Papers

The 52 problem files in FormalConjectures/Paper that state a research or textbook statement, at commit 2055e5ad, one article each.

Their docstrings and Lean statements are quoted from Formal Conjectures (Google DeepMind) at that commit, under its Apache-2.0 license.

The Auslander-Reiten conjecture to Gourevitch's series identity

• The Auslander-Reiten conjecture
• The Bollobás–Eldridge–Catlin conjecture on graph packing (1978)
• Decidability of reachability for branching vector addition systems
• The burning number conjecture
• Conjecture about cardinality of Lindelöf spaces
• Casas-Alvero Conjecture
• The Catch-Up game and conjecture
• Chvátal's Conjecture
• Claude's Cycles
• The \(S_3\)-conjecture (conjugacy classes of distinct sizes)
• The Courtade–Kumar (most informative Boolean function) conjecture
• De Giorgi's conjecture
• Degree sequences in triangle-free graphs
• Complete disjoint NP pairs
• Dubner's conjecture
• The Eisenbud-Green-Harris conjecture
• Euclidean Ramsey configurations on a circle
• Is a finite locally free group scheme killed by its order?
• Main conjecture on fusible numbers
• Gourevitch's series identity

The Hall ratio conjecture… to Moments of the Riemann zeta…

• The Hall ratio conjecture (Harris 2019) — disproved
• Hartshorne's conjecture on Vector Bundles
• Conjectures around homogeneous topological spaces
• Kaplansky's problem on the values of the \(u\)-invariant
• Kotzig's Conjecture
• Kurepa's conjecture
• Conjectures about Latin Squares
• Latin Tableau Conjecture
• Lennon–Pittel conjecture on random stable matchings
• The Manickam–Miklós–Singhi conjecture (1988)
• Monochromatic quantum graphs (inherited vertex colorings)
• Energy-critical NLS in three dimensions.
• The 1-2-3 conjecture (Karoński–Łuczak–Thomason 2004; proved by Keusch 2024)
• Parities of partition numbers
• Pfister's problem on the Pythagoras number of \(\mathbb{R}(X_1, \dots, X_n)\)
• Prime Tuples Conjecture
• Pudlák's conjectures on incompleteness in the finite domain
• Reed's omega, delta, and chi conjecture
• Equivalents to the Riemann Hypothesis
• Moments of the Riemann zeta function on the critical line

Simple zeros of the Riemann… to Zagier's Conjecture on Multiple…

• Simple zeros of the Riemann zeta function on the critical line
• Ringel's Conjecture
• Is Every Convex Polyhedron Rupert?
• Serre's uniformity conjecture over the rationals
• Shelah-Spencer's Zero-One Law for Sparse Random Graphs
• Size, Order, and Connected Domination
• Strong Sensitivity Conjecture (`bs(f) ≤ s(f)^2`)
• Tu-Deng Conjecture
• Voronovskaja-type Formula for the Bezier Variant of the Bernstein Operators
• Conjectures about Weakly First Countable spaces
• Weak tiling problems
• Zagier's Conjecture on Multiple Zeta Values

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