Tootfinder

Deterministic Lifting Theorems for One-Way Number-on-Forehead Communication
Guangxu Yang, Jiapeng Zhang
https://arxiv.org/abs/2506.12420 https://

Deterministic Lifting Theorems for One-Way Number-on-Forehead Communication
Lifting theorems are one of the most powerful tools for proving communication lower bounds, with numerous downstream applications in proof complexity, monotone circuit lower bounds, data structures, and combinatorial optimization. However, to the best of our knowledge, prior lifting theorems have primarily focused on the two-party communication. In this paper, we propose a new lifting theorem that establishes connections between two-party communication and the Number-on-Forehead (NOF) communi…

A Determination of $\alpha_s(m_Z)$ at aN$^3$LO$_{\bf QCD}\otimes {\bf NLO}_{\bf QED}$ Accuracy from a Global PDF Analysis
The NNPDF Collaboration, Richard D. Ball, Andrea Barontini, Juan Cruz-Martinez, Stefano Forte, Felix Hekhorn, Emanuele R. Nocera, Juan Rojo, Roy Stegeman
https://arxiv.org/abs/2506.13871

A Determination of $α_s(m_Z)$ at aN$^3$LO$_{\bf QCD}\otimes {\bf NLO}_{\bf QED}$ Accuracy from a Global PDF Analysis
We present a determination of the strong coupling $α_s(m_Z)$ from a global dataset including both fixed-target and collider data from deep-inelastic scattering and a variety of hadronic processes, with a simultaneous determination of parton distribution functions (PDFs) based on the NNPDF4.0 methodology. This determination is performed at NNLO and approximate N$^3$LO (aN$^3$LO) perturbative QCD accuracy, including QED corrections and a photon PDF up to NLO accuracy. We extract $α_s$ using two…

On Singer's conjecture for the fourth algebraic transfer in certain generic degrees
Dang Vo Phuc
https://arxiv.org/abs/2506.10232 https://

On Singer's conjecture for the fourth algebraic transfer in certain generic degrees
Let $A$ be the Steenrod algebra over the finite field $k := \mathbb Z_2$ and $G(q)$ be the general linear group of rank $q$ over $k.$ A well-known open problem in algebraic topology is the explicit determination of the cohomology groups of the Steenrod algebra, ${\rm Ext}^{q, *}_A(k, k),$ for all homological degrees $q \geq 0.$ The Singer algebraic transfer of rank $q,$ formulated by William Singer in 1989, serves as a valuable method for the description of such Ext groups. This transfer maps f…

Join the 2025 Maine AI 'unconference' on June 13 in Orono for face-to-face discussions whose topics will be democratically chosen by the attenders. (We've got expert panels too.) Register by this Friday—more at https://www.linkedin.com/posts/jonippolito