Publications (16)
A state sum for the total face color polynomial
Scott Baldridge, Louis H. Kauffman, Ben McCarty
The total face color polynomial is based upon the Poincaré polynomials of a family of filtered -color homologies. It counts the number of -face colorings of ribbon graphs fo…
Small examples of cube diagrams of knots
Scott Baldridge, Ben McCarty
In this short note we highlight some of the differences between cube diagrams and grid diagrams. We also list examples of small cube diagrams for all knots up to 7 crossings and gi…
On the rotation class of knotted Legendrian Tori in
Scott Baldridge, Ben McCarty
In this paper we show how to combinatorically compute the rotation class of a large family of embedded Legendrian tori in with the standard contact form. In particul…
Enhance Quantum Teleportation with Multi-Axis Measurement
Junyao Zhang, Jonathan Ku, Zhiding Liang +3
Quantum teleportation is a cornerstone of quantum information processing, enabling the nonlocal transmission of quantum states across arbitrary distances using shared entanglement…
A new way to prove configuration reducibility using gauge theory
Scott Baldridge, Ben McCarty
We show how ideas coming out of gauge theory can be used to prove configurations in the list of ``633 unavoidable configurations" are reducible. In this paper, we prove the smalles…
Lifting Lagrangian immersions in to Lagrangian cones in
Scott Baldridge, Ben McCarty, David Shea Vela-Vick
In this paper we show how to lift Lagrangian immersions in to produce Lagrangian cones in , and use this process to produce several families of…
A counterexample for the polar conjecture of Spencer-Brown
Scott Baldridge, Louis H. Kauffman, Ben McCarty
In 1976, George Spencer-Brown announced a proof of the four color theorem, using operations on Tait colorings for trivalent plane graphs. In subsequent work he formulated these ope…
New relations for the vertex polynomial
Scott Baldridge, Ben McCarty
The paper extends the vertex polynomial to graphs of any degree and establishes local relations that apply when a graph contains small cycles such as digons, triangles, quadrilater…
Unoriented Virtual Khovanov Homology
Scott Baldridge, Louis H. Kauffman, Ben McCarty
The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homo…
New relations for the Penrose polynomial
Scott Baldridge, Ben McCarty
We introduce two new relations involving the pentagon and the quadrilateral for the evaluation of the Penrose polynomial at that is proven using a new type of ribbon graph po…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Quantum state systems that count perfect matchings
Scott Baldridge, Ben McCarty
In this paper we show how to categorify the -color vertex polynomial, which is based upon one of Roger Penrose's formulas for counting the number of -edge colorings of a plan…
A topological quantum field theory approach to graph coloring
Scott Baldridge, Ben McCarty
In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a -dimensional CW complex of a smooth closed surface. The dimensio…
The 2-Factor Polynomial Detects Even Perfect Matchings
Scott Baldridge, Adam M. Lowrance, Ben McCarty
In this paper, we prove that the 2-factor polynomial, an invariant of a planar trivalent graph with a perfect matching, counts the number of 2- factors that contain the the perfect…
Cube number can detect chirality and Legendrian type of knots
Ben McCarty
For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. We will show that the cube number detects chirality…
An infinite family of Legendrian torus knots distinguished by cube number
Ben McCarty
For a knot the cube number is a knot invariant defined to be the smallest for which there is a cube diagram of size for . There is also a Legendrian version of this…