The paper analyzes the phase transitions of the noisy transformer model on the unit sphere, proving a sharp global-minimizer dichotomy that depends on the dimension and coupling strength.

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

This paper introduces the concept of 'large' zeros in linear recurrence sequences and establishes that they either do not exist or are very sparse, which could lead to decidability of the Skolem Probl…

This paper characterizes the solutions and spectral properties of a specific system in circulant graphs.

This paper establishes a Coding Theorem in the context of symmetry groups and develops a connection between subgroups of a group and subsets of binary strings.

The authors reconfirmed Lehner's formula for determining spectral edges of Kronecker-Gaussian matrices using Random Duality Theory without relying on random matrix theory and spectral methods.

The paper shows that an oddomorphism between graphs does not imply graph minor containment and introduces a new structural relation called split-off minor.

The paper constructs a family of simple quantum states (pseudoentangled states) generated by constant-depth circuits that exhibit non-trivial entanglement structure, demonstrating that entanglement st…

This paper introduces normalized persistence, a version of persistent homology in topological data analysis, and proves its quantum hardness under the standard assumption that DQC1 is not in BPP.

This paper investigates how the extremality of fixed-volume spanning trees changes based on product-grid boundary factors in two and arbitrary dimensions.

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

The paper provides a negative answer to Carlson's question about whether the depth of a finite-group cohomology ring is always realized by the dimension of one of its associated primes.

This paper presents a polynomial-time Monte Carlo algorithm to determine the symmetry Lie algebra of a parametrized variety directly from the parametrization.

This paper proves that counting quasi-trees in a connected ribbon graph is #P-complete.

The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…