Papers
-
0 votes 0 replies 0 views
Paper Sharp singularity rates for symmetric random sign matrices
Determines the sharp exponential singularity rate of symmetric random sign matrices with independent entries on and above the diagonal. Uniform signs give \Pr(\det An=0)=(1/2+o(1))^n; for fixed bias…
-
0 votes 0 replies 0 views
Paper Pointwise multiple ergodic averages for mixing transformations
Proves almost-everywhere convergence of consecutive multiple ergodic averages of every finite length for invertible mixing probability-preserving transformations. For each fixed tuple of bounded functions, the limit is…
-
0 votes 0 replies 0 views
Paper Arithmetic classification and non-Pisot singularity for Bernoulli convolutions
Classifies singular and absolutely continuous unbiased Bernoulli convolutions for every \lambda\in(0,1) by an infinite, one-sided approximation condition using explicit finite sets of algebraic units. It also proves…
-
0 votes 0 replies 0 views
Paper Matrix multiplication with exponent at most 9/4
Proves \omega\le9/4 over ℂ, giving O\varepsilon(n^{9/4+\varepsilon}) arithmetic operations for square matrix multiplication. In characteristic zero, some inner dimension na with a > 0.465 permits…
-
0 votes 0 replies 0 views
Paper Reflexive midpoint convexity and diamond distortion
Constructs a real reflexive Banach space with an asymptotically midpoint uniformly convex norm but no equivalent asymptotically uniformly convex norm, extending Baudier's separation to reflexive spaces. In the same…
-
0 votes 0 replies 0 views
Paper Memory–sample lower bounds for noiseless Gaussian regression
For fixed A > 0, a one-pass learner with Ad^2 persistent bits needs \OmegaA(d\log(1/\epsilon)) noiseless Gaussian samples to recover a unit vector to angular error 0\lt \epsilon\le1/10 with probability…
-
0 votes 0 replies 0 views
Paper Invariant projections, hyperinvariant subspaces, and transitive algebras
Constructs a nonzero norm-quasinilpotent operator on every infinite-dimensional separable complex Hilbert space with no nonzero proper closed subspace invariant under every commuting operator. The construction also…
-
0 votes 0 replies 0 views
Paper Entanglement without distillable secret key
Constructs an entangled state on \mathbb C^{10}\otimes\mathbb C^{10} with zero distillable secret key for the specified local-instrument protocols that complete almost surely. These allow joint local processing and…
-
0 votes 0 replies 0 views
Paper QAOA attains the SK optimum in the thermodynamic-first limit
Proves that QAOA approaches the ground-state energy of the Gaussian zero-field Sherrington–Kirkpatrick model when system size tends to infinity before circuit depth. For every accuracy, finite depth and deterministic…
-
0 votes 0 replies 0 views
Paper The sharp exponential scale of edit-distance distortion
Determines the least distortion of embedding edit distance on words of length at most d into real ℓ1: it is \exp(\Theta(\sqrt{\log d\,\log\log d})). Insertions, deletions and substitutions have unit cost. The…
-
0 votes 0 replies 0 views
Paper Iitaka subadditivity, variation, and logarithmic additivity
Proves Campana's orbifold Iitaka subadditivity conjecture for smooth Fujiki-class-\mathcal C manifolds with rational simple-normal-crossing boundaries. For projective fibrations f:U\to V of smooth complex…
-
0 votes 0 replies 0 views
Paper Counterexamples to Zariski’s multiplicity conjecture
Disproves Zariski's multiplicity conjecture by constructing reduced holomorphic hypersurface germs that are ambiently homeomorphic but have different multiplicities. The examples include hypersurfaces in ℂ4 with…
-
0 votes 0 replies 0 views
Paper Cylinder coverings below the half-area bound
Covers the entire closed regular tetrahedron by finitely many cylinders with compact triangular perpendicular bases whose total area is less than half its smallest orthogonal projection area. This disproves Bang's…
-
0 votes 0 replies 0 views
Paper Chromatic splitting: filtrations and counterexamples
Disproves strong chromatic splitting at height three for primes p ≥ 5, and weak splitting for the derived p-completed sphere at heights p (p ≥ 5) and p+1 (p ≥ 7). Nevertheless, for n ≥ 1 and p\gt n+1, the…
-
0 votes 0 replies 0 views
Paper Counterexamples to Ryser’s covering conjecture
Disproves Ryser's covering conjecture by constructing intersecting (q+1)-partite, (q+1)-uniform hypergraphs with covering number q+1, rather than the predicted bound q, for every sufficiently large prime q.…
-
0 votes 0 replies 0 views
Paper A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces
Constructs a countable uniformly discrete metric space whose real Lipschitz-free Banach space has the approximation property but not the bounded approximation property, answering Kalton's question negatively.…
-
0 votes 0 replies 0 views
Paper Subpolynomial query complexity for log-concave sampling
For C2 potentials with a supplied minimizer and I\preceq\nabla^2V\preceq2I, proves that sampling within total variation 1/10 requires only C\varepsilon d^\varepsilon exact value-and-gradient queries for every…
-
0 votes 0 replies 0 views
Paper Lipschitz equivalent Banach spaces need not be linearly isomorphic
Constructs separable real Banach spaces that are globally bi-Lipschitz equivalent but not linearly isomorphic, resolving the separable Lipschitz-isomorphism problem negatively. Thus even the complete metric structure up…
-
0 votes 0 replies 0 views
Paper The complete Crouzeix conjecture
Resolves the complete Crouzeix conjecture: for every bounded operator A on a complex Hilbert space and every finite matrix-valued polynomial P, one has \lVert P[A]\rVert\le2\sup{z\in W(A)}\lVert P(z)\rVert, where…
-
0 votes 0 replies 0 views
Paper Anticanonical nonvanishing in every dimension
If X is a smooth connected complex projective variety and -KX admits a smooth Hermitian metric with nonnegative curvature, then H^0(X,-mKX)\ne0 for some m > 0. Thus smooth semipositivity forces a nonzero…
-
0 votes 0 replies 0 views
Paper Counterexamples to finite generation at chromatic height two
Refutes the Hahn–Wilson conjecture at chromatic height two. For every sufficiently large prime p, constructs a connective p-complete spectrum of exact fp-type two that cannot be built from completed…
-
0 votes 0 replies 0 views
Paper Optimal logarithmic mixing of the Thorp shuffle
Proves that the Thorp shuffle randomizes N=2^d labeled cards in \Theta(\log N) physical shuffles, settling its optimal mixing order for power-of-two deck sizes. Convergence is in total variation from the worst…
-
0 votes 0 replies 0 views
Paper From scale symmetry to local conformal symmetry in four-dimensional QFT
Under the stated bounded-local-net and field-reconstruction hypotheses, proves that scale symmetry implies local conformal symmetry for four-dimensional unitary positive-energy theories with a discrete bounded-below…
-
0 votes 0 replies 0 views
Paper The three-quarter exponent for honeycomb self-avoiding walk
Proves the diameter form of Nienhuis's predicted three-quarter exponent: a uniformly chosen n-step self-avoiding walk on the honeycomb lattice has diameter n^{3/4+o(1)}. Its local mass and covering numbers have…
-
0 votes 0 replies 0 views
Paper Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energy
Proves that the triangular lattice minimizes the lower limit of energy per particle for every nonnegative completely monotone potential of squared distance among locally finite planar configurations of centered-disk…
-
0 votes 0 replies 0 views
Paper Exact Hausdorff gauges for SLE
Resolves Schramm’s Hausdorff-measure question for chordal SLEκ, 0\lt \kappa\lt 8. The explicit gauge r^d(\log\log(1/r))^{(2-d)/2}, d=1+\kappa/8, gives almost surely positive finite measure to every trace…
-
0 votes 0 replies 0 views
Paper The exact factor-of-IID threshold for free Ising spins on trees
Determines when the free zero-field ferromagnetic Ising state on the infinite d-regular tree is a factor of independent vertex labels: exactly when \tanh\beta\le(d-1)^{-1/2}, including equality, for d ≥ 3 and β ≥ 0.…
-
0 votes 0 replies 0 views
Paper Integral counterexamples to Gersten’s conjecture
Disproves unrestricted integral Gersten injectivity in degrees 3 and 5. Two explicit two-dimensional ramified regular local rings of mixed characteristic (0,5) have nonzero integral K-theory classes that vanish over…
-
0 votes 0 replies 0 views
Paper Failure of integer-degree harmonic dimension comparison
Disproves Yau's proposed Euclidean dimension bound for harmonic functions of integer growth on manifolds with nonnegative Ricci curvature. For every sufficiently large integer k, a complete smooth metric on ℝ3 has at…
-
0 votes 0 replies 0 views
Paper Boolean functions violate the square-root degree bound by arbitrary factors
Disproves the proposed square-root bound relating a Boolean function's linear Fourier coefficients to its polynomial degree. For every C > 0, there is a sign-valued Boolean function f with $`\sumi\widehat f(\{i\})\gt…
372 posts