{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T17:20:17Z","timestamp":1785345617706,"version":"3.55.0"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100007797","name":"University of Helsinki","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100007797","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This work describes and analyzes the domain derivative for a time-dependent acoustic scattering problem. We study the nonlinear operator that maps a sound-soft scattering object to the solution of the time-dependent wave equation evaluated at a finite number of points away from the obstacle. The Fr\u00e9chet derivative of this operator with respect to variations of the scatterer coincides with point evaluations of the temporal domain derivative. The latter is the solution to another time-dependent scattering problem, for which a well-posedness result is shown under sufficient temporal regularity of the incoming wave. Applying convolution quadrature to this scattering problem gives a stable and provably convergent semi-discretization in time, provided that the incoming wave is sufficient regular. Using the discrete domain derivative in a Gauss\u2013Newton method, we describe an efficient algorithm to reconstruct the boundary of an unknown scattering object from time domain measurements in a few points away from the boundary. Numerical examples for the acoustic wave equation in two dimensions demonstrate the performance of the method.<\/jats:p>","DOI":"10.1007\/s00211-025-01481-8","type":"journal-article","created":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T09:38:47Z","timestamp":1761989927000},"page":"195-227","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The temporal domain derivative in inverse acoustic obstacle scattering"],"prefix":"10.1007","volume":"158","author":[{"given":"Marvin","family":"Kn\u00f6ller","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f6rg","family":"Nick","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,11,1]]},"reference":[{"key":"1481_CR1","doi-asserted-by":"crossref","unstructured":"Abramowitz, M., Stegun, I.\u00a0A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables, volume No. 55 of National Bureau of Standards Applied Mathematics Series. U. S. Government Printing Office, Washington, DC, (1964)","DOI":"10.1115\/1.3625776"},{"issue":"3","key":"1481_CR2","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1002\/mma.1670080127","volume":"8","author":"A Bamberger","year":"1986","unstructured":"Bamberger, A., Duong, T.H.: Formulation variationnelle espace-temps pour le calcul par potentiel retard\u00e9 de la diffraction d\u2019une onde acoustique. I. Math. Methods Appl. Sci. 8(3), 405\u2013435 (1986). https:\/\/doi.org\/10.1002\/mma.1670080127","journal-title":"I. Math. Methods Appl. Sci."},{"issue":"5","key":"1481_CR3","doi-asserted-by":"publisher","first-page":"2964","DOI":"10.1137\/090775981","volume":"32","author":"L Banjai","year":"2010","unstructured":"Banjai, L.: Multistep and multistage convolution quadrature for the wave equation: Algorithms and experiments. SIAM J. Sci. Comput. 32(5), 2964\u20132994 (2010). https:\/\/doi.org\/10.1137\/090775981","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"1481_CR4","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1007\/s00211-024-01429-4","volume":"156","author":"L Banjai","year":"2024","unstructured":"Banjai, L., Ferrari, M.: Runge-Kutta convolution quadrature based on Gauss methods. Numer. Math. 156(5), 1719\u20131750 (2024). https:\/\/doi.org\/10.1007\/s00211-024-01429-4","journal-title":"Numer. Math."},{"issue":"3","key":"1481_CR5","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1093\/imanum\/dry033","volume":"39","author":"L Banjai","year":"2019","unstructured":"Banjai, L., Lubich, C.: Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations. IMA J. Numer. Anal. 39(3), 1134\u20131157 (2019). https:\/\/doi.org\/10.1093\/imanum\/dry033","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1481_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00211-011-0378-z","volume":"119","author":"L Banjai","year":"2011","unstructured":"Banjai, L., Lubich, C., Melenk, J.M.: Runge-Kutta convolution quadrature for operators arising in wave propagation. Numer. Math. 119(1), 1\u201320 (2011). https:\/\/doi.org\/10.1007\/s00211-011-0378-z","journal-title":"Numer. Math."},{"issue":"312","key":"1481_CR7","doi-asserted-by":"publisher","first-page":"1783","DOI":"10.1090\/mcom\/3279","volume":"87","author":"L Banjai","year":"2018","unstructured":"Banjai, L., Rieder, A.: Convolution quadrature for the wave equation with a nonlinear impedance boundary condition. Math. Comp. 87(312), 1783\u20131819 (2018). https:\/\/doi.org\/10.1090\/mcom\/3279","journal-title":"Math. Comp."},{"key":"1481_CR8","doi-asserted-by":"publisher","unstructured":"Banjai, L., Sayas, F.-J.: Integral Equation Methods for Evolutionary PDE: A Convolution Quadrature Approach, volume\u00a059 of Springer Series in Computational Mathematics. Springer, Cham, (2022). https:\/\/doi.org\/10.1007\/978-3-031-13220-9","DOI":"10.1007\/978-3-031-13220-9"},{"issue":"9","key":"1481_CR9","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1016\/S0764-4442(98)80066-9","volume":"326","author":"J Cagnol","year":"1998","unstructured":"Cagnol, J., Zol\u00e9sio, J.-P.: Hidden shape derivative in the wave equation with Dirichlet boundary condition. C. R. Acad. Sci. Paris S\u00e9r. I Math. 326(9), 1079\u20131084 (1998). https:\/\/doi.org\/10.1016\/S0764-4442(98)80066-9","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"issue":"2","key":"1481_CR10","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1006\/jdeq.1999.3643","volume":"158","author":"J Cagnol","year":"1999","unstructured":"Cagnol, J., Zol\u00e9sio, J.-P.: Shape derivative in the wave equation with Dirichlet boundary conditions. J. Differential Equations 158(2), 175\u2013210 (1999). https:\/\/doi.org\/10.1006\/jdeq.1999.3643","journal-title":"J. Differential Equations"},{"issue":"2","key":"1481_CR11","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1137\/18M1214809","volume":"51","author":"F Cakoni","year":"2019","unstructured":"Cakoni, F., Haddar, H., Lechleiter, A.: On the factorization method for a far field inverse scattering problem in the time domain. SIAM J. Math. Anal. 51(2), 854\u2013872 (2019). https:\/\/doi.org\/10.1137\/18M1214809","journal-title":"SIAM J. Math. Anal."},{"issue":"3","key":"1481_CR12","doi-asserted-by":"publisher","first-page":"667","DOI":"10.2140\/apde.2021.14.667","volume":"14","author":"F Cakoni","year":"2021","unstructured":"Cakoni, F., Monk, P., Selgas, V.: Analysis of the linear sampling method for imaging penetrable obstacles in the time domain. Anal. PDE 14(3), 667\u2013688 (2021). https:\/\/doi.org\/10.2140\/apde.2021.14.667","journal-title":"Anal. PDE"},{"key":"1481_CR13","doi-asserted-by":"publisher","unstructured":"Chen, Q., Haddar, H., Lechleiter, A., Monk, P.: A sampling method for inverse scattering in the time domain. Inverse Problems, 26(8): 085001, 17, (2010). https:\/\/doi.org\/10.1088\/0266-5611\/26\/8\/085001","DOI":"10.1088\/0266-5611\/26\/8\/085001"},{"issue":"1","key":"1481_CR14","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s00020-012-1955-y","volume":"73","author":"M Costabel","year":"2012","unstructured":"Costabel, M., Le Lou\u00ebr, F.: Shape derivatives of boundary integral operators in electromagnetic scattering. Part II: Application to scattering by a homogeneous dielectric obstacle. Integral Equations Operator Theory 73(1), 17\u201348 (2012). https:\/\/doi.org\/10.1007\/s00020-012-1955-y","journal-title":"Integral Equations Operator Theory"},{"issue":"1","key":"1481_CR15","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.camwa.2013.11.005","volume":"67","author":"V Dom\u00ednguez","year":"2014","unstructured":"Dom\u00ednguez, V., Lu, S.L., Sayas, F.-J.: A Nystr\u00f6m flavored Calder\u00f3n calculus of order three for two dimensional waves, time-harmonic and transient. Comput. Math. Appl. 67(1), 217\u2013236 (2014). https:\/\/doi.org\/10.1016\/j.camwa.2013.11.005","journal-title":"Comput. Math. Appl."},{"key":"1481_CR16","doi-asserted-by":"publisher","unstructured":"Fink, L., Hettlich, F.: The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition. Inverse Problems, 40(1):Paper No. 015001, 22, (2024). https:\/\/doi.org\/10.1088\/1361-6420\/ad0c92","DOI":"10.1088\/1361-6420\/ad0c92"},{"key":"1481_CR17","doi-asserted-by":"publisher","unstructured":"Gilbarg, D., Trudinger, N.\u00a0S.: Elliptic partial differential equations of second order. Grundlehren der Mathematischen Wissenschaften, Vol. 224. Springer, Berlin-New York, (1977) . https:\/\/doi.org\/10.1007\/978-3-642-96379-7","DOI":"10.1007\/978-3-642-96379-7"},{"issue":"9","key":"1481_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/29\/9\/095016","volume":"29","author":"Y Guo","year":"2013","unstructured":"Guo, Y., Monk, P., Colton, D.: Toward a time domain approach to the linear sampling method. Inverse Problems 29(9), 095016 (2013). https:\/\/doi.org\/10.1088\/0266-5611\/29\/9\/095016","journal-title":"Inverse Problems"},{"issue":"1","key":"1481_CR19","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1137\/S0036139903435413","volume":"65","author":"H Haddar","year":"2004","unstructured":"Haddar, H., Kress, R.: On the Fr\u00e9chet derivative for obstacle scattering with an impedance boundary condition. SIAM J. Appl. Math. 65(1), 194\u2013208 (2004). https:\/\/doi.org\/10.1137\/S0036139903435413","journal-title":"SIAM J. Appl. Math."},{"issue":"2","key":"1481_CR20","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1080\/00036811.2013.772583","volume":"93","author":"H Haddar","year":"2014","unstructured":"Haddar, H., Lechleiter, A., Marmorat, S.: An improved time domain linear sampling method for Robin and Neumann obstacles. Appl. Anal. 93(2), 369\u2013390 (2014). https:\/\/doi.org\/10.1080\/00036811.2013.772583","journal-title":"Appl. Anal."},{"issue":"10","key":"1481_CR21","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abaf3b","volume":"36","author":"H Haddar","year":"2020","unstructured":"Haddar, H., Liu, X.: A time domain factorization method for obstacles with impedance boundary conditions. Inverse Problems 36(10), 105011 (2020). https:\/\/doi.org\/10.1088\/1361-6420\/abaf3b","journal-title":"Inverse Problems"},{"key":"1481_CR22","doi-asserted-by":"publisher","unstructured":"Hagemann, F.: Reconstructing the shape and measuring chirality of obstacles in electromagnetic scattering. PhD thesis, Karlsruhe Institute of Technology (KIT), (2019). https:\/\/doi.org\/10.5445\/IR\/1000100295","DOI":"10.5445\/IR\/1000100295"},{"issue":"8","key":"1481_CR23","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab10cb","volume":"35","author":"F Hagemann","year":"2019","unstructured":"Hagemann, F., Arens, T., Betcke, T., Hettlich, F.: Solving inverse electromagnetic scattering problems via domain derivatives. Inverse Problems 35(8), 084005 (2019). https:\/\/doi.org\/10.1088\/1361-6420\/ab10cb","journal-title":"Inverse Problems"},{"key":"1481_CR24","doi-asserted-by":"publisher","unstructured":"Hairer, E., Wanner, G.: Solving ordinary differential equations. II: Stiff and differential-algebraic problems, volume\u00a014 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, Berlin, (1991). https:\/\/doi.org\/10.1007\/978-3-662-09947-6","DOI":"10.1007\/978-3-662-09947-6"},{"issue":"3","key":"1481_CR25","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1216\/jiea\/1190905486","volume":"19","author":"H Harbrecht","year":"2007","unstructured":"Harbrecht, H., Hohage, T.: Fast methods for three-dimensional inverse obstacle scattering problems. J. Integral Equations Appl. 19(3), 237\u2013260 (2007). https:\/\/doi.org\/10.1216\/jiea\/1190905486","journal-title":"J. Integral Equations Appl."},{"key":"1481_CR26","doi-asserted-by":"publisher","unstructured":"Hassell, M., Sayas, F.-J.: Convolution quadrature for wave simulations. In Numerical simulation in physics and engineering, volume\u00a09 of SEMA SIMAI Springer Ser., pages 71\u2013159. Springer, Cham, (2016). https:\/\/doi.org\/10.1007\/978-3-319-32146-2","DOI":"10.1007\/978-3-319-32146-2"},{"issue":"2","key":"1481_CR27","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1088\/0266-5611\/11\/2\/007","volume":"11","author":"F Hettlich","year":"1995","unstructured":"Hettlich, F.: Fr\u00e9chet derivatives in inverse obstacle scattering. Inverse Prob. 11(2), 371\u2013382 (1995). https:\/\/doi.org\/10.1088\/0266-5611\/11\/2\/007","journal-title":"Inverse Prob."},{"key":"1481_CR28","doi-asserted-by":"publisher","unstructured":"Hettlich, F.: Erratum: \u201cFrechet derivatives in inverse obstacle scattering\u201d [Inverse Problems 11 (1995), no. 2, 371\u2013382]. Inverse Problems, 14(1):209\u2013210, (1998). https:\/\/doi.org\/10.1088\/0266-5611\/14\/1\/017","DOI":"10.1088\/0266-5611\/14\/1\/017"},{"key":"1481_CR29","unstructured":"Hettlich, F.: The domain derivative in inverse obstacle problems. Habilitation thesis, University of Erlangen, Erlangen, (1999)"},{"issue":"14","key":"1481_CR30","doi-asserted-by":"publisher","first-page":"1681","DOI":"10.1002\/mma.2548","volume":"35","author":"F Hettlich","year":"2012","unstructured":"Hettlich, F.: The domain derivative of time-harmonic electromagnetic waves at interfaces. Math. Methods Appl. Sci. 35(14), 1681\u20131689 (2012). https:\/\/doi.org\/10.1002\/mma.2548","journal-title":"Math. Methods Appl. Sci."},{"key":"1481_CR31","unstructured":"Hohage, T.: Iterative methods in inverse obstacle scattering : regularization theory of linear and nonlinear exponentially ill-posed problems. PhD thesis, University of Linz, (1999)"},{"issue":"5","key":"1481_CR32","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1088\/0266-5611\/14\/5\/008","volume":"14","author":"T Hohage","year":"1998","unstructured":"Hohage, T., Schormann, C.: A Newton-type method for a transmission problem in inverse scattering. Inverse Prob. 14(5), 1207\u20131227 (1998). https:\/\/doi.org\/10.1088\/0266-5611\/14\/5\/008","journal-title":"Inverse Prob."},{"issue":"1","key":"1481_CR33","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1088\/0266-5611\/9\/1\/005","volume":"9","author":"A Kirsch","year":"1993","unstructured":"Kirsch, A.: The domain derivative and two applications in inverse scattering theory. Inverse Prob. 9(1), 81\u201396 (1993). https:\/\/doi.org\/10.1088\/0266-5611\/9\/1\/005","journal-title":"Inverse Prob."},{"key":"1481_CR34","doi-asserted-by":"publisher","unstructured":"Kirsch, A., Hettlich, F.: The mathematical theory of time-harmonic Maxwell\u2019s equations: Expansion-, Integral-, and Variational methods, volume 190 of Applied Mathematical Sciences. Springer, Cham, (2015). https:\/\/doi.org\/10.1007\/978-3-319-11086-8","DOI":"10.1007\/978-3-319-11086-8"},{"issue":"4","key":"1481_CR35","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1515\/cmam-2021-0190","volume":"22","author":"T L\u00e4hivaara","year":"2022","unstructured":"L\u00e4hivaara, T., Monk, P., Selgas, V.: The time domain linear sampling method for determining the shape of multiple scatterers using electromagnetic waves. Comput. Methods Appl. Math. 22(4), 889\u2013913 (2022). https:\/\/doi.org\/10.1515\/cmam-2021-0190","journal-title":"Comput. Methods Appl. Math."},{"issue":"3","key":"1481_CR36","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s002110050033","volume":"67","author":"C Lubich","year":"1994","unstructured":"Lubich, C.: On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Numer. Math. 67(3), 365\u2013389 (1994). https:\/\/doi.org\/10.1007\/s002110050033","journal-title":"Numer. Math."},{"issue":"348","key":"1481_CR37","doi-asserted-by":"publisher","first-page":"1529","DOI":"10.1090\/mcom\/3914","volume":"93","author":"J Nick","year":"2024","unstructured":"Nick, J.: Numerical analysis for electromagnetic scattering with nonlinear boundary conditions. Math. Comp. 93(348), 1529\u20131568 (2024). https:\/\/doi.org\/10.1090\/mcom\/3914","journal-title":"Math. Comp."},{"issue":"2","key":"1481_CR38","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1088\/0266-5611\/10\/2\/016","volume":"10","author":"R Potthast","year":"1994","unstructured":"Potthast, R.: Fr\u00e9chet differentiability of boundary integral operators in inverse acoustic scattering. Inverse Prob. 10(2), 431\u2013447 (1994). https:\/\/doi.org\/10.1088\/0266-5611\/10\/2\/016","journal-title":"Inverse Prob."},{"issue":"15","key":"1481_CR39","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1002\/(SICI)1099-1476(199610)19:15<1157::AID-MMA814>3.0.CO;2-Y","volume":"19","author":"R Potthast","year":"1996","unstructured":"Potthast, R.: Domain derivatives in electromagnetic scattering. Math. Methods Appl. Sci. 19(15), 1157\u20131175 (1996). https:\/\/doi.org\/10.1002\/(SICI)1099-1476(199610)19:15<1157::AID-MMA814>3.0.CO;2-Y","journal-title":"Math. Methods Appl. Sci."},{"issue":"1","key":"1481_CR40","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1515\/jiip.1996.4.1.67","volume":"4","author":"R Potthast","year":"1996","unstructured":"Potthast, R.: Fr\u00e9chet differentiability of the solution to the acoustic Neumann scattering problem with respect to the domain. J. Inverse Ill-Posed Probl. 4(1), 67\u201384 (1996). https:\/\/doi.org\/10.1515\/jiip.1996.4.1.67","journal-title":"J. Inverse Ill-Posed Probl."},{"key":"1481_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2022.117430","volume":"545","author":"SW Rienstra","year":"2023","unstructured":"Rienstra, S.W.: A class of cylindrically symmetric exact solutions of the wave equation. J. Sound Vib. 545, 117430 (2023). https:\/\/doi.org\/10.1016\/j.jsv.2022.117430","journal-title":"J. Sound Vib."},{"key":"1481_CR42","doi-asserted-by":"publisher","unstructured":"Sayas, F.-J.: Retarded potentials and time domain boundary integral equations: A road map, volume\u00a050 of Springer Series in Computational Mathematics. Springer, Cham, (2016). https:\/\/doi.org\/10.1007\/978-3-319-26645-9","DOI":"10.1007\/978-3-319-26645-9"},{"key":"1481_CR43","doi-asserted-by":"publisher","unstructured":"Sokolowski, J., Zol\u00e9sio, J.-P.: Introduction to shape optimization, volume\u00a016 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, (1992). Shape sensitivity analysis. https:\/\/doi.org\/10.1007\/978-3-642-58106-9","DOI":"10.1007\/978-3-642-58106-9"},{"key":"1481_CR44","unstructured":"Team Pancho. deltaBEM. https:\/\/team-pancho.github.io\/deltaBEM\/index.html"},{"issue":"5","key":"1481_CR45","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.3934\/ipi.2021037","volume":"15","author":"L Zhao","year":"2021","unstructured":"Zhao, L., Dong, H., Ma, F.: Inverse obstacle scattering for acoustic waves in the time domain. Inverse Probl. Imaging 15(5), 1269\u20131286 (2021). https:\/\/doi.org\/10.3934\/ipi.2021037","journal-title":"Inverse Probl. Imaging"},{"issue":"4","key":"1481_CR46","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1088\/1361-6420\/ac531c","volume":"38","author":"L Zhao","year":"2022","unstructured":"Zhao, L., Dong, H., Ma, F.: Inverse obstacle scattering for elastic waves in the time domain. Inverse Prob. 38(4), 30 (2022). https:\/\/doi.org\/10.1088\/1361-6420\/ac531c","journal-title":"Inverse Prob."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-025-01481-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-025-01481-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-025-01481-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T12:30:23Z","timestamp":1770640223000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-025-01481-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,1]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["1481"],"URL":"https:\/\/doi.org\/10.1007\/s00211-025-01481-8","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,1]]},"assertion":[{"value":"15 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 June 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}