Relevant bibliographies by topics / Homotopy type

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Homotopy type'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Homotopy type"

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Awodey, Steve, and Robert Harper. "Homotopy type theory." ACM SIGLOG News 2, no. 1 (2015): 37–44. http://dx.doi.org/10.1145/2728816.2728825.

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Umble, Ronald N. "Homotopy conditions that determine rational homotopy type." Journal of Pure and Applied Algebra 60, no. 2 (1989): 205–17. http://dx.doi.org/10.1016/0022-4049(89)90128-x.

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AVIGAD, JEREMY, KRZYSZTOF KAPULKIN, and PETER LEFANU LUMSDAINE. "Homotopy limits in type theory." Mathematical Structures in Computer Science 25, no. 5 (2015): 1040–70. http://dx.doi.org/10.1017/s0960129514000498.

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Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to the formalizing homotopy-theoretic material. We also compare our constructions with the more classical approach to homotopy limits via fibration categories.
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Mandell, Michael A. "Cochains and homotopy type." Publications mathématiques de l'IHÉS 103, no. 1 (2006): 213–46. http://dx.doi.org/10.1007/s10240-006-0037-6.

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MELLOR, BLAKE. "FINITE TYPE LINK HOMOTOPY INVARIANTS." Journal of Knot Theory and Its Ramifications 08, no. 06 (1999): 773–87. http://dx.doi.org/10.1142/s0218216599000481.

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In [2], Bar-Natan used unitrivalent diagrams to show that finite type invariants classify string links up to homotopy. In this paper, I will construct the correct spaces of chord diagrams and unitrivalent diagrams for links up to homotopy. I will use these spaces to show that, far from classifying links up to homotopy, the only rational finite type invariants of link homotopy are the linking numbers of the components.
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Kazemi-Baneh, M. Z. "Homotopic Chain Maps Have Equals-Homology andd-Homology." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/5647548.

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The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies andd-homologies of homotopic chain maps is established. As a special case, ifXandYare the same homotopy type, then theirnthd-homologyR-modules are isomorphic, and ifXis a contractible space, then itsnthd-homologyR-modules forn≠0are trivial.
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Tom Dieck, Tammo. "The homotopy type of group actions on homotopy spheres." Archiv der Mathematik 45, no. 2 (1985): 174–79. http://dx.doi.org/10.1007/bf01270489.

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SHULMAN, MICHAEL. "Univalence for inverse diagrams and homotopy canonicity." Mathematical Structures in Computer Science 25, no. 5 (2014): 1203–77. http://dx.doi.org/10.1017/s0960129514000565.

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We describe a homotopical version of the relational and gluing models of type theory, and generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy theory on inverse diagrams, and relies on the fact that Reedy fibrant diagrams correspond to contexts of a certain shape in type theory. This has two main applications. First, by considering inverse diagrams in Voevodsky's univalent model in simplicial sets, we obtain new models of univalence in a number of (∞, 1)-toposes; this answers a question raised at the Oberwolfach workshop on homotopical type theory. Second, by
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RIJKE, EGBERT, and BAS SPITTERS. "Sets in homotopy type theory." Mathematical Structures in Computer Science 25, no. 5 (2015): 1172–202. http://dx.doi.org/10.1017/s0960129514000553.

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Homotopy type theory may be seen as an internal language for the ∞-category of weak ∞-groupoids. Moreover, weak ∞-groupoids model the univalence axiom. Voevodsky proposes this (language for) weak ∞-groupoids as a new foundation for Mathematics called the univalent foundations. It includes the sets as weak ∞-groupoids with contractible connected components, and thereby it includes (much of) the traditional set theoretical foundations as a special case. We thus wonder whether those ‘discrete’ groupoids do in fact form a (predicative) topos. More generally, homotopy type theory is conjectured to
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Lipshitz, Robert, and Sucharit Sarkar. "A Khovanov stable homotopy type." Journal of the American Mathematical Society 27, no. 4 (2014): 983–1042. http://dx.doi.org/10.1090/s0894-0347-2014-00785-2.

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Dissertations / Theses on the topic "Homotopy type"

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Quirin, Kevin. "Lawvere-Tierney sheafification in Homotopy Type Theory." Thesis, Nantes, Ecole des Mines, 2016. http://www.theses.fr/2016EMNA0298/document.

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Le but principal de cette thèse est de définir une extension de la traduction de double-négation de Gödel à tous les types tronqués, dans le contexte de la théorie des types homotopique. Ce but utilisera des théories déjà existantes, comme la théorie des faisceaux de Lawvere-Tierney, quenous adapterons à la théorie des types homotopiques. En particulier, on définira le fonction de faisceautisation de Lawvere-Tierney, qui est le principal théorème présenté dans cette thèse.Pour le définir, nous aurons besoin de concepts soit déjà définis en théorie des types, soit non existants pour l’instant.
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Su, Zhixu. "Rational homotopy type of manifolds." [Bloomington, Ind.] : Indiana University, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3378383.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2009.<br>Title from PDF t.p. (viewed on Jul 9, 2010). Source: Dissertation Abstracts International, Volume: 70-10, Section: B, page: 6263. Adviser: James F. Davis.
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Silva, Júnior João Alves. "First steps in homotopy type theory." Universidade Federal de Pernambuco, 2014. https://repositorio.ufpe.br/handle/123456789/13853.

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Submitted by Natalia de Souza Gonçalves (natalia.goncalves@ufpe.br) on 2015-05-08T13:12:46Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertation.pdf: 1398032 bytes, checksum: ba6c27cf093110dd1dcf9fea1b529c41 (MD5)<br>Made available in DSpace on 2015-05-08T13:12:46Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertation.pdf: 1398032 bytes, checksum: ba6c27cf093110dd1dcf9fea1b529c41 (MD5) Previous issue date: 2014-02-27<br>CNPq<br>Em abril de 2013, o Programa de Fundamentos Unival
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Kraus, Nicolai. "Truncation levels in homotopy type theory." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/28986/.

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Homotopy type theory (HoTT) is a branch of mathematics that combines and benefits from a variety of fields, most importantly homotopy theory, higher dimensional category theory, and, of course, type theory. We present several original results in homotopy type theory which are related to the truncation level of types, a concept due to Voevodsky. To begin, we give a few simple criteria for determining whether a type is 0-truncated (a set), inspired by a well-known theorem by Hedberg, and these criteria are then generalised to arbitrary n. This naturally leads to a discussion of functions that ar
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Biss, Daniel Kálmán 1977. "The homotopy type of the matroid Grassmannian." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8400.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.<br>Includes bibliographical references (p. 37-38).<br>In this thesis, I establish a homotopy equivalence between the matroid Grassmannian [parallel] MacP(k, n) [parallel] and the real Grassmannian G(k, n) of k-planes in [Real set]n. This is accomplished by finding a Schubert stratification of the former space and analyzing its relationship to the ordinary Schubert cell decomposition of the Grassmannian. Since the classifying spaces for rank k matroid bundles and rank k vector bundles are, respectively, obtained
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Orton, Richard Ian. "Cubical models of homotopy type theory : an internal approach." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/289441.

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This thesis presents an account of the cubical sets model of homotopy type theory using an internal type theory for elementary topoi. Homotopy type theory is a variant of Martin-Lof type theory where we think of types as spaces, with terms as points in the space and elements of the identity type as paths. We actualise this intuition by extending type theory with Voevodsky's univalence axiom which identifies equalities between types with homotopy equivalences between spaces. Voevodsky showed the univalence axiom to be consistent by giving a model of homotopy type theory in the category of Kan s
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Gallozzi, Cesare. "Homotopy type-theoretic interpretations of constructive set theories." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22317/.

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This thesis deals primarily with type-theoretic interpretations of constructive set theories using notions and ideas from homotopy type theory. We introduce a family of interpretations [.]_k,h for 2 ≤ k ≤ ∞ and 1 ≤ h ≤ ∞ of the set theory BCS into the type theory H, in which sets and formulas are interpreted respectively as types of homotopy level k and h. Depending on the values of the parameters k and h we are able to interpret different theories, like Aczel's CZF and Myhill's CST. We relate the family [.]_k,h to the other interpretations of CST into homotopy type theory already studied in t
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Pöder, Balkeståhl Sebastian. "Simple homotopy type of the Hamiltonian Floer complex." Licentiate thesis, Uppsala universitet, Matematiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-393298.

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For an aspherical symplectic manifold M, closed or with convex contact boundary, and with vanishing first Chern class, a Floer chain complex is defined for Hamiltonians linear at infinity with coefficients in the group ring of the fundamental group of M. For two non-degenerate Hamiltonians of the same slope continuation maps are shown to be simple homotopy equivalences. As a corollary the number of contractible Hamiltonian orbits of period 1 can be bounded from below.
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Vişinescu, Bogdan C. "K-Theory and Homotopy Type of Certain Infinite C*-Algebras." University of Cincinnati / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1178909005.

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Fass'so, Velenik Agnese. "Relative homotopy invariants of the type of the Lusternik-Schnirelmann category." [S.l.] : [s.n.], 2003. http://www.diss.fu-berlin.de/2003/277/index.html.

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Books on the topic "Homotopy type"

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Wen-tsün, Wu. Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0081997.

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Baues, Hans J. Homotopy type and homology. Clarendon Press, 1996.

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Wen-tsün, Wu. Rational homotopy type: A constructive study via the theory of the I*-measure. Springer-Verlag, 1987.

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France, Société mathématique de, ed. Les préfaisceaux comme modèles des types d'homotopie. Société mathématique de France, 2006.

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Ronald, Brown. Topology: A geometric account of general topology, homotopy types, and the fundamental groupoid. E. Horwood, 1988.

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Rational Homotopy Type. Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1987.

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Corfield, David. Modal Homotopy Type Theory. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198853404.001.0001.

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In[KF1] 1914, in an essay entitled ‘Logic as the Essence of Philosophy’, Bertrand Russell promised to revolutionize philosophy by introducing there the ‘new logic’ of Frege and Peano: “The old logic put thought in fetters, while the new logic gives it wings.” A century later, this book proposes a comparable revolution with a newly emerging logic, modal homotopy type theory. Russell’s prediction turned out to be accurate. Frege’s first-order logic, along with its extension to modal logic, is to be found throughout anglophone analytic philosophy. This book provides a considerable array of eviden
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Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Foundations Program Institute for Advanced Study, 2013.

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Shulman, Michael. Homotopy Type Theory: A Synthetic Approach to Higher Equalities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0003.

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Homotopy type theory and univalent foundations (HoTT/UF) is a new foundation of mathematics, based not on set theory but on “infinity-groupoids”, which consist of collections of objects, ways in which two objects can be equal, ways in which those ways-to-be-equal can be equal, ad infinitum. Though apparently complicated, such structures are increasingly important in mathematics. Philosophically, they are an inevitable result of the notion that whenever we form a collection of things, we must simultaneously consider when two of those things are the same. The “synthetic” nature of HoTT/UF enable
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Corfield, David. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy. Oxford University Press, 2020.

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Book chapters on the topic "Homotopy type"

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Rutter, John W. "Homotopy type, homotopy groups." In Spaces of Homotopy Self-Equivalences. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0093755.

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Wen-tsün, Wu. "Fundamental concepts. Measure and calculability." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0081998.

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Wen-tsün, Wu. "Dga and minimal model." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0081999.

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Wen-tsün, Wu. "The de rham-sullivan theorem and I*-measure." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0082000.

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Wen-tsün, Wu. "I*-measure and homotopy." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0082001.

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Wen-tsün, Wu. "I*-measure of a homogeneous space — The cartan theorem." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0082002.

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Wen-tsün, Wu. "Effective computation and axiomatic system of I*-measure." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0082003.

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Wen-tsün, Wu. "I*-measures connected with fibrations." In Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0082004.

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Awodey, Steve. "Homotopy Type Theory." In Logic and Its Applications. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-45824-2_1.

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Blanc, David. "Homotopy Operations and Rational Homotopy Type." In Categorical Decomposition Techniques in Algebraic Topology. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7863-0_4.

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Conference papers on the topic "Homotopy type"

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Awodey, Steve, Nicola Gambino, and Kristina Sojakova. "Inductive Types in Homotopy Type Theory." In 2012 27th Annual IEEE Symposium on Logic in Computer Science (LICS 2012). IEEE, 2012. http://dx.doi.org/10.1109/lics.2012.21.

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Badiger, Chidanand, and T. Venkatesh. "Generalised (g) homotopy and generalised (g) homotopy type spaces." In 4TH INTERNATIONAL CONFERENCE ON THE SCIENCE AND ENGINEERING OF MATERIALS: ICoSEM2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0028740.

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Frumin, Dan, Herman Geuvers, Léon Gondelman, and Niels van der Weide. "Finite sets in homotopy type theory." In the 7th ACM SIGPLAN International Conference. ACM Press, 2018. http://dx.doi.org/10.1145/3176245.3167085.

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Kunii, Tosiyasu L., and Masaki Hilaga. "Homotopy Type Theory for Big Data." In 2015 International Conference on Cyberworlds (CW). IEEE, 2015. http://dx.doi.org/10.1109/cw.2015.9.

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Buchholtz, Ulrik, Floris van Doorn, and Egbert Rijke. "Higher Groups in Homotopy Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2018. http://dx.doi.org/10.1145/3209108.3209150.

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Buchholtz, Ulrik, and Kuen-Bang Hou Favonia. "Cellular Cohomology in Homotopy Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2018. http://dx.doi.org/10.1145/3209108.3209188.

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Sojakova, Kristina, Floris van Doorn, and Egbert Rijke. "Sequential Colimits in Homotopy Type Theory." In LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2020. http://dx.doi.org/10.1145/3373718.3394801.

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Frumin, Dan, Herman Geuvers, Léon Gondelman, and Niels van der Weide. "Finite sets in homotopy type theory." In CPP '18: Certified Proofs and Programs. ACM, 2018. http://dx.doi.org/10.1145/3167085.

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Kraus, Nicolai, and Jakob von Raumer. "Path Spaces of Higher Inductive Types in Homotopy Type Theory." In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2019. http://dx.doi.org/10.1109/lics.2019.8785661.

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Gilbert, Gaëtan. "Formalising real numbers in homotopy type theory." In CPP '17: Certified Proofs and Programs. ACM, 2017. http://dx.doi.org/10.1145/3018610.3018614.

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