{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:41:29Z","timestamp":1758404489474,"version":"3.37.3"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T00:00:00Z","timestamp":1681948800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T00:00:00Z","timestamp":1681948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2024,3]]},"DOI":"10.1007\/s00454-023-00501-4","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T19:46:19Z","timestamp":1682019979000},"page":"688-707","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Discrete $$\\ell ^{1}$$ Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution"],"prefix":"10.1007","volume":"71","author":[{"given":"Parker","family":"Duncan","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0174-1786","authenticated-orcid":false,"given":"Rory","family":"O\u2019Dwyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Eviatar B.","family":"Procaccia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,20]]},"reference":[{"issue":"1","key":"501_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02097679","volume":"131","author":"K Alexander","year":"1990","unstructured":"Alexander, K., Chayes, J.T., Chayes, L.: The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation. Commun. Math. Phys. 131(1), 1\u201350 (1990)","journal-title":"Commun. Math. Phys."},{"key":"501_CR2","doi-asserted-by":"crossref","unstructured":"Alonso, L., Cerf, R.: The three dimensional polyominoes of minimal area. Electron. J. Combin. 3(1), #\u00a0R27 (1996)","DOI":"10.37236\/1251"},{"issue":"9","key":"501_CR3","doi-asserted-by":"publisher","first-page":"1483","DOI":"10.1002\/cpa.21558","volume":"68","author":"M Biskup","year":"2015","unstructured":"Biskup, M., Louidor, O., Procaccia, E.B., Rosenthal, R.: Isoperimetry in two-dimensional percolation. Commun. Pure Appl. Math. 68(9), 1483\u20131531 (2015)","journal-title":"Commun. Pure Appl. Math."},{"issue":"3","key":"501_CR4","doi-asserted-by":"publisher","first-page":"1033","DOI":"10.1063\/1.533180","volume":"41","author":"T Bodineau","year":"2000","unstructured":"Bodineau, T., Ioffe, D., Velenik, Y.: Rigorous probabilistic analysis of equilibrium crystal shapes. J.\u00a0Math. Phys. 41(3), 1033\u20131098 (2000)","journal-title":"J.\u00a0Math. Phys."},{"key":"501_CR5","volume-title":"The Wulff Crystal in Ising and Percolation Models. Lecture Notes in Mathematics","author":"R Cerf","year":"2006","unstructured":"Cerf, R.: The Wulff Crystal in Ising and Percolation Models. Lecture Notes in Mathematics, vol. 1878. Springer, Berlin (2006)"},{"key":"501_CR6","doi-asserted-by":"crossref","unstructured":"Duncan, P., O\u2019Dwyer, R., Procaccia, E.B.: An elementary proof for the double bubble problem in $$\\ell ^1$$ norm. J. Geom. Anal. 33(1), #\u00a031 (2023)","DOI":"10.1007\/s12220-022-01008-9"},{"issue":"1","key":"501_CR7","doi-asserted-by":"publisher","first-page":"47","DOI":"10.2140\/pjm.1993.159.47","volume":"159","author":"J Foisy","year":"1993","unstructured":"Foisy, J., Alfaro, M., Brock, J., Hodges, N., Zimba, J.: The standard double soap bubble in $$\\textbf{R}^2$$ uniquely minimizes perimeter. Pac. J. Math. 159(1), 47\u201359 (1993)","journal-title":"Pac. J. Math."},{"key":"501_CR8","unstructured":"Friedrich, M., G\u00f3rny, W., Stefanelli, U.: The double-bubble problem on the square lattice (2021). arXiv:2109.01697"},{"issue":"2","key":"501_CR9","doi-asserted-by":"publisher","first-page":"459","DOI":"10.2307\/3062123","volume":"155","author":"M Hutchings","year":"2002","unstructured":"Hutchings, M., Morgan, F., Ritor\u00e9, M., Ros, A.: Proof of the double bubble conjecture. Ann. Math. 155(2), 459\u2013489 (2002)","journal-title":"Ann. Math."},{"key":"501_CR10","unstructured":"Milman, E., Neeman, J.: The Gaussian double-bubble conjecture (2018). arXiv:1801.09296"},{"issue":"1","key":"501_CR11","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BF02922110","volume":"8","author":"F Morgan","year":"1998","unstructured":"Morgan, F., French, Ch., Greenleaf, S.: Wulff clusters in $${ {\\bf R}}^2$$. J. Geom. Anal. 8(1), 97\u2013115 (1998)","journal-title":"J. Geom. Anal."},{"key":"501_CR12","doi-asserted-by":"crossref","unstructured":"Procaccia, E.B., Rosenthal, R.: Concentration estimates for the isoperimetric constant of the supercritical percolation cluster. Electron. Commun. Probab. 17, #\u00a030 (2012)","DOI":"10.1214\/ECP.v17-2185"},{"issue":"3\u20134","key":"501_CR13","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1007\/s00440-015-0668-y","volume":"166","author":"EB Procaccia","year":"2016","unstructured":"Procaccia, E.B., Rosenthal, R., Sapozhnikov, A.: Quenched invariance principle for simple random walk on clusters in correlated percolation models. Probab. Theory Relat. Fields 166(3\u20134), 619\u2013657 (2016)","journal-title":"Probab. Theory Relat. Fields"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00501-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-023-00501-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00501-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T23:02:18Z","timestamp":1707001338000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-023-00501-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,20]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["501"],"URL":"https:\/\/doi.org\/10.1007\/s00454-023-00501-4","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2023,4,20]]},"assertion":[{"value":"17 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}