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Local inequalities for $cA_k$ singularities
Igor Krylov, Takuzo Okada, Erik Paemurru
https://arxiv.org/abs/2508.21676 https://arxiv.org/pdf/2508.21676

Local inequalities for $cA_k$ singularities
We generalize an intersection-theoretic local inequality of Fulton-Lazarsfeld to weighted blowups. As a consequence, we obtain the $4n^2/(k+1)$-inequality for isolated $cA_k$ singularities, an analogue of the $4 n^2$-inequality for smooth points. We use this to prove birational rigidity of many families of Fano 3-fold weighted complete intersections with terminal quotient singularities and isolated $cA_k$ singularities, including sextic double solids with $cA_1$ and ordinary $cA_2$ points.

Inverse Kazhdan-Lusztig polynomials of matroids under deletion
Tom Braden, Luis Ferroni, Jacob P. Matherne, Nutan Nepal
https://arxiv.org/abs/2510.01086 https://

Inverse Kazhdan-Lusztig polynomials of matroids under deletion
We provide a deletion formula for the inverse Kazhdan--Lusztig polynomial and the inverse $Z$-polynomial of a matroid. Our formulas provide analogues to the deletion formulas of Braden--Vysogorets for Kazhdan--Lusztig and $Z$-polynomials. We discuss several consequences, which include closed formulas and recursions for these invariants on uniform matroids, projective geometries, glued cycles, and arbitrary matroids of corank $2$. As a relevant application of our deletion formula, we show the ex…

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Jess Gillam shares music with baritone and cabaret star Le Gateau Chocolat, including music by Margaret Bonds, Tchaikovsky and Anonhi.
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https://www.bbc.co.uk/programmes/m002lc46

Unboundedness for motivic invariants of birational automorphisms
Hsueh-Yung Lin, Evgeny Shinder
https://arxiv.org/abs/2510.00290 https://arxiv.org/pdf/2510…

Unboundedness for motivic invariants of birational automorphisms
We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the (usual) motivic invariants vanish for birational automorphisms of threefolds over algebraically closed fields of characteristic zero. On the other hand, we prove that the motivic invariants of the birational automorphism group of many types of varieties, including projective spaces of dimension at least four over a f…

BABY 1L: First Tritium Breeding Campaign Results
R\'emi Delaporte-Mathurin, Nikola Goles, Collin Dunn, Emily Edwards, Sara Ferry, Ross MacDonald, Ethan Peterson, Davide Pettinari, Stefano Segantin, Weiyue Zhou, Kevin B. Woller
https://arxiv.org/abs/2509.26174

BABY 1L: First Tritium Breeding Campaign Results
Achieving tritium self-sufficiency is a critical challenge for future fusion power plants. The BABY 1L experiment, part of the LIBRA project at MIT, aims to benchmark tritium breeding and release in molten salt breeder systems under deuterium-tritium (DT) neutron irradiation. Building on the initial \SI{100}{mL} campaign, BABY 1L introduces a tenfold increase in breeder volume, improved thermal and gas handling systems, and enhanced neutron diagnostics, including a proton recoil telescope. We r…

Which Programming Language and Model Work Best With LLM-as-a-Judge For Code Retrieval?
Lucas Roberts, Denisa Roberts
https://arxiv.org/abs/2510.00324 https://

Which Programming Language and Model Work Best With LLM-as-a-Judge For Code Retrieval?
Code search is an important information retrieval application. Benefits of better code search include faster new developer on-boarding, reduced software maintenance, and ease of understanding for large repositories. Despite improvements in search algorithms and search benchmarks, the domain of code search has lagged behind. One reason is the high cost of human annotation for code queries and answers. While humans may annotate search results in general text QA systems, code annotations require s…

As humans, we •all• live our lives with our heads up our butts — including but not limited to the Britannica writers. If we’re lucky, someone will help us see what we’re missing. If we’re wise, we listen. At its best, that’s what Wikipedia can do — and in public, at scale, for everyone.
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Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models
D. Kang, J. C. Arteaga-Vel\'azquez, M. Bertaina, A. Chiavassa, A. L. Colmenero-C\'esar, K. Daumiller, V. de Souza, R. Engel, A. Gherghel-Lascu, C. Grupen, A. Haungs, J. R. H\"orandel, T. Huege, K. -H. Kampert, K. Link, H. J. Mathes, S. Ostapchenko, T. Pierog, D. Rivera-Rangel, M. Roth, H. Schieler, F. G. Schr\"oder, O. Sima, A. Weindl, J. Wochele, J. Zabierowski
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Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models
KASCADE-Grande was dedicated to measuring the energy spectrum and mass composition of cosmic rays in the energy range of 10 PeV to 1 EeV. We observed a knee-like structure in the heavy mass component at around 100 PeV and an ankle-like structure in the light component. In this contribution, we present updated energy spectra based on shower size measurements, using the post-LHC hadronic models QGSJet-II-04, EPOS-LHC, and SIBYLL 2.3d, including accounting for shower-to-shower fluctuations. In add…

The Impact of Spectroscopic Redshift Errors on Cosmological Measurements
Shengyu He, Jiaxi Yu, Antoine Rocher, Daniel Forero-S\'anchez, Jean-Paul Kneib, Cheng Zhao, Etienne Burtin
https://arxiv.org/abs/2508.21182

The Impact of Spectroscopic Redshift Errors on Cosmological Measurements
Spectroscopic redshift errors, including redshift uncertainty and catastrophic failures, can bias cosmological measurements from galaxy redshift surveys at sub-percent level. We investigate their impact on full-shape clustering analysis using contaminated mock catalogs. We find that redshift uncertainty introduces a damping effect on the power spectrum. This damping is scale-dependent and absorbed by counterterms in the clustering model, keeping parameter biases below $5\%$ for the DESI survey.…

The Wikipedia article also includes this sentence in its opening paragraph:
❝However, France only controlled a small fraction of this area, most of which was inhabited by Native Americans; effectively, for the majority of the area, the United States bought the preemptive right to obtain Indian lands by treaty or by conquest, to the exclusion of other colonial powers.❞
Britannica has nothing like that. It discusses the Louisiana Purchase without a single mention that the indigenous people of North America even exist.
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