Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
12 problems
Determine the leading asymptotic of the largest eigenvalue of the N-Majorana quartic SYK Hamiltonian as N → ∞. The preprint proves λ_1/√N → 4∫_0^∞ g_0(t)^4 dt ≈ 0.32504 almost surely, via the limiting free energy at every fixed positive…
Do the tree-level amplitudes A_n(1^-, 2^+, …, n^+) vanish identically, or can they be nonzero in half-collinear kinematics - and if nonzero, what is their all-n closed form?
Can the critical-exponent relation a + b = 1 at the jamming transition, observed numerically to high precision in the full replica-symmetry-breaking solution of hard spheres, be derived analytically from the scaling equations?
Does there exist a single real-valued, divergence-free, time-independent Lipschitz velocity field u∈ W^1,∞( T^3; R^3), chosen independently of magnetic diffusivity, that is a fast dynamo for the kinematic induction equation on the flat…
How many nondegenerate equilibrium points can the potential of three positive point charges have? Gabrielov, Novikov and Shapiro had proved at most 12, and observed that their method would give 6 if an auxiliary polynomial system had at…
Do n point charges whose electrostatic potential has only non-degenerate critical points always have at most (n-1)^2 of them? A configuration of five charges - three at the vertices of an equilateral triangle plus two small central charges…
For the Sachdev-Ye-Kitaev Hamiltonian on n Majorana modes with k-body interactions, the paper proves E|H|_op = (1-o(1))√2n/k for super-constant k ≤ o(√n), confirming predictions of Garcia-Garcia, Jia and Verbaarschot and answering a…
The dimer constant of Z^3, the exponential growth rate of perfect matchings of the cubic lattice, has no closed form and is pinned only by bounds. The upper bound improves from Lundow's 0.457547, standing since 2001, to 0.452130, via…
In the half-collinear single-minus graviton recursion of Guevara, Lupsasca, Skinner, Strominger and Weil, the multipoint vertex weights depend on global cut tests, which blocks a direct matrix-tree formula outside a restricted decay…
At the critical inverse temperature β=1 in the Sherrington-Kirkpatrick spin glass model, Talagrand conjectured that the expected squared overlap of two independent Gibbs replicas has an exact N^-2/3 scaling: there exists a constant a>0…
Is the EMD coupling square a^2 a function of the metric three-jet on an explicit active, non-null, simple-spectrum family of truncated Einstein-Maxwell-dilaton data, and can one more derivative recover it? Proved: no function of the common…
The paper proves a closed-string remodeling statement for the affine binary dihedral Calabi–Yau orbifold threefold, a target outside the toric setting of the Bouchard–Klemm–Mariño–Pasquetti remodeling conjecture, replacing the toric mirror…