2026-10-08-baseline/families/130/review-2026-10-08-v1.md) | 020 |
| 131 | [Rapid mixing of graph switches for every degree sequence](snapshots/2026-10-08-baseline/families/131/source.json) | [Graph switching: host, event-time and exactness boundaries](snapshots/2026-10-08-baseline/families/131/review-2026-10-09-v2.md) | 003, 005 |
| 132 | [A superquadratic separation of sensitivity and block sensitivity](snapshots/2026-10-08-baseline/families/132/source.json) | [Sensitivity counterexample generator](snapshots/2026-10-08-baseline/families/132/review-2026-10-08-v1.md) | First-pass assessment only |
| 133 | [The computational complexity of Weisfeiler–Leman refinement](snapshots/2026-10-08-baseline/families/133/source.json) | [Graph refinement cost and capability evaluator](snapshots/2026-10-08-baseline/families/133/review-2026-10-08-v1.md) | First-pass assessment only |
| 134 | [Generalized star height at most three](snapshots/2026-10-08-baseline/families/134/source.json) | [Generalized regular expression research compiler](snapshots/2026-10-08-baseline/families/134/review-2026-10-08-v1.md) | First-pass assessment only |
| 135 | [Homogeneous depth-five lower bounds for iterated matrix multiplication](snapshots/2026-10-08-baseline/families/135/source.json) | [Arithmetic circuit restriction benchmark](snapshots/2026-10-08-baseline/families/135/review-2026-10-08-v1.md) | First-pass assessment only |
| 136 | [A quasilinear PCP theorem for PPAD](snapshots/2026-10-08-baseline/families/136/source.json) | [Robust local verification research toolkit](snapshots/2026-10-08-baseline/families/136/review-2026-10-08-v1.md) | First-pass assessment only |
| 137 | [One-tape time simulation in two-fifths-power space](snapshots/2026-10-08-baseline/families/137/source.json) | [Memory-constrained simulation explorer](snapshots/2026-10-08-baseline/families/137/review-2026-10-08-v1.md) | First-pass assessment only |
| 138 | [Subset Sum in $`O(2^{0.49n})`$ time](snapshots/2026-10-08-baseline/families/138/source.json) | [Subset-sum decisions: resource, identity and assurance boundary](snapshots/2026-10-08-baseline/families/138/review-2026-10-09-v2.md) | 017 |
| 139 | [Subpolynomial query complexity for log-concave sampling](snapshots/2026-10-08-baseline/families/139/source.json) | [Oracle sampling cost audit](snapshots/2026-10-08-baseline/families/139/review-2026-10-08-v1.md) | 020 |
| 140 | [Memory–sample lower bounds for noiseless Gaussian regression](snapshots/2026-10-08-baseline/families/140/source.json) | [Streaming inference precision budget model](snapshots/2026-10-08-baseline/families/140/review-2026-10-08-v1.md) | First-pass assessment only |
| 141 | [Existential–universal real sentences in the counting hierarchy](snapshots/2026-10-08-baseline/families/141/source.json) | [Real constraint complexity scope explorer](snapshots/2026-10-08-baseline/families/141/review-2026-10-08-v1.md) | First-pass assessment only |
| 142 | [Deterministic polynomial factorization over prime fields](snapshots/2026-10-08-baseline/families/142/source.json) | [Deterministic finite-field factorization backend](snapshots/2026-10-08-baseline/families/142/review-2026-10-08-v1.md) | 016 |

## Topology

| Family | Result and source directory | Latest application assessment | Dossier IDs |
| --- | --- | --- | --- |
| 304 | [The Hilbert–Smith conjecture in every dimension](snapshots/2026-10-08-baseline/families/304/source.json) | [Continuous symmetry classification contract](snapshots/2026-10-08-baseline/families/304/review-2026-10-09-v1.md) | First-pass assessment only |
| 305 | [Four-dimensional disk embedding and Wall's conjecture](snapshots/2026-10-08-baseline/families/305/source.json) | [Four-dimensional embedding obstruction fixture](snapshots/2026-10-08-baseline/families/305/review-2026-10-09-v1.md) | First-pass assessment only |
| 306 | [The purely cosmetic surgery conjecture](snapshots/2026-10-08-baseline/families/306/source.json) | [Knot surgery distinctness research contract](snapshots/2026-10-08-baseline/families/306/review-2026-10-09-v1.md) | First-pass assessment only |
| 307 | [Failure of rational injectivity for maximal coarse assembly](snapshots/2026-10-08-baseline/families/307/source.json) | [Coarse assembly counterexample ledger](snapshots/2026-10-08-baseline/families/307/review-2026-10-09-v1.md) | First-pass assessment only |
| 308 | [Finite Smith–Toda complexes at every height](snapshots/2026-10-08-baseline/families/308/source.json) | [Chromatic finite-complex existence catalog](snapshots/2026-10-08-baseline/families/308/review-2026-10-09-v1.md) | First-pass assessment only |
| 309 | [The Kervaire invariant problem at the prime three](snapshots/2026-10-08-baseline/families/309/source.json) | [Odd-primary Kervaire witness registry](snapshots/2026-10-08-baseline/families/309/review-2026-10-09-v1.md) | First-pass assessment only |
| 310 | [Quillen's conjecture in rational homology](snapshots/2026-10-08-baseline/families/310/source.json) | [Finite-group poset homology contract](snapshots/2026-10-08-baseline/families/310/review-2026-10-09-v1.md) | First-pass assessment only |
| 311 | [The Hovey–Strickland and Chai conjectures](snapshots/2026-10-08-baseline/families/311/source.json) | [Chromatic tensor-ideal classification ledger](snapshots/2026-10-08-baseline/families/311/review-2026-10-09-v1.md) | First-pass assessment only |
| 312 | [The Grothendieck homotopy hypothesis](snapshots/2026-10-08-baseline/families/312/source.json) | [Infinity-groupoid model correspondence evidence](snapshots/2026-10-08-baseline/families/312/review-2026-10-09-v1.md) | First-pass assessment only |
| 313 | [Finite generation for the $`K(n)`$-local sphere](snapshots/2026-10-08-baseline/families/313/source.json) | [Localized homotopy finite-generation contract](snapshots/2026-10-08-baseline/families/313/review-2026-10-09-v1.md) | First-pass assessment only |
| 314 | [Cyclic length and chromatic fixed-point loss](snapshots/2026-10-08-baseline/families/314/source.json) | [Cyclic-chain length is computable for bounded finite examples](snapshots/2026-10-08-baseline/families/314/review-2026-10-09-v2.md) | First-pass assessment only |
| 315 | [The four-dimensional Singer conjecture](snapshots/2026-10-08-baseline/families/315/source.json) | [Four-dimensional L2 homology contract](snapshots/2026-10-08-baseline/families/315/review-2026-10-09-v1.md) | First-pass assessment only |
| 316 | [Curtis’s conjecture](snapshots/2026-10-08-baseline/families/316/source.json) | [Stable Hurewicz image reference](snapshots/2026-10-08-baseline/families/316/review-2026-10-09-v1.md) | First-pass assessment only |
| 317 | [Thomason model structures in all strict higher dimensions](snapshots/2026-10-08-baseline/families/317/source.json) | [Categorical homotopy model interoperability](snapshots/2026-10-08-baseline/families/317/review-2026-10-09-v1.md) | First-pass assessment only |
| 318 | [Chromatic splitting: filtrations and counterexamples](snapshots/2026-10-08-baseline/families/318/source.json) | [Chromatic splitting regime audit](snapshots/2026-10-08-baseline/families/318/review-2026-10-09-v1.md) | First-pass assessment only |
| 319 | [Counterexamples to finite generation at chromatic height two](snapshots/2026-10-08-baseline/families/319/source.json) | [Finite-building assumption counterexample](snapshots/2026-10-08-baseline/families/319/review-2026-10-09-v1.md) | First-pass assessment only |
| 320 | [Nonhomeomorphic closed aspherical four-manifolds](snapshots/2026-10-08-baseline/families/320/source.json) | [Homotopy-to-homeomorphism inference fixture](snapshots/2026-10-08-baseline/families/320/review-2026-10-09-v1.md) | First-pass assessment only |
| 321 | [A counterexample to Wall's finite D(2) problem](snapshots/2026-10-08-baseline/families/321/source.json) | [Cell-dimension simplification contract](snapshots/2026-10-08-baseline/families/321/review-2026-10-09-v1.md) | First-pass assessment only |