{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T05:22:43Z","timestamp":1774070563079,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T00:00:00Z","timestamp":1728950400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T00:00:00Z","timestamp":1728950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2019-106188GB-I00"],"award-info":[{"award-number":["PID2019-106188GB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010784","name":"Banco Santander","doi-asserted-by":"publisher","award":["21.SI03.64658"],"award-info":[{"award-number":["21.SI03.64658"]}],"id":[{"id":"10.13039\/100010784","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010784","name":"Banco Santander","doi-asserted-by":"publisher","award":["PID2022-137283NB-C21"],"award-info":[{"award-number":["PID2022-137283NB-C21"]}],"id":[{"id":"10.13039\/100010784","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010784","name":"Banco Santander","doi-asserted-by":"publisher","award":["PRE2020-092702"],"award-info":[{"award-number":["PRE2020-092702"]}],"id":[{"id":"10.13039\/100010784","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006365","name":"Universidad de Cantabria","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006365","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,6]]},"abstract":"Abstract<\/jats:title>\n Let \n \n $$\\Delta _{k}(n)$$<\/jats:tex-math>\n \n \n \n \u0394<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> denote the simplicial complex of \n \n $$(k+1)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n k<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-crossing-free subsets of edges in \n \n $${\\left( {\\begin{array}{c}[n]\\\\ 2\\end{array}}\\right) }$$<\/jats:tex-math>\n \n \n \n \n \n \n \n [<\/mml:mo>\n n<\/mml:mi>\n ]<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n \n \n \n \n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. Here \n \n $$k,n\\in \\mathbb {N}$$<\/jats:tex-math>\n \n \n k<\/mml:mi>\n ,<\/mml:mo>\n n<\/mml:mi>\n \u2208<\/mml:mo>\n N<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n $$n\\ge 2k+1$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n \u2265<\/mml:mo>\n 2<\/mml:mn>\n k<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. Jonsson (2003) proved that [neglecting the short edges that cannot be part of any \n \n $$(k+1)$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n k<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-crossing], \n \n $$\\Delta _{k}(n)$$<\/jats:tex-math>\n \n \n \n \u0394<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is a shellable sphere of dimension \n \n $$k(n-2k-1)-1$$<\/jats:tex-math>\n \n \n k<\/mml:mi>\n (<\/mml:mo>\n n<\/mml:mi>\n -<\/mml:mo>\n 2<\/mml:mn>\n k<\/mml:mi>\n -<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n -<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, and conjectured it to be polytopal. The same result and question arose in the work of Knutson and Miller (Adv Math 184(1):161-176, 2004) on subword complexes. Despite considerable effort, the only values of (k<\/jats:italic>,\u00a0n<\/jats:italic>) for which the conjecture is known to hold are \n \n $$n\\le 2k+3$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n \u2264<\/mml:mo>\n 2<\/mml:mn>\n k<\/mml:mi>\n +<\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> (Pilaud and Santos, Eur J Comb. 33(4):632\u2013662, 2012. https:\/\/doi.org\/10.1016\/j.ejc.2011.12.003<\/jats:ext-link>) and (2,\u00a08) (Bokowski and Pilaud, On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon. In: Proceedings of the 21st annual Canadian conference on computational geometry, 2009). Using ideas from rigidity theory and choosing points along the moment curve we realize \n \n $$\\Delta _{k}(n)$$<\/jats:tex-math>\n \n \n \n \u0394<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> as a polytope for \n \n $$(k,n)\\in \\{(2,9), (2,10) , (3,10)\\}$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n k<\/mml:mi>\n ,<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n \u2208<\/mml:mo>\n {<\/mml:mo>\n (<\/mml:mo>\n 2<\/mml:mn>\n ,<\/mml:mo>\n 9<\/mml:mn>\n )<\/mml:mo>\n ,<\/mml:mo>\n (<\/mml:mo>\n 2<\/mml:mn>\n ,<\/mml:mo>\n 10<\/mml:mn>\n )<\/mml:mo>\n ,<\/mml:mo>\n (<\/mml:mo>\n 3<\/mml:mn>\n ,<\/mml:mo>\n 10<\/mml:mn>\n )<\/mml:mo>\n }<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. We also realize it as a simplicial fan for all \n \n $$n\\le 13$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n \u2264<\/mml:mo>\n 13<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and arbitrary k<\/jats:italic>, except the pairs (3,\u00a012) and (3,\u00a013). Finally, we also show that for \n \n $$k\\ge 3$$<\/jats:tex-math>\n \n \n k<\/mml:mi>\n \u2265<\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n $$n\\ge 2k+6$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n \u2265<\/mml:mo>\n 2<\/mml:mn>\n k<\/mml:mi>\n +<\/mml:mo>\n 6<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> no choice of points can realize \n \n $$\\Delta _{k}(n)$$<\/jats:tex-math>\n \n \n \n \u0394<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> via bar-and-joint rigidity with points along the moment curve or, more generally, via cofactor rigidity with arbitrary points in convex position.<\/jats:p>","DOI":"10.1007\/s00454-024-00698-y","type":"journal-article","created":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T14:52:20Z","timestamp":1729003940000},"page":"973-1015","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Realizations of Multiassociahedra via Rigidity"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0317-6066","authenticated-orcid":false,"given":"Luis","family":"Crespo Ruiz","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2120-9068","authenticated-orcid":false,"given":"Francisco","family":"Santos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,10,15]]},"reference":[{"issue":"1","key":"698_CR1","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s00454-015-9691-0","volume":"54","author":"N Bergeron","year":"2015","unstructured":"Bergeron, N., Ceballos, C., Labb\u00e9, J.-P.: Fan realizations of subword complexes and multi-associahedra via Gale duality. Discrete Comput. Geom. 54(1), 195\u2013231 (2015)","journal-title":"Discrete Comput. Geom."},{"key":"698_CR2","unstructured":"Bokowski, J., Pilaud, V.: On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon. In: Proceedings of the 21st Annual Canadian Conference on Computational Geometry, Vancouver, BC, Canada, 17\u201319 Aug 2009 (2009)"},{"issue":"1","key":"698_CR3","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0095-8956(92)90003-G","volume":"56","author":"V Capoyleas","year":"1992","unstructured":"Capoyleas, V., Pach, J.: A Tur\u00e1n-type theorem on chords of a convex polygon. J. Comb. Theory B 56(1), 9\u201315 (1992)","journal-title":"J. Comb. Theory B"},{"issue":"1","key":"698_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s10801-013-0437-x","volume":"39","author":"C Ceballos","year":"2014","unstructured":"Ceballos, C., Labb\u00e9, J.-P., Stump, C.: Subword complexes, cluster complexes, and generalized multi-associahedra. J. Algebraic Comb. 39(1), 17\u201351 (2014)","journal-title":"J. Algebraic Comb."},{"issue":"5","key":"698_CR5","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/s00493-014-2959-9","volume":"35","author":"C Ceballos","year":"2015","unstructured":"Ceballos, C., Santos, F., Ziegler, G.M.: Many non-equivalent realizations of the associahedron. Combinatorica 35(5), 513\u2013551 (2015)","journal-title":"Combinatorica"},{"key":"698_CR6","doi-asserted-by":"crossref","unstructured":"Crespo Ruiz, L.: Realizations of multiassociahedra via bipartite rigidity (preprint March 2023). arXiv:2212.14265","DOI":"10.1007\/s00454-024-00698-y"},{"key":"698_CR7","doi-asserted-by":"crossref","unstructured":"Crespo Ruiz, L., Santos, F.: Bar-and-joint rigidity on the moment curve coincides with cofactor rigidity on a conic. Comb. Theory 3(1), #15 (2023)","DOI":"10.5070\/C63160428"},{"issue":"2","key":"698_CR8","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1137\/22M1527507","volume":"8","author":"L Crespo Ruiz","year":"2024","unstructured":"Crespo Ruiz, L., Santos, F.: Multitriangulations and tropical Pfaffians. SIAM J. Appl. Algebra Geom. 8(2), 302\u2013332 (2024)","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"698_CR9","volume-title":"Polyhedra","author":"PR Cromwell","year":"1997","unstructured":"Cromwell, P.R.: Polyhedra. Cambridge University Press, Cambridge (1997)"},{"key":"698_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12971-1","volume-title":"Triangulations: Structures for Algorithms and Applications","author":"JA De Loera","year":"2010","unstructured":"De Loera, J.A., Rambau, J., Santos, F.: Triangulations: Structures for Algorithms and Applications. Springer, Berlin (2010)"},{"key":"698_CR11","unstructured":"Dress, A., Gr\u00fcnewald, S., Jonsson, J., Moulton, V.: The simplicial complex $$\\Delta _{n,k}$$ of $$k$$-compatible line arrangements in the hyperbolic plane. Part 1: the structure of $$\\Delta _{n,k}$$. Unpublished manuscript (2007)"},{"issue":"5","key":"698_CR12","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1006\/eujc.2002.0582","volume":"23","author":"A Dress","year":"2002","unstructured":"Dress, A., Koolen, J.H., Moulton, V.: On line arrangements in the hyperbolic plane. Eur. J. Comb. 23(5), 549\u2013557 (2002)","journal-title":"Eur. J. Comb."},{"key":"698_CR13","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1137\/0404032","volume":"4","author":"JE Graver","year":"1991","unstructured":"Graver, J.E.: Rigidity matroids. SIAM Discrete Math. 4, 355\u2013368 (1991)","journal-title":"SIAM Discrete Math."},{"key":"698_CR14","unstructured":"Graver, J.E., Servatius, B., Servatius, H.: Combinatorial Rigidity, Graduate Studies in Mathematics, vol. 2. American Mathematical Society, Providence. ISBN 0-8218-3801-6"},{"key":"698_CR15","volume-title":"Tilings and Patterns","author":"B Gr\u00fcnbaum","year":"1989","unstructured":"Gr\u00fcnbaum, B., Shephard, G.C.: Tilings and Patterns. W. H. Freeman & Co., New York (1989)"},{"key":"698_CR16","unstructured":"Jonsson, J.: Generalized triangulations of the $$n$$-gon. Unpublished manuscript (2003)"},{"key":"698_CR17","unstructured":"Jonsson, J.: Generalized Triangulations of the $$n$$-gon, Lecture Notes in Mathematics, vol. 132, p. 281. Mathematisches Forschungsinstitut Oberwolfach, 5 Jan\u201324 May 2003 (Handwritten Abstract for the Oberwolfach Workshop Topological and Geometric Combinatorics)"},{"key":"698_CR18","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF02582930","volume":"1","author":"G Kalai","year":"1985","unstructured":"Kalai, G.: Hyperconnectivity of graphs. Graphs Comb. 1, 65\u201379 (1985)","journal-title":"Graphs Comb."},{"issue":"1","key":"698_CR19","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0001-8708(03)00142-7","volume":"184","author":"A Knutson","year":"2004","unstructured":"Knutson, A., Miller, E.: Subword complexes in Coxeter groups. Adv. Math. 184(1), 161\u2013176 (2004)","journal-title":"Adv. Math."},{"issue":"4","key":"698_CR20","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1080\/10586458.2017.1289866","volume":"27","author":"T Manneville","year":"2017","unstructured":"Manneville, T.: Fan realizations for some 2-associahedra. Exp. Math. 27(4), 377\u2013394 (2017)","journal-title":"Exp. Math."},{"key":"698_CR21","first-page":"736","volume":"29","author":"J Morgan","year":"1975","unstructured":"Morgan, J., Scott, R.: A nodal basis for $$C^1$$ piecewise polynomials of degree $$n\\ge 5$$. Math. Comput. 29, 736\u2013740 (1975)","journal-title":"Math. Comput."},{"issue":"2","key":"698_CR22","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/S0304-3975(99)00199-1","volume":"235","author":"T Nakamigawa","year":"2000","unstructured":"Nakamigawa, T.: A generalization of diagonal flips in a convex polygon. Theor. Comput. Sci. 235(2), 271\u2013282 (2000)","journal-title":"Theor. Comput. Sci."},{"key":"698_CR23","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1137\/090762051","volume":"24","author":"V-H Nguyen","year":"2010","unstructured":"Nguyen, V.-H.: On abstract rigidity matroids. SIAM Discrete Math. 24, 363\u2013369 (2010)","journal-title":"SIAM Discrete Math."},{"key":"698_CR24","doi-asserted-by":"publisher","first-page":"11946","DOI":"10.3390\/app112411946","volume":"11","author":"A Nixon","year":"2021","unstructured":"Nixon, A., Schulze, B., Whiteley, W.: Rigidity through a projective lens. Appl. Sci. 11, 11946 (2021)","journal-title":"Appl. Sci."},{"key":"698_CR25","unstructured":"Oberwolfach Workshop: Topological and Geometric Combinatorics (Bj\u00f6rner, A., Kalai, G., Ziegler, G.M., orgs.), 6\u2013 12 April 2003, Mathematisches Forschungsinstitut Oberwolfach, Report No. 16\/2003"},{"key":"698_CR26","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1007\/s00454-012-9408-6","volume":"41","author":"V Pilaud","year":"2012","unstructured":"Pilaud, V., Pocchiola, M.: Multitriangulations, pseudotriangulations and primitive sorting networks. Discrete Comput. Geom. 41, 142\u2013191 (2012)","journal-title":"Discrete Comput. Geom."},{"key":"698_CR27","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1007\/s00454-008-9078-6","volume":"41","author":"V Pilaud","year":"2009","unstructured":"Pilaud, V., Santos, F.: Multitriangulations as complexes of star polygons. Discrete Comput. Geom. 41, 284\u2013317 (2009)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"698_CR28","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1016\/j.ejc.2011.12.003","volume":"33","author":"V Pilaud","year":"2012","unstructured":"Pilaud, V., Santos, F.: The brick polytope of a sorting network. Eur. J. Comb. 33(4), 632\u2013662 (2012)","journal-title":"Eur. J. Comb."},{"key":"698_CR29","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s00013-023-01895-6","volume":"121","author":"V Pilaud","year":"2023","unstructured":"Pilaud, V., Santos, F., Ziegler, G.M.: Celebrating Loday\u2019s associahedron. Arch. Math. 121, 559\u2013601 (2023)","journal-title":"Arch. Math."},{"issue":"4","key":"698_CR30","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1287\/moor.5.4.576","volume":"5","author":"S Provan","year":"1980","unstructured":"Provan, S., Billera, L.: Decompositions of simplicial complexes related to diameters of convex polyhedra. Math. Oper. Res. 5(4), 576\u2013594 (1980)","journal-title":"Math. Oper. Res."},{"key":"698_CR31","first-page":"129","volume-title":"Perspectives on Projective Geometry","author":"J Richter-Gebert","year":"2010","unstructured":"Richter-Gebert, J.: Perspectives on Projective Geometry, pp. 129\u2013143. Springer, Berlin (2010)"},{"key":"698_CR32","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/978-3-642-55566-4_33","volume-title":"Discrete and Computational Geometry\u2014The Goodman\u2013Pollack Festschrift: Algorithms and Combinatorics","author":"G Rote","year":"2003","unstructured":"Rote, G., Santos, F., Streinu, I.: Expansive motions and the polytope of pointed pseudo-triangulations. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds.) Discrete and Computational Geometry\u2014The Goodman\u2013Pollack Festschrift: Algorithms and Combinatorics, vol. 25, pp. 699\u2013736. Springer, Berlin (2003)"},{"issue":"6","key":"698_CR33","doi-asserted-by":"publisher","first-page":"1794","DOI":"10.1016\/j.jcta.2011.03.001","volume":"118","author":"C Stump","year":"2011","unstructured":"Stump, C.: A new perspective on $$k$$-triangulations. J. Comb. Theory A 118(6), 1794\u20131800 (2011)","journal-title":"J. Comb. Theory A"},{"key":"698_CR34","first-page":"23","volume":"16","author":"W Whiteley","year":"1990","unstructured":"Whiteley, W.: Vertex splitting in isostatic frameworks. Struct. Topol. 16, 23\u201330 (1990)","journal-title":"Struct. Topol."},{"key":"698_CR35","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1090\/conm\/197\/02540","volume-title":"Matroid Theory: Contemporary Mathematics","author":"W Whiteley","year":"1996","unstructured":"Whiteley, W.: Some matroids from discrete applied geometry. In: Bonin, J.E., Oxley, J.G., Servatius, B. (eds.) Matroid Theory: Contemporary Mathematics, vol. 197, pp. 171\u2013311. Oxford University Press, Oxford (1996)"},{"key":"698_CR36","volume-title":"Geometry of Bivariate Splines","author":"W Whiteley","year":"1987","unstructured":"Whiteley, W.: Geometry of Bivariate Splines. Researchgate, Berlin (1987). (preprint)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00698-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-024-00698-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00698-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T18:49:35Z","timestamp":1746816575000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-024-00698-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,15]]},"references-count":36,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["698"],"URL":"https:\/\/doi.org\/10.1007\/s00454-024-00698-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,15]]},"assertion":[{"value":"26 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 September 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}