Tootfinder

New Dallas Cowboys 'triplets' land near the top in NFL rankings https://www.si.com/nfl/cowboys/news/new-dallas-cowboys-triplets-land-near-top-nfl-rankings

Raiders Defensive Triplets Ranked https://www.si.com/nfl/raiders/las-vegas-pete-carroll-maxx-crosby-elandon-roverts-jakorian-bennett

Patterns Within the Markov Tree
Robert A. Gore
https://arxiv.org/abs/2506.04299 https://arxiv.org/pdf/2506.04299

Patterns Within the Markov Tree
An analysis of the Markov tree is presented. Markov triplets, {x,R,z}, are the positive integer solutions to the Diophantine equation x2 + R2 + z2 = 3xRz. Inspired by patterns of the Fibonacci and Pell triplets in Region 1 and Region 2 of the tree, an investigation of interior regions of the Markov tree finds generating functions and sequence functions for all triplets of all regions. These sequence functions lead to the discovery of a Pell equation for the Markov region numbers along the edges…

Cartesian Prime Graphs and Cospectral Families
Abhinav Bitragunta, Hareshkumar Jadav, Ranveer Singh
https://arxiv.org/abs/2505.24358 https://

Cartesian Prime Graphs and Cospectral Families
We introduce a method for constructing larger families of connected cospectral graphs from two given cospectral families of sizes $p$ and $q$. The resulting family size depends on the Cartesian primality of the input graphs and can be one of $pq$, $p + q - 1$, or $\max(p, q)$, based on the strictness of the applied conditions. Under the strictest condition, our method generates $O(p^3q^3)$ new cospectral triplets, while the more relaxed conditions yield $\varOmega(pq^3 + qp^3)$ such triplets. W…

Three-pion Bose-Einstein correlations measured in proton-proton collisions
LHCb collaboration
https://arxiv.org/abs/2506.03072 https://

Three-pion Bose-Einstein correlations measured in proton-proton collisions
A study on the Bose-Einstein correlations for triplets of same-sign pions is presented. The analysis is performed using proton-proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 7 TeV, recorded by the LHCb experiment, corresponding to an integrated luminosity of 1.0 fb$^{-1}$. For the first time, the results are interpreted in the core-halo model. The parameters of the model are determined in regions of charged-particle multiplicity. This measurement provides insight into the nature o…

Cowboys' defensive 'triplets' fly under-the-radar in NFL rankings https://www.si.com/nfl/cowboys/news/dallas-cowboys-defensive-triplets-fly-under-the-radar-in-nfl-rankings

Capacity Matters: a Proof-of-Concept for Transformer Memorization on Real-World Data
Anton Changalidis, Aki H\"arm\"a
https://arxiv.org/abs/2506.14704

Capacity Matters: a Proof-of-Concept for Transformer Memorization on Real-World Data
This paper studies how the model architecture and data configurations influence the empirical memorization capacity of generative transformers. The models are trained using synthetic text datasets derived from the Systematized Nomenclature of Medicine (SNOMED) knowledge graph: triplets, representing static connections, and sequences, simulating complex relation patterns. The results show that embedding size is the primary determinant of learning speed and capacity, while additional layers provi…

The QUEST Database of Highly-Accurate Excitation Energies
Pierre-Fran\c{c}ois Loos, Martial Boggio-Pasqua, Aymeric Blondel, Filippo Lipparini, Denis Jacquemin
https://arxiv.org/abs/2506.11590

The QUEST Database of Highly-Accurate Excitation Energies
We report theoretical best estimates of vertical transition energies (VTEs) for a large number of excited states and molecules: the \textsc{quest} database. This database includes 1489 \emph{aug}-cc-pVTZ VTEs (731 singlets, 233 doublets, 461 triplets, and 64 quartets) for both valence and Rydberg transitions occurring in molecules containing from 1 to 16 non-hydrogen atoms. \textsc{Quest} also includes a significant list of VTEs for states characterized by a partial or genuine double-excitation…

This https://arxiv.org/abs/2506.03072 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepe…

Three-pion Bose-Einstein correlations measured in proton-proton collisions
A study on the Bose-Einstein correlations for triplets of same-sign pions is presented. The analysis is performed using proton-proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 7 TeV, recorded by the LHCb experiment, corresponding to an integrated luminosity of 1.0 fb$^{-1}$. For the first time, the results are interpreted in the core-halo model. The parameters of the model are determined in regions of charged-particle multiplicity. This measurement provides insight into the nature o…