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Monday 21 September

History and Overview of Mathematics

From foundations to applications: reverse mathematics and philosophy

Benedict Eastaugh

Reverse mathematics is a branch of mathematical logic dedicated to determining the minimal set existence principles necessary and sufficient to derive ordinary mathematical theorems about concrete structures like the real line. Since the mid-1970s, reverse mathematics has developed a systematic classification of the strength of theorems in areas of mathematics ranging from real and complex analysis to infinitary combinatorics. This essay will place reverse mathematics in its historical and philosophical context, and reveal its relevance to central issues in the philosophy of mathematics, from the foundational programmes of Hilbert and Brouwer to contemporary debates about realism, determinacy, and applicability of mathematics. In doing so, it will discuss the role of computability theory in measuring the strength of set existence principles, as well as related questions about idealisation when these principles are applied in the physical sciences and in philosophy.
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High Energy Physics (Phenomenology)

System-size dependence of bottomonium suppression from Pb-Pb to light-ion collisions

Nora Brambilla, Tom Magorsch and Antonio Vairo

We test the system-size dependence of bottomonium suppression using the same open-quantum-system transport framework for Pb-Pb, O-O, and Ne-Ne collisions. The microscopic transport coefficients are retained from previous Pb-Pb analyses. Using QTraj, we solve the next-to-leading-order pNRQCD Lindblad equation in anisotropic hydrodynamic backgrounds and calculate integrated $\Upsilon$ double ratios. The QGP-induced evolution reproduces the observed sequential hierarchy and overall magnitude of the O-O suppression measured by CMS and LHCb. We quantify the sensitivity to both transport coefficients and to the termination temperature of the in-medium evolution. The Ne-Ne measurement favors somewhat stronger suppression than predicted, although the present experimental uncertainty is large. The extension from Pb-Pb to light ions supports, at least for observables less sensitive to cold nuclear matter effects, a common microscopic origin of bottomonium suppression in deconfined matter, characterized by the same temperature-dependent transport coefficients despite the large change in collision-system size.
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Combinatorics

On Smooth Combinatorial Products of Simplices

Juliana Curtis, Tuong Le and Chayim Lowen

We show that every lattice weak Minkowski summand of a smooth polytope combinatorially isomorphic to a product of simplices has a quadratic triangulation. This is achieved by identifying this class of polytopes with the class of Nakajima polytopes. We combine these results to give a new proof that two lattice weak Minkowski summands of the same such smooth polytope are relatively IDP. Along the way, we prove a structure theorem for simple polytopes whose 2-faces are triangles and trapezoids.
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Data Structures and Algorithms

On the Offline Version of the Time-Optimal k-Server Problem

Oleg Lomachenko

We consider the offline problem of parallel relocation of k identical mobile resources. After each request, known in advance, the resources may move simultaneously, and the duration of a step is determined by the longest individual movement. This model is equivalent to the offline version of the time-optimal k-server problem. We prove that the decision version is strongly NP-complete already on metrics of finite subsets of the Euclidean line, or equivalently, on vertex metrics of weighted paths. Thus, the computational hardness persists even under a linear arrangement of the admissible resource locations. As a positive result, we show that the problem can be solved exactly in polynomial time on metrics of undirected unweighted graphs with a universal vertex.
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Machine Learning

Multi-Term Fourier Graph Neural Network with Sample Relationship Learning for Enhanced Remaining Useful Life Prediction

Ya Song, Laurens Bliek, Yaoxin Wu et al. (+1 more)

Predicting the remaining useful life (RUL) is essential for effective predictive maintenance. Spatio-Temporal Graph Neural Networks (ST-GNNs), which can model both temporal and spatial relationships by representing time series data as a sequence of graphs, have shown exceptional performance in RUL prediction. However, current ST-GNNs face several drawbacks. First, they require domain expertise or significant computational power to establish graph structures prior to deploying GNNs. Second, the models are restricted to capture temporal dependencies within a predefined fixed-size lookback window. This restriction ignores the common issue of varying time series lengths, leading the prediction model to miss short-term or long-term dependencies. Finally, conventional models often fail to capture the inherent relationships between samples generated from adjacent time windows, which are crucial for improving both the accuracy and robustness of predictions. To address the aforementioned issues, we introduce a novel framework called Multi-Term Fourier Graph Neural Network with Sample Relationship Learning (MTFGN-SRL). Rather than treating the sample as a sequence of graphs, we consider it as a single complete graph and utilize a Fourier Graph Neural Network (FGN) to capture the spatio-temporal information in the frequency domain. We propose a multi-term learning module that utilizes multiple lookback windows to generate samples with varying terms, which are then fed into the FGN to enhance the extraction of useful information from the data. Finally, we develop a sample relationship learning module by training a heterogeneous GNN to identify inter-sample relationships, resulting in enhanced accuracy and robustness in predictions. Evaluations on the CMAPSS dataset demonstrate MTFGN-SRL's superior performance over state-of-the-art methods in RUL prediction.
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All authors Ya Song, Laurens Bliek, Yaoxin Wu, Yingqian Zhang

High Energy Physics (Experiment)

Discovery of an unexpectedly light and narrow beauty-strange state

LHCb collaboration: R. Aaij, M. Abdelfatah, A.S.W. Abdelmotteleb et al. (+1176 more)

As the essential building blocks of visible matter, hadrons have traditionally been classified by the quark model as mesons composed of quark-antiquark pairs and baryons built from three valence quarks. Yet, this classical picture does not account for the intricate chiral dynamics of the strong force and the emergence of exotic multi-quark hadrons. While experimental evidence for such unconventional dynamics has surfaced in the charm sector, the open-beauty system remains the long-sought frontier for testing the universality of these mechanisms. Here the observation of a new resonance in the beauty-strange sector with a global significance exceeding seven standard deviations is reported using proton-proton collision data recorded by the Large Hadron Collider beauty (LHCb) experiment at the European Organization for Nuclear Research (CERN). It exhibits a narrow natural width and a substantial mass deficit compared to the conventional quark model predictions. This result marks the first observation of a nonconventional single-beauty hadron, providing crucial insights into the chiral dynamics of the strong interaction and heavy-quark spin symmetry in the exotic domain.
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All authors LHCb collaboration: R. Aaij, M. Abdelfatah, A.S.W. Abdelmotteleb, C. Abellan Beteta, F. Abudinén, T. Ackernley, A.A. Adefisoye, B. Adeva, M. Adinolfi, P. Adlarson, C. Agapopoulou, C.A. Aidala, S. Akar, K. Akiba, H. Al Saleh, P. Albicocco, J. Albrecht, R. Aleksiejunas, F. Alessio, P. Alvarez Cartelle, S. Amato, J.L. Amey, Y. Amhis, Z. Amos, L. An, L. Anderlini, P. Andreola, M. Andreotti, S. Andres Estrada, A. Anelli, D. Ao, C. Arata, F. Archilli, Z. Areg, M. Argenton, S. Arguedas Cuendis, L. Arnone, M. Artuso, E. Aslanides, R. Ataíde Da Silva, M. Atzeni, B. Audurier, J.A. Authier, D. Bacher, I. Bachiller Perea, S. Bachmann, M. Bachmayer, J.J. Back, M. Bai, Z.B. Bai, V. Balagura, A. Balboni, W. Baldini, Z. Baldwin, L. Balzani, H. Bao, J. Baptista de Souza Leite, C. Barbero Pretel, M. Barbetti, I.R. Barbosa, W. Barker, R.J. Barlow, M. Barnyakov, S. Baron, S. Barsuk, W. Barter, J. Bartz, S. Bashir, B. Batsukh, P.B. Battista, A. Bavarchee, A. Bay, A. Beck, M. Becker, F. Bedeschi, I.B. Bediaga, N.A. Behling, S. Belin, A. Bellavista, I. Belyaev, G. Bencivenni, E. Ben-Haim, J.L.M. Berkey, R. Bernet, A. Bertolin, L. Bertsch, F. Betti, J. Bex, O. Bezshyyko, S. Bhattacharya, M.S. Bieker, N.V. Biesuz, A. Biolchini, M. Birch, F.C.R. Bishop, A. Bitadze, A. Bizzeti, T. Blake, F. Blanc, J.E. Blank, S. Blusk, J.A. Boelhauve, O. Boente Garcia, T. Boettcher, A. Bohare, C. Bolognani, R.B. Bonacci, A. Bordelius, F. Borgato, S. Borghi, M. Borsato, J.T. Borsuk, E. Bottalico, S.A. Bouchiba, M. Bovill, T.J.V. Bowcock, A. Boyer, C. Bozzi, J.D. Brandenburg, A. Brea Rodriguez, N. Breer, C. Breitfeld, J. Brodzicka, J. Brown, E. Buchanan, M. Burgos Marcos, C. Burr, C. Buti, J.S. Butter, J. Buytaert, W. Byczynski, S. Cadeddu, H. Cai, Y. Cai, Y. Cai, A. Caillet, R. Calabrese, L. Calefice, M. Calvi, M. Calvo Gomez, P. Camargo Magalhaes, J.I. Cambon Bouzas, P. Campana, A. Campomagnani, A.C. Campos, A.F. Campoverde Quezada, Y. Cao, S. Capelli, M. Caporale, L. Capriotti, R. Caravaca-Mora, A. Carbone, L. Carcedo Salgado, R. Cardinale, A. Cardini, P. Carniti, L. Carus, A. Casais Vidal, R. Caspary, G. Casse, M. Cattaneo, G. Cavallero, V. Cavallini, S. Celani, I. Celestino, S. Cesare, A.J. Chadwick, M. Charles, Ph. Charpentier, E. Chatzianagnostou, R. Cheaib, M. Chefdeville, C. Chen, J. Chen, S. Chen, Z. Chen, A. Chen Hu, M. Cherif, S. Chernyshenko, X. Chiotopoulos, G. Chizhik, V. Chobanova, A. Christakakis, M. Chrzaszcz, Y. Chu, V. Chulikov, P. Ciambrone, X. Cid Vidal, P. Cifra, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, C. Cocha Toapaxi, V. Coco, A. Codovini, C.S. Codovini, J. Cogan, E. Cogneras, L. Cojocariu, S. Collaviti, P. Collins, T. Colombo, M. Colonna, A. Comerma-Montells, L. Congedo, J. Connaughton, A. Contu, N. Cooke, G. Cordova, C. Coronel, I. Corredoira, A. Correia, G. Corti, G.C. Costantino, C. Cotirlan, J. Cottee Meldrum, B. Couturier, D.C. Craik, N. Crepet, M. Cruz Torres, M. Cubero Campos, E. Curras Rivera, R. Currie, C.L. Da Silva, X. Dai, J. Dalseno, C. D'Ambrosio, G. Darze, A. Davidson, O. De Aguiar Francisco, C. De Angelis, F. De Benedetti, J. de Boer, K. De Bruyn, S. De Capua, M. De Cian, U. De Freitas Carneiro Da Graca, F. De Gregorio, E. De Lucia, J.M. De Miranda, L. De Paula, A. De Robertis, E. De Santis, M. De Serio, P. De Simone, F. De Vellis, J.A. de Vries, F. Debernardis, D. Decamp, S. Dekkers, L. Del Buono, B. Delaney, B. Demaire-Lepape, J. Deng, O. Deschamps, F. Dettori, B. Dey, P. Di Nezza, S. Ding, Y. Ding, L. Dittmann, J.F. Diverchy, A.D. Docheva, A. Doheny, C. Dong, F. Dordei, J. Dorta Moreno, A.C. dos Reis, J. Dos Santos Oliveira, A.D. Dowling, L. Dreyfus, W. Duan, P. Duda, L. Dufour, V. Duk, P. Durante, M.M. Duras, J.M. Durham, O.D. Durmus, K. Duwe, A. Dziurda, S. Easo, E. Eckstein, U. Egede, S. Eisenhardt, E. Ejopu, L. Eklund, M. Elashri, D. Elizondo Blanco, J. Ellbracht, S. Ely, A. Ene, T. Evans, F. Fabiano, S. Faghih, L.N. Falcao, B. Fang, R. Fantechi, L. Fantini, M. Faria, K. Farmer, F. Fassin, D. Fazzini, L. Felkowski, C. Feng, M. Feng, A. Fernandez Casani, M. Fernandez Gomez, B. Fernandez Rodino, J. Fernandez-John, A.D. Fernez, F. Ferrari, F. Ferreira Rodrigues, R.A. Fini, R. Fiorenza, M. Fiorini, M. Firlej, D.S. Fitzgerald, C. Fitzpatrick, T. Fiutowski, F. Fleuret, A. Fomin, M. Fontana, M. Fontes Vaz, L.A. Foreman, R. Forty, D. Foulds-Holt, V. Franco Lima, M. Franco Sevilla, M. Frank, E. Franzoso, G. Frau, C. Frei, D.A. Friday, J. Fu, Y. Fu, Q. Führing, T. Fulghesu, G. Galati, M.D. Galati, A. Gallas Torreira, D. Galli, S. Gambetta, M. Gandelman, P. Gandini, B. Ganie, H. Gao, R. Gao, T.Q. Gao, Y. Gao, Y. Gao, Y. Gao, L.M. Garcia Martin, P. Garcia Moreno, J. García Pardiñas, P. Gardner, L. Garrido, C. Gaspar, A. Gavrikov, E. Gersabeck, M. Gersabeck, T. Gershon, S. Ghizzo, Z. Ghorbanimoghaddam, F.I. Giasemis, V. Gibson, H.K. Giemza, A.L. Gilman, M. Giovannetti, A. Gioventù, L. Girardey, M.A. Giza, F.C. Glaser, V.V. Gligorov, C. Göbel, L. Golinka-Bezshyyko, E. Golobardes, A. Golutvin, S. Gomez Fernandez, A.G. Gomez Mongui, W. Gomulka, F. Goncalves Abrantes, I. Gonçales Vaz, M. Goncerz, G. Gong, S. Gong, J.A. Gooding, C. Gotti, E. Govorkova, J.P. Grabowski, L.A. Granado Cardoso, R. Grande Quartieri, E. Graugés, E. Graverini, L. Grazette, G. Graziani, A.T. Grecu, N.A. Grieser, L. Grillo, C. Gu, M. Guarise, L. Guerry, A.-K. Guseinov, Y. Guz, T. Gys, K. Habermann, T. Hadavizadeh, C. Hadjivasiliou, G. Haefeli, C. Haen, S. Haken, G. Hallett, P.M. Hamilton, Q. Han, S. Han, X. Han, S. Hansmann-Menzemer, N. Harnew, T.J. Harris, L. Hartman, M. Hartmann, S. Hashmi, J. He, N. Heatley, A. Hedes, F. Hemmer, C. Henderson, R. Henderson, R.D.L. Henderson, A.M. Hennequin, K. Hennessy, J. Herd, P. Herrero Gascon, J. Heuel, A. Heyn, A. Hicheur, G. Hijano Mendizabal, J. Horswill, R. Hou, Y. Hou, D.C. Houston, N. Howarth, W. Hu, X. Hu, W. Hulsbergen, R.J. Hunter, D. Hutchcroft, M. Idzik, P. Ilten, A. Iohner, S. Jacevicius, H. Jage, S.J. Jaimes Elles, S. Jakobsen, T. Jakoubek, E. Jans, A. Jawahery, C. Jayaweera, A. Jelavic, V. Jevtic, Z. Jia, E. Jiang, X. Jiang, Y. Jiang, Y.J. Jiang, E. Jimenez Moya, N. Jindal, M. John, A. John Rubesh Rajan, D. Johnson, C.R. Jones, S. Joshi, B. Jost, J. Juan Castella, N. Jurik, I. Juszczak, K. Kalecinska, D. Kaminaris, S. Kandybei, M. Kane, Y. Kang, C. Kar, M. Karacson, A. Kauniskangas, J.W. Kautz, M.K. Kazanecki, F. Keizer, M. Kenzie, T. Ketel, B. Khanji, S. Kholodenko, V. Kholoimov, G. Khreich, F. Kiraz, T. Kirn, V.S. Kirsebom, N. Kleijne, A. Kleimenova, D. Klekots, K. Klimaszewski, M.R. Kmiec, T. Knospe, R. Kolb, S. Koliiev, L. Kolk, A. Konoplyannikov, P. Kopciewicz, P. Koppenburg, A. Korchin, I. Kostiuk, O. Kot, S. Kotriakhova, E. Kowalczyk, O. Kravcov, M. Kreps, W. Krupa, W. Krzemien, O. Kshyvanskyi, S. Kubis, M. Kucharczyk, A. Kupsc, A. Kurzina, V. Kushnir, B. Kutsenko, J. Kvapil, I. Kyryllin, D. Lacarrere, P. Laguarta Gonzalez, A. Lai, A. Lampis, D. Lancierini, C. Landesa Gomez, G. Lanfranchi, C. Langenbruch, T. Latham, F. Lazzari, C. Lazzeroni, R. Le Gac, H. Lee, R. Lefèvre, M. Lehuraux, E. Lemos Cid, O. Leroy, T. Lesiak, E.D. Lesser, B. Leverington, A. Li, C. Li, C. Li, H. Li, J. Li, K. Li, L. Li, L. Li, P. Li, P.-R. Li, Q. Li, T. Li, T. Li, W. Li, Y. Li, Y. Li, Y. Li, Z. Li, Z. Lian, Q. Liang, X. Liang, Z. Liang, S. Libralon, A. Lightbody, J. Lin, S. Lin, T. Lin, R. Lindner, H. Linton, R. Litvinov, D. Liu, F.L. Liu, G. Liu, K. Liu, S. Liu, W. Liu, Y. Liu, Y. Liu, Y.L. Liu, G. Loachamin Ordonez, I. Lobo, A. Lobo Salvia, A. Loi, T. Long, F.C.L. Lopes, J.H. Lopes, A. Lopez Huertas, C. Lopez Iribarnegaray, Q. Lu, C. Lucarelli, D. Lucchesi, M. Lucio Martinez, Y. Luo, A. Lupato, M. Lupberger, E. Luppi, K. Lynch, J. Lyu, S. Lyu, X.-R. Lyu, H. Ma, S. Maccolini, F. Machefert, F. Maciuc, B. Mack, I. Mackay, L.M. Mackey, L.R. Madhan Mohan, M.J. Madurai, D. Magdalinski, J.J. Malczewski, S. Malde, L. Malentacca, G. Manca, C. Mancuso, R. Manera Escalero, A. Mangalasseri, F.M. Manganella, R. Mangrulkar, D. Manuzzi, S. Mao, D. Marangotto, J.F. Marchand, R. Marchevski, U. Marconi, E. Mariani, S. Mariani, C. Marin Benito, J. Marks, A.M. Marshall, L. Martel, G. Martelli, G. Martellotti, L. Martinazzoli, M. Martinelli, C. Martinez, A. Martinez Armas, D. Martinez Gomez, D. Martinez Santos, F. Martinez Vidal, A. Martorell i Granollers, A. Massafferri, R. Matev, A. Mathad, C. Matteuzzi, K.R. Mattioli, L. Matzner, A. Mauri, E. Maurice, J. Mauricio, P. Mayencourt, J. Mazorra de Cos, M. Mazurek, D. Mazzanti Tarancon, M. McCann, N.T. McHugh, A. McNab, R. McNulty, B. Meadows, S.E.R. Medaer, D. Melnychuk, D. Mendoza Granada, P. Menendez Valdes Perez, F.M. Meng, M. Merk, A. Merli, L. Meyer Garcia, D. Miao, H. Miao, M. Mikhasenko, D.A. Milanes, A. Minotti, E. Minucci, B. Mitreska, D.S. Mitzel, R. Mocanu, A. Modak, L. Moeser, R.D. Moise, E.F. Molina Cardenas, T. Mombächer, M. Monk, T. Monnard, S. Monteil, A. Morcillo Gomez, G. Morello, M.J. Morello, M.P. Morgenthaler, A. Moro, J. Moron, W. Morren, A.B. Morris, A.G. Morris, R. Mountain, Z. Mu, N. Muangkod, E. Muhammad, F. Muheim, M. Mulder, K. Müller, F. Muñoz-Rojas, V. Mytrochenko, P. Naik, T. Nakada, R. Nandakumar, G. Napoletano, I. Nasteva, M. Needham, N. Neri, S. Neubert, N. Neufeld, J. Nicolini, D. Nicotra, E.M. Niel, L. Nisi, Q. Niu, B.K. Njoki, P. Nogarolli, P. Nogga, J. Nombela Royo, C. Normand, A. Novo Cal, J. Novoa Fernandez, G. Nowak, H.N. Nur, A. Oblakowska-Mucha, T. Oeser, O. Okhrimenko, R. Oldeman, F. Oliva, E. Olivart Pino, M. Olocco, R.H. O'Neil, J.S. Ordonez Soto, D. Osthues, J.M. Otalora Goicochea, P. Owen, A. Oyanguren, O. Ozcelik, F. Paciolla, A. Padee, K.O. Padeken, B. Pagare, T. Pajero, A. Palano, L. Palini, L. Palombini, M. Palutan, C. Pan, X. Pan, S. Panebianco, S. Paniskaki, L. Paolucci, A. Papanestis, M. Pappagallo, L.L. Pappalardo, C. Pappenheimer, C. Parkes, D. Parmar, G. Passaleva, D. Passaro, A. Pastore, M. Patel, J. Patoc, C. Patrignani, A. Paul, C.J. Pawley, A. Pellegrino, J. Peng, X. Peng, M. Pepe Altarelli, S. Perazzini, H. Pereira Da Costa, M. Pereira Martinez, A. Pereiro Castro, C. Perez, A. Perez Casas, P. Perret, A. Perrevoort, A. Perro, M.J. Peters, A. Petkovic, K. Petridis, A. Petrolini, S. Pezzulo, J.P. Pfaller, H. Pham, L. Pica, M. Piccini, L. Piccolo, B. Pietrzyk, R.N. Pilato, D. Pinci, F. Pisani, M. Pizzichemi, V.M. Placinta, M. Plo Casasus, T. Poeschl, F. Polci, M. Poli Lener, A. Poluektov, I. Polyakov, E. Polycarpo, S. Ponce, D. Popov, K. Popp, K. Prasanth, C. Prouve, D. Provenzano, V. Pugatch, A. Puicercus Gomez, G. Punzi, J.R. Pybus, Q. Qian, W. Qian, N. Qin, R. Quagliani, R.I. Rabadan Trejo, B. Rachwal, R. Racz, J.H. Rademacker, M. Rama, M. Ramírez García, V. Ramos De Oliveira, M. Ramos Pernas, G. Ramsey, M.S. Rangel, G. Raven, M. Rebollo De Miguel, F. Redi, J. Reich, F. Reiss, Z. Ren, P.K. Resmi, M. Ribalda Galvez, R. Ribatti, G. Ricart, D. Riccardi, S. Ricciardi, K. Richardson, M. Richardson-Slipper, F. Riehn, K. Rinnert, P. Robbe, G. Robertson, E. Rodrigues, A. Rodriguez Alvarez, E. Rodriguez Fernandez, J.A. Rodriguez Lopez, E. Rodriguez Rodriguez, J. Roensch, A. Rogovskiy, D.L. Rolf, P. Roloff, A. Romano, V. Romanovskiy, A. Romero Vidal, G. Romolini, F. Ronchetti, T. Rong, W. Rose, M. Rotondo, M.S. Rudolph, M. Ruiz Diaz, J. Ruiz Vidal, J. Ruz Armendariz, J.J. Saavedra-Arias, J.J. Saborido Silva, D. Sahoo, N. Sahoo, B. Saitta, M. Salomoni, I. Sanderswood, R. Santacesaria, C. Santamarina Rios, M. Santimaria, L. Santoro, E. Santovetti, A. Saputi, A. Sarnatskiy, G. Sarpis, M. Sarpis, C. Satriano, A. Satta, M. Saur, H. Sazak, F. Sborzacchi, A. Scarabotto, S. Schael, S. Scherl, M. Schiller, H. Schindler, M. Schmelling, B. Schmidt, N. Schmidt, S. Schmitt, H. Schmitz, O. Schneider, A. Schopper, N. Schulte, H. Schumacher, M.H. Schune, G. Schwering, B. Sciascia, A. Sciuccati, G. Scriven, I. Segal, S. Sellam, M. Senghi Soares, A. Sergi, N. Serra, L. Sestini, B. Sevilla Sanjuan, Y. Shang, D.M. Shangase, R.S. Sharma, L. Shchutska, T. Shears, S. Shelton, J. Shen, Z. Shen, S. Sheng, B. Shi, J. Shi, Q. Shi, W.S. Shi, E. Shmanin, R. Silva Coutinho, G. Simi, S. Simone, M. Singha, I. Siral, N. Skidmore, T. Skwarnicki, M.W. Slater, E. Smith, M. Smith, L. Soares Lavra, M.D. Sokoloff, F.J.P. Soler, A. Solomin, K. Solovieva, N.S. Sommerfeld, R. Song, Y. Song, Y. Song, Y.S. Song, F.L. Souza De Almeida, G. Souza De Castro, B. Souza De Paula, K.M. Sowa, E. Spadaro Norella, E. Spedicato, J.G. Speer, P. Spradlin, F. Stagni, M. Stahl, S. Stahl, S. Stanislaus, M. Stefaniak, O. Steinkamp, F. Suljik, J. Sun, L. Sun, M. Sun, D. Sundfeld, P. Svihra, V. Svintozelskyi, J. Swallow, K. Swientek, F. Swystun, A. Szabelski, T. Szumlak, Y. Tan, Y. Tang, Y.T. Tang, M.D. Tat, J.A. Teijeiro Jimenez, F. Terzuoli, F. Teubert, E. Thomas, D.J.D. Thompson, A.R. Thomson-Strong, R. Thornton, H. Tilquin, V. Tisserand, S. T'Jampens, M. Tobin, T.T. Todorov, L. Tomassetti, G. Tonani, X. Tong, T. Tork, L. Toscano, D.Y. Tou, C. Trippl, G. Tuci, N. Tuning, L.H. Uecker, A. Ukleja, A. Upadhyay, B. Urbach, A. Usachov, U. Uwer, V. Vagnoni, A. Vaitkevicius, A. Valassi, V. Valcarce Cadenas, G. Valenti, N. Valls Canudas, J. van Eldik, H. Van Hecke, E. van Herwijnen, C.B. Van Hulse, R. Van Laak, M. van Veghel, P. Varrella, R. Vazquez Gomez, P. Vazquez Regueiro, C. Vázquez Sierra, S. Vecchi, J. Velilla Serna, J.J. Velthuis, M. Veltri, A. Venkateswaran, M. Verdoglia, M. Vesterinen, W. Vetens, D. Vico Benet, P. Vidrier Villalba, M. Vieites Diaz, X. Vilasis-Cardona, E. Vilella Figueras, A. Villa, P. Vincent, B. Vivacqua, F.C. Volle, D. vom Bruch, K. Vos, C. Vrahas, J. Wagner, J. Walsh, N. Walter, E.J. Walton, G. Wan, A. Wang, B. Wang, C. Wang, C. Wang, G. Wang, H. Wang, J. Wang, J. Wang, J. Wang, J. Wang, M. Wang, N.W. Wang, X. Wang, X. Wang, X. Wang, X.W. Wang, Y. Wang, Y. Wang, Y.H. Wang, Z. Wang, Z. Wang, J.A. Ward, M. Waterlaat, N.K. Watson, D. Websdale, Y. Wei, Z. Weida, J. Wendel, B.D.C. Westhenry, A.S. White, C. White, M. Whitehead, E. Whiter, A.R. Wiederhold, D. Wiedner, M.A. Wiegertjes, C. Wild, G. Wilkinson, M.K. Wilkinson, M. Williams, M.J. Williams, M.R.J. Williams, R. Williams, S. Williams, Z. Williams, F.F. Wilson, M. Winn, W. Wislicki, M. Witek, L. Witola, T. Wolf, E. Wood, G. Wormser, S.A. Wotton, H. Wu, J. Wu, X. Wu, Y. Wu, Z. Wu, K. Wyllie, S. Xian, Z. Xiang, Y. Xie, T.X. Xing, A. Xu, L. Xu, M. Xu, R. Xu, Z. Xu, Z. Xu, Z. Xu, Z. Xu, S. Yadav, K. Yang, X. Yang, Y. Yang, Y. Yang, Z. Yang, Z. Yang, H. Yeung, H. Yin, X. Yin, C.Y. Yu, J. Yu, K. Yu, X. Yuan, Y Yuan, S. Zalambani, J.A. Zamora Saa, F. Zangari, M. Zavertyaev, M. Zdybal, F. Zenesini, C. Zeng, M. Zeng, S.H Zeng, C. Zhang, C. Zhang, D. Zhang, J. Zhang, L. Zhang, Q.Z. Zhang, R. Zhang, S. Zhang, S.L. Zhang, Y. Zhang, Z. Zhang, J. Zhao, M. Zhao, Y. Zhao, A. Zhelezov, S.Z. Zheng, X.Z. Zheng, Y. Zheng, T. Zhou, X. Zhou, V. Zhovkovska, L.Z. Zhu, X. Zhu, X. Zhu, Y. Zhu, V. Zhukov, J. Zhuo, T. Zies, D. Zuliani, G. Zunica, X. Zuo

Combinatorics

Characterization of tree-child networks in terms of mu vectors

Toni Fuentes, Vincent Moulton, Katharina T. Huber et al. (+1 more)

We characterize tree-child phylogenetic networks in terms of their mu-representations. First, we give a structural characterization of tree-child networks by means of ordered tree-path decompositions. We then translate this decomposition into a set of purely vectorial conditions on finite subsets M in N^n. We prove that such a set M is the mu-representation of a tree-child phylogenetic network if and only if it is tree-child mu-compatible. This provides a feasibility criterion for tree-child mu-representations which can be used as a basis for reconstruction and further algorithmic applications. Note that this paper presents results arising from ongoing research on tree-child networks and that the results will be further developed and placed into proper context in subsequent versions.
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All authors Toni Fuentes, Vincent Moulton, Katharina T. Huber, Joan Carles Pons

Audio and Speech Processing

Qwen-Audio-3.1-Realtime: Towards Reliable Agentic Voice Interaction

Lujia Bao, Qian Chen, Luyao Cheng et al. (+15 more)

Real-time voice assistants must reason over evolving requests, execute actions, and follow conversational rules. Qwen-Audio-3.1-Realtime brings these requirements together through Think, Act, and Speak and Coordinate. Think combines Core-Cocktail supervised fine-tuning with Multimodality and Multi-Teacher On-Policy Distillation (M$^{2}$-OPD) to transfer language capabilities and develop native audio skills. Act uses self-evolving executable environments and multi-granularity rollouts for Group Relative Policy Optimization (GRPO), teaching the model to use tools, interpret feedback, and complete tasks. Speak and Coordinate aligns whether, when, and how the assistant speaks or acts. We evaluate audio reasoning, multilingual understanding, tool use, conversational behavior, full-duplex interaction, and safety. Compared with Qwen-Audio-3.0-Realtime, 3.1 raises overall task success from 78.4% to 82.0% on our half-duplex speech-to-text adaptation of $\tau$-Voice. On speech-to-speech Full-Duplex-Bench v1.5, the response rate to background speech falls from 73.0% to 13.0%. We also present a separate Voice Harness prototype, using Qwen-Audio-3.0-Realtime as its foreground, that extends spoken interaction to persistent tasks through foreground–background coordination and memory.
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All authors Lujia Bao, Qian Chen, Luyao Cheng, Chong Deng, Yuxiang Kong, Xiangang Li, Xu Li, Jiaqing Liu, Chao-Hong Tan, Haoyu Wang, Wen Wang, Xilou Wang, Haoxiang Xu, Junhao Xu, Liang Yi, Binbin Zhang, Qinglin Zhang, Qiquan Zhang

Nuclear Theory

Quarkyonic matter suppresses neutron-star $g$ modes and reverses their mass trend

Probit J Kalita and Bharat Kumar

Gravity (g) modes are the only neutron-star oscillations that report on the composition of dense matter rather than on its stiffness, and work on hybrid stars has established that a first-order quark transition raises their frequency. Quarkyonic matter does the opposite. Quark-nucleon chemical equilibrium is maintained by the strong interaction, so the quarks acquire no thermodynamic freedom on an oscillation period and $c_s^2-c_e^2$ reduces to a positive-definite quadratic form in the lepton gradients alone. The nucleon momentum shell stiffens both sound speeds together instead of separating them, so the buoyancy factor collapses by a factor of 9.5 to 19 at an early transition and the core is left only weakly stratified. Solving the $l=2$ relativistic Cowling problem for ten equations of state that share one isoscalar sector, seven quarkyonic and three nucleonic controls at matched symmetry-energy slope, we found the g-mode confined to the nucleonic shell outside the core, with the horizontal flow that it lives on excluded from the core while the core is displaced almost rigidly. Its frequency falls from 158-522 Hz across the controls to $81-254$~Hz across the quarkyonic models, and by 14% at 1.4$M_\odot$ for the matched pair at $L=50\mev$; more important than the shift, it decreases with mass where the controls rise. Writing each frequency as the dynamical frequency $(GM/R^3)^{1/2}$ times a dimensionless remainder separates structure from composition. The $f$ and $p_1$ trends prove to be inherited from the mass–radius relation; the $g_1$ remainder, constant to $2-9\%$ along a nucleonic sequence, falls by a quarter to a third along a quarkyonic one and departs by a factor of two from the nucleonic $g$-mode relation at fixed compactness and $L/K_0$. These are Cowling values, lower bounds at the ten-per-cent level, and the sign of the trend survives a correction of that size.
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Representation Theory

A geometric realization of socle-projective categories for posets of type $\mathbb{D}$

Gabriel Bravo Rios, Ralf Schiffler and Robinson-Julian Serna

We introduce posets of type $\mathbb{D}$, a family of posets described by an admissible Dynkin quiver of type $D_n$ together with a compatible set of extra arrows (alien arrows), and show that their socle-projective representation category is of finite representation type. Continuing, in the same spirit, a program initiated for posets of type $\mathbb{A}$ [R. Schiffler, R-J. Serna, A geometric realization of socle-projective categories for posets of type $\mathbb{A}$, J. Pure Appl. Algebra 224 (2020), no. 12, 106436], we build on an existing geometric model for cluster-tilted algebras of type $D_n$, whose geometric combinatorics is more intricate than that of type $\mathbb{A}$. Our main result establishes a $\Bbbk$-linear categorical equivalence $\Theta$ between a full subcategory $(\mathcal C/T)_F$ of the arc category of a punctured $(n+3)$-gon, whose objects are certain $sp$-arcs, and the category of finitely generated socle-projective $\Bbbk\mathscr{P}$-modules, for $\mathscr{P}$ a poset of type $\mathbb{D}$. As a consequence, when the set of alien arrows is empty, we conclude that the cluster subalgebra generated by the $sp$-arcs coincides with the full cluster algebra.
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Cryptography and Security

Attack Success Rate Is Not a Number: On Measurement Validity in Agentic AI Security Evaluation

Chetan Pathade, Prathamesh Pawar and Shubham Patil

Attack success rate (ASR) is the headline metric in nearly every published evaluation of attacks on, and defenses for, LLM agents. We argue that ASR as currently used is not a single quantity but a family of metrics parameterized by six design choices that papers seldom specify and never hold constant across the literature. We support this with two studies that require no proprietary access. First, a full-text meta-analysis of 259 agentic-security papers posted to arXiv between February 2025 and September 2026 finds that most report neither a variance estimate nor repeated runs for their headline attack metric: 58% (95% CI 44-71) in a hand-coded random sample of 50, 65.3% by automated coding of all 259. Only 30.9% disclose enough about decoding to establish whether their evaluation was even stochastic, and of the 64 papers we confirm use an LLM judge, 29.7% report any agreement check against human labels. Second, an analytical study shows that these omissions are not cosmetic: on a 100-instance benchmark, the minimum difference in ASR detectable at conventional power is 18.2 percentage points, and two defenses whose true ASRs differ by 5 points are ranked in the wrong order by a single-run evaluation roughly 21% of the time. Because several of the six axes shift ASR in a system-dependent way, the resulting incomparability is not a constant offset that cancels in comparison. We conclude that cross-paper ASR comparison is currently unsupported, and propose a ten-item reporting checklist targeted at each failure we measure. Our aim is not to dispute any individual result but to supply the shared measurement contract the field has so far done without.
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Algebraic Geometry

Local Logarithmic Cartier Transform

Sami Fersi

This article is the first of three articles whose goal is to generalize the Cartier transform of Ogus and Vologodsky to the logarithmic setting. In this article, we generalize a local version, due to Shiho, of the Cartier transform to log smooth schemes. More precisely, let $k$ be a perfect field of positive characteristic and equip $\operatorname{Spec}k$ with the trivial logarithmic structure. For a log smooth morphism of logarithmic schemes $X \rightarrow S,$ where $S$ is log flat and locally of finite type over $\operatorname{Spec}k,$ we obtain, under the assumption that the exact relative Frobenius lifts over the Witt vectors of $k$ to a morphism between log smooth schemes over $S,$ a fully faithful functor from the category of quasi-coherent modules on the base change $X'=X\times_{S,F_S}S$ of $X$ by the Frobenius $F_S$ of $S,$ equipped with a quasi-nilpotent Higgs field, to the category of quasi-coherent modules on $X$ equipped with a quasi-nilpotent integrable connection. For this, we prove a log flat descent theorem for morphisms, based on previous work by Kato.
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Number Theory

A density version for the sum of nine cubes of primes

Kaijie Li, Tianze Wang and Xiaodong Zhao

Let $\mathbb{P}$ be the set of primes. Suppose that $P_{i}$, $i=1,2,\ldots,9$ are nine subsets of $\mathbb{P}$ with relative lower density $\underline{d}_{\mathbb{P}}(P_{i})=\mu_{i}$. When $\sum_{i=1}^{9} \mu_{i}^{3}>8$, we prove that every sufficiently large odd integer can be written as $n=\sum_{i=1}^{9} p_{i}^{3}$ with $p_{i} \in P_{i}$, $i=1,2,\ldots,9$.
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Analysis of PDEs

Universal Spacelikeness Estimates and Liouville Rigidity for Lorentzian $\sigma_k$ Curvature Equations

Shujun Shi and Yuzhou Zhang

We study nonnegative entire spacelike graphs in Lorentz–Minkowski space satisfying $\sigma_k(A[u])=u^p$. For $2\le k<n$ and $p\ge k$, pointwise strict spacelikeness and closed $k$-admissibility yield universal bounds for the height and Lorentz factor. Their proof combines block coercivity in the full Gårding cone, a Lorentzian cutoff, and hyperbolic-cap comparison. For $2\le k<n/2$ and $k\le p\le k(n+2)/(n-2k)$, every such solution vanishes, without symmetry, decay, finite-energy, curvature-pinching, or global Hessian assumptions. In the subcritical range we use a trace-free Newton tensor, a weighted divergence identity, and a finite descent. At the critical endpoint, the divergence identity retains an exact nonnegative defect and a positive quartic term. Direct estimates cover $2k<n\le4k+2$. For $n\ge4k+3$, we use compactness, concentration of the $k$-Hessian measure at the first crossing, a single-pole Pohozaev argument, core counting, a recursive defect estimate, and Souplet-type radius selection. A geometric corollary gives a rigidity result for complete spacelike immersions under the corresponding curvature equation.
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Physics and Society

Statistical physics of language change inferred from time evolving maps

James Burridge and Bert Vaux

Language change may be studied by tracking linguistic variant frequencies through space and time. Observed frequencies may be viewed as realisations of a statistical field. We first set out an efficient cross validated method for inferring the empirical field — the variant frequency distribution estimated directly from data — in our case, high resolution surveys from 20th century USA. We then derive a model of the statistical field, assuming that individuals diffuse locally, periodically migrate, and copy one another based on a form of replicator dynamics involving both bias and linguistic accommodation. We infer model parameters by comparing changes in model and empirical fields. Our inferences demonstrate that spatial linguistic patterns can be rapidly destroyed by migration but that accommodation can create them, protect them, and in combination with diffusion, produce partially predictable pattern dynamics. The results provide the strongest evidence yet for surface tension driven phase ordering in human dialects. We quantify the model's forecasting ability up to a time horizon of twenty five years using the Kullback-Leibler divergence between forecasts and observations.
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Number Theory

Moulds, Bimoulds, and some Lie algebras

Annika Burmester, Ulf Kühn and Leila Schneps

The Lie algebra of multiple zeta values is realized as the space $\operatorname{ARI}^{\operatorname{pol}}_{\underline{al}\ast \underline{il}}$ of alternal moulds whose swap is alternil up to a constant mould, equipped with the $ari$ bracket. In this paper, we study the larger space $\operatorname{BARI}_{\underline{il},swap}^{\operatorname{pol}}$ of alternil, swap-invariant bimoulds, which is conjecturally the Lie algebra for multiple $q$-zeta values. We propose an explicit formula for a Lie bracket $uri$ on this space. Moreover, we prove that the Lie algebra $\operatorname{ARI}^{\operatorname{pol}}_{\underline{al}\ast \underline{il}}$ embeds into $\operatorname{BARI}_{\underline{il},swap}^{\operatorname{pol}}$, with the $ari$ bracket translating directly into the $uri$ bracket. Finally, we examine the associated-depth graded of $\operatorname{BARI}_{\underline{il},swap}^{\operatorname{pol}}$, extending the known depth-graded setup for $\operatorname{ARI}_{\underline{al}\ast \underline{il}}^{\operatorname{pol}}$.
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Commutative Algebra

Notes on Matlis reflexive modules

Peter Schenzel

Let $M$ denote a module over a local Noetherian ring $(R,\mathfrak{m})$ with residue field $\Bbbk$ and its injective hull $E_R$. Let $D_R(\cdot) = \operatorname{Hom}_R(\cdot,E_R)$ denote the Matlis duality functor. Then $M$ is called Matlis reflexive whenever the injection $M \to D_R^2(M)$ is an isomorphism. The following results are proved: (1) For an ideal of $R$ a reflexive module is quasi-complete, generalizing part of Belshoff's results (see \cite{Br}). (2) We improve Zöschinger's numerical criterion for Matlis reflexivity (see \cite{Zh2}). (3) As shown by Enochs (see \cite{Ee}) for a prime ideal and the injective hull $E_R(R/\mathfrak{p})$ it follows that $D_R(E_R(R/\mathfrak{p}))$ is the completion of a free $R_{\mathfrak{p}}$-module of rank $\tau_{\mathfrak{p}}$, the Enochs number of $\mathfrak{p}$. We characterize when $\tau_{\mathfrak{p}} = 1$, extending author's result (see \cite{Sp16}).
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Machine Learning

Mitigating Sequential Reappearance in Diffusion Data-Point Unlearning

Donghyun Kim, Taehyuk Lee, Jinyeong Kim et al. (+4 more)

Diffusion data-point unlearning is typically evaluated immediately after each deletion, even though subsequent requests may repeatedly update the same model. We identify sequential reappearance, a failure mode in which an instance that is initially judged to be forgotten later returns to the memorized regime without reuse of the deleted data or adversarial fine-tuning. To capture this behavior, we introduce a target-level evaluation protocol that tracks whether each target is forgotten immediately, remains forgotten at the end of the sequence, or reappears during subsequent deletions. We further find that targets that later reappear exhibit sharper local denoising-loss geometry after deletion than targets that remain forgotten.
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All authors Donghyun Kim, Taehyuk Lee, Jinyeong Kim, Youngmin Oh, Dohyeong Kim, Jaehyuk Ryu, Sangwoo Hong

Artificial Intelligence

Ovis-Embedding: Pushing the Frontiers of Universal Omni-Modal Embeddings

Ovis-Embedding Team

In this report, we introduce Ovis-Embedding, a state-of-the-art omni-modal embedding family built on native integration of text, image, video, and audio. Instead of assembling separate modality towers, Ovis-Embedding uses a shared multimodal backbone to encode different modalities in a common representation space. Specifically, we make three key advances: (1) native omni-modal initialization: we adopt a pretrained Qwen-omni model as the embedding backbone and adapt it through contrastive training with low-rank initialization; (2) data-centric omni-modal training: we construct a broad, high-quality corpus spanning text, images, video, audio, and interleaved multimodal data. To improve data efficiency, we introduce homogeneous-source sampling to form task-consistent batches with informative in-batch negatives; and (3) embedding-specific training and inference optimization: we use focal loss to emphasize hard examples and similarity-based Embedding Distillation to transfer fine-grained similarity structure from complementary experts. At inference time, low-rank feature decomposition enables compact embeddings with flexible dimensionality and minimal performance loss. Empirical evaluations show that the Ovis-Embedding family achieves state-of-the-art performance on MMEB-v3, MMEB-v2, MVEB, MAEB, and RTEB, demonstrating its effectiveness across text, image, video, and audio modalities. These results highlight the potential of unified omni-modal training to overcome modality fragmentation and advance universal embedding models for any-to-any retrieval.
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Nuclear Theory

Persistent State Method for Resonances on Classical and Quantum Computers

Cong-Wu Wang, Lukas Bovermann, Evgeny Epelbaum et al. (+4 more)

We introduce a new method for extracting resonance pole positions that does not require non-Hermitian extensions of a Hamiltonian. The complex resonance poles are extracted from unitary time evolution of a persistent state, a compact trial state chosen such that its survival amplitude is governed by a single exponential over an extended time window. We solve several two- and three-body systems interacting via short- and long-range forces on a lattice and show that the pole positions obtained using the persistent state method converge approximately exponentially with the linear size of the system. We also consider a gate-based quantum implementation of our method using the Rodeo algorithm and a Hamiltonian variational ansatz, and outline an extension to two-cluster scattering.
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All authors Cong-Wu Wang, Lukas Bovermann, Evgeny Epelbaum, Hermann Krebs, Dean Lee, Yu-Gang Ma, Avik Sarkar

Machine Learning

Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian

Lakshmi Priya P. K. and Andreas Schwung

The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives, thereby facilitating a fully data-driven feedback linearization framework. Furthermore, practical closed-loop stability is established by deriving sufficient conditions under which bounded identification errors lead to bounded tracking errors. The derived theoretical results are validated through their application to an armature controlled DC motor.
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Nuclear Theory

Universal $Z^{2/3}/\sqrt{Q_\alpha}$ Scaling Law in Alpha Decay from Nuclei to Neutron-Star Mergers

Hisham Anwer, B. Salah and A. R. Abdulghany

We establish a universal scaling law for $\alpha$-decay half-lives based on the variable $X_a = Z^a/\sqrt{Q_\alpha}$, which collapses experimental and theoretical data spanning over twenty orders of magnitude onto a single linear correlation. Global optimization over the complete set of even-even $\alpha$ emitters reveals a uniquely sharp optimum at $a \simeq 2/3$. This exponent is theoretically motivated by the leading geometric scaling of heavy nuclei and emerges quantitatively from the correlated nuclear systematics, driven by the correlated $(Z, Q_\alpha)$ manifold of the nuclear chart. Strikingly, five structurally distinct semi-empirical models and an independent microscopic WKB calculation, when independently optimized with respect to the exponent $a$, yield values clustered around $2/3$, while the corresponding $a=2/3$ correlations remain highly linear without refitting the original model parameters. This emergent scaling law implies smooth variations of decay times along the heavy $r$-process path. We demonstrate analytically that, given a roughly uniform distribution of this variable, the scaling law naturally supports a quasi-power-law radioactive heating rate ($\dot{\epsilon} \propto t^{-1.24}$), consistent with full network calculations. Furthermore, integrating these scaling predictions directly into nuclear source terms for radiative-diffusion models yields multimessenger observables that accurately reproduce the kilonova AT2017gfo associated with the gravitational-wave event GW170817, demonstrating that the $Z^{2/3}/\sqrt{Q_\alpha}$ scaling coordinate provides a robust tool for modeling the radioactive engines of neutron-star mergers.
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High Energy Physics (Theory)

On Thermodynamic Universalities and Optics of B-deformed Reissner–Nordström–AdS Black Holes

Adil Belhaj and Maryem Jemri

Using machine learning techniques, we study the Reissner–Nordström–AdS black holes in the framework of extended space-time derivatives inspired by non-commutative geometry in string theory where the deformation parameters are related to the inverse of the NS-NS B-field. We refer to these solutions as B-deformed Reissner–Nordström–AdS black holes. Precisely, we examine the thermodynamic and the optical behaviors of such stringy deformed AdS black holes. Exploiting advanced numerical computations, we first examine the corresponding thermodynamic Van der Waals behaviors by calculating the universal ratios describing the P-V criticality and the Joule-Thomson expansion features. Applying such numerical results, we construct reliable training data for a fully connected neural network being developed to determine whether such stringy black hole configurations exhibit thermodynamic Van der Waals aspects. Concretely, we reveal that the fully connected and trained neural network accurately detects Van der Waals behaviors. Supported by the observational data reported by the Event Horizon Telescope international collaborations, we investigate the optical shadows of such B-deformed Reissner–Nordström–AdS black holes using machine learning methods. In order to provide corroborated models, we constraint the involved parameters including the stringy one B by making use of M87* and Sgr A* black hole empirical data.
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Chemical Physics

Reply to Comment on "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets"

Susi Lehtola, Lucas Visscher and Eberhard Engel

We reply to the Comment by Surjuse, Deng, Asadchev, and Valeev [arXiv:2603.16989] on our article "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets" [J. Chem. Phys. 152, 144105 (2020)]. We do not disagree with their work, but point out that they appear to have misinterpreted a statement in our original abstract: our suggestion to evaluate the matrix elements of the superposition of atomic potentials (SAP) using two-electron integral code was made on grounds of portability rather than as a recommendation against a dedicated one-electron implementation. Such an implementation is in fact already available in existing codes - in Dirac, for example, where a Gaussian SAP potential is formally indistinguishable from a Gaussian finite-nucleus model at the level of the nuclear attraction integral routine. We further note that both routes reduce to the same three-Gaussian overlap kernel through the Obara-Saika Laplace transform, and that SAP itself enjoys a rigorous theoretical justification through Theophilou's theorem on spherical densities and its extensions by Nagy.
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Representation Theory

Monoidal Gröbner systems and categories of affine Brauer type

Sigiswald Barbier and Léo Schelstraete

We introduce an analogue of Gröbner bases, or equivalently, Bergman's diamond lemma, for linear (super)monoidal categories. It gives a systematic way to study monoidal ideals and to prove basis theorems. The central notion is that of a monoidal Gröbner system and is based on higher linear rewriting theory. We then apply the theory to categories of affine Brauer type: linear (super)monoidal categories that have the same hom-basis as the affine Brauer category, but possibly distinct composition and tensor product. Our main result is a criterion for a category to be of affine Brauer type, reducing the question to an explicit list of local computations, which we partially implement in the computer algebra system FORM. This gives new combinatorial proofs of the basis theorems for the affine Brauer category, the nil-Brauer category and the affine VW supercategory, and yields new examples. In particular, we construct the odd nil-Brauer category, a conjectural supercategorification of the split $\imath$quantum group of rank one, and the quantized affine VW supercategory, whose non-affine part is the quantized periplectic Brauer category and which we expect to satisfy a higher quantum Schur–Weyl duality. Finally, we classify the categories of affine Brauer type admitting a sufficiently simple presentation.
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High Energy Physics (Experiment)

Observation of $\eta(2600)$ and Threshold Enhancements in the $\Lambda\bar{\Lambda}$ System

BESIII Collaboration: M. Ablikim, M. N. Achasov, P. Adlarson et al. (+740 more)

Using $2712.4 \pm 14.3$ million $\psi(3686)$ events collected with the BESIII detector, the $\Lambda\bar{\Lambda}$ system produced in $\psi(3686)$ radiative decays is studied. A model-independent partial wave analysis reveals a significant threshold enhancement structure dominated by the $^1S_0$ and $^3P_0$ partial waves, corresponding to $J^{PC} = 0^{-+}$ and $0^{++}$, respectively. In addition, a new pseudoscalar resonance, designated as $\eta(2600)$, is observed in the $^1S_0$ partial wave with a mass value consistent with the previously reported $X(2600)$ state, which represents the heaviest light meson observed to date. These results enhance our understanding of baryon-antibaryon threshold dynamics and the pseudoscalar light hadron spectroscopy.
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All authors BESIII Collaboration: M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, Y. Bai, O. Bakina, Y. Ban, H.-R. Bao, X. L. Bao, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. B. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, T. T. Chang, G. R. Che, Y. Z. Che, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. M. Chen, T. Chen, W. Chen, X. R. Chen, X. T. Chen, X. Y. Chen, Y. B. Chen, Y. Q. Chen, Z. K. Chen, J. Cheng, L. N. Cheng, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. Cottee-Meldrum, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denisenko, M. Destefanis, F. De Mori, X. X. Ding, Y. Ding, Y. Ding, Y. X. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, M. C. Du, S. X. Du, S. X. Du, X. L. Du, Y. Q. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, Y. H. Fan, J. Fang, J. Fang, S. S. Fang, W. X. Fang, Y. Q. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, L. Feng, Q. X. Feng, Y. T. Feng, M. Fritsch, C. D. Fu, J. L. Fu, Y. W. Fu, H. Gao, Y. Gao, Y. N. Gao, Y. N. Gao, Y. Y. Gao, Z. Gao, S. Garbolino, I. Garzia, L. Ge, P. T. Ge, Z. W. Ge, C. Geng, E. M. Gersabeck, A. Gilman, K. Goetzen, J. Gollub, J. B. Gong, J. D. Gong, L. Gong, W. X. Gong, W. Gradl, S. Gramigna, M. Greco, M. D. Gu, M. H. Gu, C. Y. Guan, A. Q. Guo, J. N. Guo, L. B. Guo, M. J. Guo, R. P. Guo, X. Guo, Y. P. Guo, Z. Guo, A. Guskov, J. Gutierrez, J. Y. Han, T. T. Han, X. Han, F. Hanisch, K. D. Hao, X. Q. Hao, F. A. Harris, C. Z. He, K. K. He, K. L. He, F. H. Heinsius, C. H. Heinz, Y. K. Heng, C. Herold, P. C. Hong, G. Y. Hou, X. T. Hou, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, Q. P. Hu, S. L. Hu, T. Hu, Y. Hu, Y. X. Hu, Z. M. Hu, G. S. Huang, K. X. Huang, L. Q. Huang, P. Huang, X. T. Huang, Y. P. Huang, Y. S. Huang, T. Hussain, N. Hüsken, N. in der Wiesche, J. Jackson, Q. Ji, Q. P. Ji, W. Ji, X. B. Ji, X. L. Ji, L. K. Jia, X. Q. Jia, Z. K. Jia, D. Jiang, H. B. Jiang, P. C. Jiang, S. J. Jiang, X. S. Jiang, Y. Jiang, J. B. Jiao, J. K. Jiao, Z. Jiao, L. C. L. Jin, S. Jin, Y. Jin, M. Q. Jing, X. M. Jing, T. Johansson, S. Kabana, X. L. Kang, X. S. Kang, B. C. Ke, V. Khachatryan, A. Khoukaz, O. B. Kolcu, B. Kopf, L. Kröger, L. Krümmel, Y. Y. Kuang, M. Kuessner, X. Kui, N. Kumar, A. Kupsc, W. Kühn, Q. Lan, W. N. Lan, T. T. Lei, M. Lellmann, T. Lenz, C. Li, C. Li, C. H. Li, C. K. Li, C. K. Li, D. M. Li, F. Li, G. Li, H. B. Li, H. J. Li, H. L. Li, H. N. Li, H. P. Li, Hui Li, J. S. Li, J. W. Li, K. Li, K. L. Li, L. J. Li, Lei Li, M. H. Li, M. R. Li, P. L. Li, P. R. Li, Q. M. Li, Q. X. Li, R. Li, S. Li, S. X. Li, S. Y. Li, Shanshan Li, T. Li, T. Y. Li, W. D. Li, W. G. Li, X. Li, X. H. Li, X. K. Li, X. L. Li, X. Y. Li, X. Z. Li, Y. Li, Y. G. Li, Y. P. Li, Z. H. Li, Z. J. Li, Z. L. Li, Z. X. Li, Z. Y. Li, C. Liang, H. Liang, Y. F. Liang, Y. T. Liang, G. R. Liao, L. B. Liao, M. H. Liao, Y. P. Liao, J. Libby, A. Limphirat, C. C. Lin, D. X. Lin, T. Lin, B. J. Liu, B. X. Liu, C. Liu, C. X. Liu, F. Liu, F. H. Liu, Feng Liu, G. M. Liu, H. Liu, H. B. Liu, H. M. Liu, Huihui Liu, J. B. Liu, J. J. Liu, K. Liu, K. Liu, K. Y. Liu, Ke Liu, L. Liu, L. C. Liu, Lu Liu, M. H. Liu, P. L. Liu, Q. Liu, S. B. Liu, T. Liu, W. M. Liu, W. T. Liu, X. Liu, X. K. Liu, X. L. Liu, X. P. Liu, X. Y. Liu, Y. Liu, Y. Liu, Y. B. Liu, Z. A. Liu, Z. D. Liu, Z. L. Liu, Z. Q. Liu, Z. Y. Liu, X. C. Lou, H. J. Lu, J. G. Lu, X. L. Lu, Y. Lu, Y. H. Lu, Y. P. Lu, Z. H. Lu, C. L. Luo, J. R. Luo, J. S. Luo, M. X. Luo, T. Luo, X. L. Luo, Z. Y. Lv, X. R. Lyu, Y. F. Lyu, Y. H. Lyu, F. C. Ma, H. L. Ma, Heng Ma, J. L. Ma, L. L. Ma, L. R. Ma, Q. M. Ma, R. Q. Ma, R. Y. Ma, T. Ma, X. T. Ma, X. Y. Ma, Y. M. Ma, F. E. Maas, I. MacKay, M. Maggiora, S. Malde, Q. A. Malik, H. X. Mao, Y. J. Mao, Z. P. Mao, S. Marcello, A. Marshall, F. M. Melendi, Y. H. Meng, Z. X. Meng, G. Mezzadri, H. Miao, T. J. Min, R. E. Mitchell, X. H. Mo, B. Moses, N. Yu. Muchnoi, J. Muskalla, Y. Nefedov, F. Nerling, H. Neuwirth, Z. Ning, S. Nisar, Q. L. Niu, W. D. Niu, Y. Niu, C. Normand, S. L. Olsen, Q. Ouyang, S. Pacetti, X. Pan, Y. Pan, A. Pathak, Y. P. Pei, M. Pelizaeus, G. L. Peng, H. P. Peng, X. J. Peng, Y. Y. Peng, K. Peters, K. Petridis, J. L. Ping, R. G. Ping, S. Plura, V. Prasad, F. Z. Qi, H. R. Qi, M. Qi, S. Qian, W. B. Qian, C. F. Qiao, J. H. Qiao, J. J. Qin, J. L. Qin, L. Q. Qin, L. Y. Qin, P. B. Qin, X. P. Qin, X. S. Qin, Z. H. Qin, J. F. Qiu, Z. H. Qu, J. Rademacker, C. F. Redmer, A. Rivetti, M. Rolo, G. Rong, S. S. Rong, F. Rosini, Ch. Rosner, M. Q. Ruan, N. Salone, A. Sarantsev, Y. Schelhaas, K. Schoenning, M. Scodeggio, W. Shan, X. Y. Shan, Z. J. Shang, J. F. Shangguan, L. G. Shao, M. Shao, C. P. Shen, H. F. Shen, W. H. Shen, X. Y. Shen, B. A. Shi, H. Shi, J. L. Shi, J. Y. Shi, M. H. Shi, S. Y. Shi, X. Shi, H. L. Song, J. J. Song, M. H. Song, T. Z. Song, W. M. Song, Y. X. Song, Zirong Song, S. Sosio, S. Spataro, S. Stansilaus, F. Stieler, M. Stolte, S. S Su, G. B. Sun, G. X. Sun, H. Sun, H. K. Sun, J. F. Sun, K. Sun, L. Sun, R. Sun, S. S. Sun, T. Sun, W. Y. Sun, Y. C. Sun, Y. H. Sun, Y. J. Sun, Y. Z. Sun, Z. Q. Sun, Z. T. Sun, C. J. Tang, G. Y. Tang, J. Tang, J. J. Tang, L. F. Tang, Y. A. Tang, L. Y. Tao, M. Tat, J. X. Teng, J. Y. Tian, W. H. Tian, Y. Tian, Z. F. Tian, I. Uman, E. van der Smagt, B. Wang, B. Wang, Bo Wang, C. Wang, C. Wang, Cong Wang, D. Y. Wang, H. J. Wang, H. R. Wang, J. Wang, J. J. Wang, J. P. Wang, K. Wang, L. L. Wang, L. W. Wang, M. Wang, M. Wang, N. Y. Wang, S. Wang, Shun Wang, T. Wang, T. J. Wang, W. Wang, W. P. Wang, X. F. Wang, X. L. Wang, X. N. Wang, Xin Wang, Y. Wang, Y. D. Wang, Y. F. Wang, Y. H. Wang, Y. J. Wang, Y. L. Wang, Y. N. Wang, Y. N. Wang, Yaqian Wang, Yi Wang, Yuan Wang, Z. Wang, Z. Wang, Z. L. Wang, Z. Q. Wang, Z. Y. Wang, Ziyi Wang, D. Wei, D. H. Wei, H. R. Wei, F. Weidner, S. P. Wen, U. Wiedner, G. Wilkinson, M. Wolke, J. F. Wu, L. H. Wu, L. J. Wu, Lianjie Wu, S. G. Wu, S. M. Wu, X. W. Wu, Z. Wu, H. L. Xia, L. Xia, B. H. Xiang, D. Xiao, G. Y. Xiao, H. Xiao, Y. L. Xiao, Z. J. Xiao, C. Xie, K. J. Xie, Y. Xie, Y. G. Xie, Y. H. Xie, Z. P. Xie, T. Y. Xing, D. B. Xiong, C. J. Xu, G. F. Xu, H. Y. Xu, M. Xu, Q. J. Xu, Q. N. Xu, T. D. Xu, X. P. Xu, Y. Xu, Y. C. Xu, Z. S. Xu, F. Yan, L. Yan, W. B. Yan, W. C. Yan, W. H. Yan, W. P. Yan, X. Q. Yan, Y. Y. Yan, H. J. Yang, H. L. Yang, H. X. Yang, J. H. Yang, R. J. Yang, Y. Yang, Y. H. Yang, Y. H. Yang, Y. M. Yang, Y. Q. Yang, Y. Z. Yang, Z. Y. Yang, Z. P. Yao, M. Ye, M. H. Ye, Z. J. Ye, Junhao Yin, Z. Y. You, B. X. Yu, C. X. Yu, G. Yu, J. S. Yu, L. W. Yu, T. Yu, X. D. Yu, Y. C. Yu, Y. C. Yu, C. Z. Yuan, H. Yuan, J. Yuan, J. Yuan, L. Yuan, M. K. Yuan, S. H. Yuan, Y. Yuan, C. X. Yue, Ying Yue, A. A. Zafar, F. R. Zeng, S. H. Zeng, X. Zeng, Y. J. Zeng, Y. J. Zeng, Y. C. Zhai, Y. H. Zhan, S. N. Zhang, B. L. Zhang, B. X. Zhang, D. H. Zhang, G. Y. Zhang, G. Y. Zhang, H. Zhang, H. Zhang, H. C. Zhang, H. H. Zhang, H. Q. Zhang, H. R. Zhang, H. Y. Zhang, J. Zhang, J. J. Zhang, J. L. Zhang, J. Q. Zhang, J. S. Zhang, J. W. Zhang, J. X. Zhang, J. Y. Zhang, J. Y. Zhang, J. Z. Zhang, Jianyu Zhang, Jin Zhang, L. M. Zhang, Lei Zhang, N. Zhang, P. Zhang, Q. Zhang, Q. Y. Zhang, Q. Z. Zhang, R. Y. Zhang, S. H. Zhang, Shulei Zhang, X. M. Zhang, X. Y. Zhang, Y. Zhang, Y. Zhang, Y. T. Zhang, Y. H. Zhang, Y. P. Zhang, Z. D. Zhang, Z. H. Zhang, Z. L. Zhang, Z. L. Zhang, Z. X. Zhang, Z. Y. Zhang, Z. Y. Zhang, Z. Y. Zhang, Zh. Zh. Zhang, G. Zhao, J.-P. Zhao, J. Y. Zhao, J. Z. Zhao, L. Zhao, L. Zhao, M. G. Zhao, R. P. Zhao, S. J. Zhao, Y. B. Zhao, Y. L. Zhao, Y. P. Zhao, Y. X. Zhao, Z. G. Zhao, A. Zhemchugov, B. Zheng, B. M. Zheng, J. P. Zheng, W. J. Zheng, W. Q. Zheng, X. R. Zheng, Y. H. Zheng, B. Zhong, C. Zhong, H. Zhou, J. Q. Zhou, S. Zhou, X. Zhou, X. K. Zhou, X. R. Zhou, X. Y. Zhou, Y. X. Zhou, Y. Z. Zhou, A. N. Zhu, J. Zhu, K. Zhu, K. J. Zhu, K. S. Zhu, L. X. Zhu, Lin Zhu, S. H. Zhu, T. J. Zhu, W. D. Zhu, W. J. Zhu, W. Z. Zhu, Y. C. Zhu, Z. A. Zhu, X. Y. Zhuang, J. H. Zou

Commutative Algebra

Ideal Structures in Idealizations and Cardinalities of Annihilating Ideals

Reza Nikandish

We describe the ideals of an idealization $D\ltimes M$ by triples $(I,N,\varphi)$, where $I$ is an ideal of $D$, $N$ is a submodule of $M$ with $IM\subseteq N$, and $\varphi\in\operatorname{Hom}_D(I,M/N)$. For a domain $D$ and torsion-free $M$, the nonzero proper ideals of $D\ltimes M$ with nonzero annihilator are exactly $0\ltimes N$. As an application, for $R=\mathbb R[[t]]\ltimes\mathbb R[[t]]$, the nonzero proper annihilating ideals form a countable set, while the set of all nonzero proper ideals has cardinality $2^{\aleph_0}$. This answers negatively a question of Behboodi and Rakeei.
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Instrumentation and Detectors

Pulse-shape discrimination with machine learning for CZT detectors at the DA$\Phi$NE beam test facility

Simone Manti, Francesco Artibani, Leonardo Abbene et al. (+36 more)

Cadmium zinc telluride (CZT) detectors offer versatility, operational simplicity, and room-temperature X- and gamma-ray spectroscopy, making them attractive for collider applications, yet their use under high-flux conditions remains limited. Here, we present a preliminary feature-based pulse-shape analysis employing machine learning, on data acquired with a quasi-hemispherical CZT detector at the DA$\\Phi$NE beam test facility of the National Laboratory of Frascati of INFN. A 300-MeV electron beam impinging on a lead target produced characteristic Pb X-rays together with a broad background extending up to the electron-positron annihilation region. Physically motivated temporal and morphological features were extracted from the recorded waveforms and used to distinguish nominal photon-like pulses from anomalous events. An XGBoost classifier trained and validated on 10,000 labeled waveforms achieved an accuracy of approximately 97%, with most of its classification performance reached using only a few hundred labeled examples. The trained model was applied to more than 700,000 events, substantially reducing the spectral continuum and coincidence peaks, while preserving the characteristic Pb X-ray lines up to the 511-keV annihilation peak. These preliminary results demonstrate the potential of machine-learning-assisted pulse-shape discrimination for improving CZT spectroscopy in collider environments.
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All authors Simone Manti, Francesco Artibani, Leonardo Abbene, Massimiliano Bazzi, Manuele Bettelli, Giacomo Borghi, Damir Bosnar, Mario Bragadireanu, Antonino Buttacavoli, Mario Carminati, Alberto Clozza, Francesco Clozza, Luca De Paolis, Raffaele Del Grande, Kamil Dulski, Carlo Fiorini, Ivica Friščić, Gaetano Gerardi, Carlo Guaraldo, Mihai Iliescu, Masa Iwasaki, Alexander Khreptak, Johan Marton, Pawel Moskal, Hiroaki Ohnishi, Kristian Piscicchia, Fabio Principato, Alessandro Scordo, Francesco Sgaramella, Michał Silarski, Diana Sirghi, Florin Sirghi, Magdalena Skurzok, Antonio Spallone, Kairo Toho, Oton Vazquez Doce, Andrea Zappettini, Johann Zmeskal, Catalina Curceanu

Machine Learning (Statistics)

Empirical Auditing of Edge-Private Graph Generators

Anum Fatima, Stratis Limnios, James Adams et al. (+4 more)

We empirically audit privacy leakage by testing whether outputs from edge-neighbouring inputs remain distinguishable, using statistically valid lower bounds on the privacy loss witnessed by our attacks. Our framework compares direct-edge, local-structural, and GNN-based attacks through the geometry surrounding a target edge. Experiments across two generators and two networks show that privacy leakage is both mechanism- and network-dependent, with learned representations revealing information not captured by conventional local statistics.
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All authors Anum Fatima, Stratis Limnios, James Adams, Lukasz Szpruch, Carsten Maple, Gesine Reinert, Andrew Elliott

Cryptography and Security

Benchmarking Neural Defend ARCAS 1B: A Foundational Multimodal Deepfake Detection Model

Sivashankar Selvarajan, Piyush Verma, Sumit Kumar et al. (+1 more)

AI-generated imagery evolves faster than benchmark-specific detector evaluations, making a single score an incomplete account of generalization. This paper evaluates Neural Defend ARCAS 1B across benchmark families without benchmark-specific parameter updates. We retain native aggregation and supplement it with record-level measures, coverage accounting, and subgroup diagnostics. Each Results subsection identifies the release and evaluation population, reports the official metric, and describes observed error patterns. A combined analysis synthesizes shared patterns while preserving the distinction between native and pooled quantities. Cross-paper comparisons are restricted to aligned evidence; differences in release, population, preprocessing, training, or benchmark exposure are context rather than rank. The findings characterize performance on evaluated records, not universal reliability, calibration, attribution, or future adaptive attacks. By keeping benchmark-native outcomes distinct from pooled summaries, the study makes test-population, class-balance, and missing-record-coverage differences visible. It supports interpretation of detector results in research, platform-safety, and forensic-review settings, foregrounding traceable protocol conditions over claims or leaderboard comparisons.
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All authors Sivashankar Selvarajan, Piyush Verma, Sumit Kumar, Sharayu N. Deshmukh