@article{lieb1984, author = {Lieb, E. H.}, title = {Bound on the maximum negative ionization of atoms and molecules}, journal = {Phys. Rev. A}, volume = {29}, number = {6}, pages = {3018--3028}, year = {1984}, doi = {10.1103/PhysRevA.29.3018}, url = {https://doi.org/10.1103/PhysRevA.29.3018} } @article{nam2012, author = {Nam, P. T.}, title = {New bounds on the maximum ionization of atoms}, journal = {Commun. Math. Phys.}, volume = {312}, pages = {427--445}, year = {2012}, doi = {10.1007/s00220-012-1479-y}, url = {https://doi.org/10.1007/s00220-012-1479-y}, note = {1009.2367}, archivePrefix = {arXiv}, primaryClass = {math-ph} } @article{sims2017, author = {Sims, J. S.}, title = {{Hylleraas-Configuration Interaction} study of the {$^{1}S$} ground state of the negative {Li} ion}, journal = {J. Phys. B: At. Mol. Opt. Phys.}, volume = {50}, number = {24}, pages = {245003}, eid = {245003}, year = {2017}, doi = {10.1088/1361-6455/aa961e}, url = {https://doi.org/10.1088/1361-6455/aa961e} } @article{king1995, author = {King, F. W.}, title = {Lower bound for the nonrelativistic ground state energy of the lithium atom}, journal = {J. Chem. Phys.}, volume = {102}, number = {20}, pages = {8053--8058}, year = {1995}, doi = {10.1063/1.469004}, url = {https://doi.org/10.1063/1.469004} } @article{bellazzini2014, author = {Bellazzini, J. and Frank, R. L. and Lieb, E. H. and Seiringer, R.}, title = {Existence of ground states for negative ions at the binding threshold}, journal = {Rev. Math. Phys.}, volume = {26}, number = {1}, pages = {1350021}, eid = {1350021}, year = {2014}, doi = {10.1142/S0129055X13500219}, url = {https://doi.org/10.1142/S0129055X13500219}, note = {1301.5370}, archivePrefix = {arXiv}, primaryClass = {math-ph} } @book{teschl2009, author = {Teschl, G.}, title = {Mathematical Methods in Quantum Mechanics: With Applications to {Schr{\"o}dinger} Operators}, series = {Graduate Studies in Mathematics}, volume = {99}, edition = {1}, publisher = {American Mathematical Society}, address = {Providence, RI}, year = {2009}, isbn = {978-0-8218-4660-5}, doi = {10.1090/gsm/099}, url = {https://doi.org/10.1090/gsm/099} } @article{fournais2009, author = {Fournais, S. and Hoffmann-Ostenhof, M. and Hoffmann-Ostenhof, T. and {{\O}stergaard S{\o}rensen}, T.}, title = {Analytic structure of many-body {Coulombic} wave functions}, journal = {Commun. Math. Phys.}, volume = {289}, number = {1}, pages = {291--310}, year = {2009}, doi = {10.1007/s00220-008-0664-5}, url = {https://doi.org/10.1007/s00220-008-0664-5}, note = {0806.1004}, archivePrefix = {arXiv}, primaryClass = {math-ph} } @misc{Ju+26, author = {Ju, Haocheng and Gao, Guoxiong and Jiang, Jiedong and Wu, Bin and Sun, Zeming and Liu, Shurui and Chen, Leheng and Wang, Yutong and Wang, Yuefeng and Wang, Zichen and He, Wanyi and Wu, Peihao and Xiao, Liang and Liu, Ruochuan and Dai, Bryan and Dong, Bin}, title = {Automated Conjecture Resolution with Formal Verification}, year = {2026}, doi = {10.48550/arXiv.2604.03789}, url = {https://doi.org/10.48550/arXiv.2604.03789}, note = {2604.03789}, archivePrefix = {arXiv}, primaryClass = {cs.LG} } % 118 is the newsletter issue, not a volume. The unchanged style % issues one harmless 'number but no volume' warning for this record. @article{nam2020, author = {Nam, P. T.}, title = {The ionization problem}, journal = {EMS Newsl.}, volume = {118}, pages = {22--27}, year = {2020}, doi = {10.4171/NEWS/118/6}, url = {https://doi.org/10.4171/NEWS/118/6} } % Chapter pages/identity verified against Simon's own publication list. @incollection{simon2000, author = {Simon, B.}, title = {{Schr{\"o}dinger} operators in the twenty-first century}, booktitle = {Mathematical Physics 2000}, editor = {Fokas, A. and Grigoryan, A. and Kibble, T. and Zegarlinski, B.}, publisher = {Imperial College Press}, address = {London}, pages = {283--288}, year = {2000}, doi = {10.1142/9781848160224\_0014}, url = {https://doi.org/10.1142/9781848160224_0014}, repositoryId = {00-78}, archivePrefix = {mp_arc}, eprinturl = {https://web.ma.utexas.edu/mp_arc-bin/mpa?yn=00-78} } @article{andersen2004, author = {Andersen, T.}, title = {Atomic negative ions: structure, dynamics and collisions}, journal = {Phys. Rep.}, volume = {394}, number = {4--5}, pages = {157--313}, year = {2004}, doi = {10.1016/j.physrep.2004.01.001}, url = {https://doi.org/10.1016/j.physrep.2004.01.001} } @article{ruskai1982a, author = {Ruskai, M. B.}, title = {Absence of discrete spectrum in highly negative ions}, journal = {Commun. Math. Phys.}, volume = {82}, pages = {457--469}, year = {1982}, doi = {10.1007/BF01961235}, url = {https://doi.org/10.1007/BF01961235} } @article{ruskai1982b, author = {Ruskai, M. B.}, title = {Absence of discrete spectrum in highly negative ions. {II}. {Extension} to fermions}, journal = {Commun. Math. Phys.}, volume = {85}, pages = {325--327}, year = {1982}, doi = {10.1007/BF01254463}, url = {https://doi.org/10.1007/BF01254463} } @article{sigal1982, author = {Sigal, I. M.}, title = {Geometric methods in the quantum many-body problem. {Nonexistence} of very negative ions}, journal = {Commun. Math. Phys.}, volume = {85}, pages = {309--324}, year = {1982}, doi = {10.1007/BF01254462}, url = {https://doi.org/10.1007/BF01254462} } @article{sigal1984, author = {Sigal, I. M.}, title = {How many electrons can a nucleus bind?}, journal = {Ann. Phys.}, volume = {157}, number = {2}, pages = {307--320}, year = {1984}, doi = {10.1016/0003-4916(84)90062-9}, url = {https://doi.org/10.1016/0003-4916(84)90062-9} } @article{bethe1929, author = {Bethe, H.}, title = {Berechnung der {Elektronenaffinit{\"a}t} des {Wasserstoffs}}, journal = {Z. Phys.}, volume = {57}, pages = {815--821}, year = {1929}, doi = {10.1007/BF01340659}, url = {https://doi.org/10.1007/BF01340659} } @article{hylleraas1930, author = {Hylleraas, E. A.}, title = {Die {Elektronenaffinit{\"a}t} des {Wasserstoffatoms} nach der {Wellenmechanik}}, journal = {Z. Phys.}, volume = {60}, pages = {624--630}, year = {1930}, doi = {10.1007/BF01339758}, url = {https://doi.org/10.1007/BF01339758} } @article{hill1977, author = {Hill, R. N.}, title = {Proof that the {$\mathrm{H}^{-}$} ion has only one bound state}, journal = {Phys. Rev. Lett.}, volume = {38}, number = {12}, pages = {643--646}, year = {1977}, doi = {10.1103/PhysRevLett.38.643}, url = {https://doi.org/10.1103/PhysRevLett.38.643} } @article{lieb1988, author = {Lieb, E. H. and Sigal, I. M. and Simon, B. and Thirring, W.}, title = {Approximate neutrality of large-{$Z$} ions}, journal = {Commun. Math. Phys.}, volume = {116}, number = {4}, pages = {635--644}, year = {1988}, doi = {10.1007/BF01224904}, url = {https://doi.org/10.1007/BF01224904} } @article{fefferman1990, author = {Fefferman, C. L. and Seco, L. A.}, title = {Asymptotic neutrality of large ions}, journal = {Commun. Math. Phys.}, volume = {128}, number = {1}, pages = {109--130}, year = {1990}, doi = {10.1007/BF02097048}, url = {https://doi.org/10.1007/BF02097048} } @article{seco1990, author = {Seco, L. A. and Sigal, I. M. and Solovej, J. P.}, title = {Bound on the ionization energy of large atoms}, journal = {Commun. Math. Phys.}, volume = {131}, number = {2}, pages = {307--315}, year = {1990}, doi = {10.1007/BF02161416}, url = {https://doi.org/10.1007/BF02161416} } @misc{hundertmark2025, author = {Hundertmark, D. and Pattakos, N. and Schulz, M. R.}, title = {On the excess charge problem of atoms}, year = {2025}, note = {2504.18487}, archivePrefix = {arXiv}, primaryClass = {math-ph}, doi = {10.48550/arXiv.2504.18487}, url = {https://doi.org/10.48550/arXiv.2504.18487} } % No DOI is assigned in the Hexagon record; version 1 is intentional. @misc{shelley2026, author = {Shelley, A. and Tartakovsky, D. M.}, title = {A bound helium dianion does not exist}, year = {2026}, eprint = {2611.00041v1}, archivePrefix = {Hexagon}, primaryClass = {math-ph}, url = {https://hexagonmath.org/2611.00041v1} } @article{hoffmann1983, author = {Hoffmann-Ostenhof, M. and Hoffmann-Ostenhof, T. and Simon, B.}, title = {A multiparticle {Coulomb} system with bound state at threshold}, journal = {J. Phys. A: Math. Gen.}, volume = {16}, number = {6}, pages = {1125--1131}, year = {1983}, doi = {10.1088/0305-4470/16/6/007}, url = {https://doi.org/10.1088/0305-4470/16/6/007} } @article{gridnev2012, author = {Gridnev, D. K.}, title = {Bound states at threshold resulting from {Coulomb} repulsion}, journal = {J. Math. Phys.}, volume = {53}, number = {10}, pages = {102108}, eid = {102108}, year = {2012}, doi = {10.1063/1.4758076}, url = {https://doi.org/10.1063/1.4758076}, note = {1112.1234}, archivePrefix = {arXiv}, primaryClass = {math-ph} } @article{haeffler1996, author = {Haeffler, G. and Hanstorp, D. and Kiyan, I. and Klinkm{\"u}ller, A. E. and Ljungblad, U. and Pegg, D. J.}, title = {Electron affinity of {Li}: A state-selective measurement}, journal = {Phys. Rev. A}, volume = {53}, number = {6}, pages = {4127--4131}, year = {1996}, doi = {10.1103/PhysRevA.53.4127}, url = {https://doi.org/10.1103/PhysRevA.53.4127}, note = {physics/9703013}, archivePrefix = {arXiv}, primaryClass = {physics.atom-ph} } @article{hales2017, author = {Hales, Thomas and Adams, Mark and Bauer, Gertrud and Dang, Tat Dat and Harrison, John and Hoang, Le Truong and Kaliszyk, Cezary and Magron, Victor and McLaughlin, Sean and Nguyen, Tat Thang and Nguyen, Quang Truong and Nipkow, Tobias and Obua, Steven and Pleso, Joseph and Rute, Jason and Solovyev, Alexey and Ta, Thi Hoai An and Tran, Nam Trung and Trieu, Thi Diep and Urban, Josef and Vu, Ky and Zumkeller, Roland}, title = {A formal proof of the {Kepler} conjecture}, journal = {Forum Math. Pi}, volume = {5}, pages = {e2}, eid = {e2}, year = {2017}, doi = {10.1017/fmp.2017.1}, url = {https://doi.org/10.1017/fmp.2017.1}, note = {1501.02155}, archivePrefix = {arXiv}, primaryClass = {math.MG} } @book{tucker2011, author = {Tucker, W.}, title = {Validated Numerics: A Short Introduction to Rigorous Computations}, publisher = {Princeton University Press}, address = {Princeton, NJ}, year = {2011}, isbn = {978-0-691-14781-9}, doi = {10.1515/9781400838974}, url = {https://doi.org/10.1515/9781400838974} } @misc{hofacker2026, author = {Hofacker, M.}, title = {Rigorous lower bounds for atomic and ionic ground-state energies}, year = {2026}, note = {2610.34480}, archivePrefix = {arXiv}, primaryClass = {math-ph}, doi = {10.48550/arXiv.2610.34480}, url = {https://doi.org/10.48550/arXiv.2610.34480} } @article{ireland2022lower, author = {Ireland, Robbie T. and Jeszenszki, Peter and M{\'a}tyus, Edit and Martinazzo, Rocco and Ronto, Miklos and Pollak, Eli}, title = {Lower Bounds for Nonrelativistic Atomic Energies}, journal = {ACS Phys. Chem. Au}, volume = {2}, number = {1}, pages = {23--37}, year = {2022}, doi = {10.1021/acsphyschemau.1c00018}, url = {https://doi.org/10.1021/acsphyschemau.1c00018} }