The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

The paper introduces a novel public key encryption scheme with high security by leveraging the conjectured intractability of two types of highly corrupted constraint satisfaction problems (CSPs).

This paper provides the first unconditional proof for Weber's Conjecture for the case $k ext{ up to } 12$, which is crucial for lattice-based cryptography.

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 resolves three conjectures related to arrow pattern avoidance in permutations using two different proof methods.

This paper disproves a conjecture about the longest-path lengths of MaxSTN and MinSTN algorithms for producing $st$-orientations of biconnected graphs.

The paper studies the affine family of signings for a d-regular graph and shows that averaging over it converts the sign problem of the Bilu-Linial conjecture into a counting problem, proving matched…

This paper shows #P-completeness for several graph counting problems using a new technique.

The paper shows that every problem asking if a given graph has an edge-coloring without an edge-colored clique from a fixed family is poly-time equivalent to a Constraint Satisfaction Problem, resulti…

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…

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…

This paper investigates the production-evaluation gap in Large Reasoning Models (LRMs), finding that while LRMs excel at generating solutions, they struggle significantly to evaluate flawed reasoning,…

The paper establishes bijections between tree records, girth of connected endofunctions, and genesis sequences, deriving generating functions for tree and forest record numbers using Cayley's tree fun…

A new polynomial-time algorithm is presented for optimally coloring perfect graphs using graph-theoretic operations and iterative walk counting.