{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:43:08Z","timestamp":1760143388847,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T00:00:00Z","timestamp":1707177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FONDECYT, Chile","award":["1201894"],"award-info":[{"award-number":["1201894"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider basic diffeological structures that can be highlighted naturally within the theory of the Vinogradov spectral sequence and equation manifolds. These interrelated features are presented in a rigorous and accurate way, that complements some heuristic formulations appearing in very recent literature. We also propose a refined definition of the Vinogradov spectral sequence using diffeologies.<\/jats:p>","DOI":"10.3390\/sym16020192","type":"journal-article","created":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T05:36:43Z","timestamp":1707197803000},"page":"192","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Equation Manifolds, the Vinogradov Spectral Sequence, and Related Diffeological Structures"],"prefix":"10.3390","volume":"16","author":[{"given":"Jean-Pierre","family":"Magnot","sequence":"first","affiliation":[{"name":"CNRS, Laboratoire Angevin de REcherche en Math\u00e9matiques (LAREMA), SFR MATHSTIC, University of Angers, 49000 Angers, France"},{"name":"Lyc\u00e9e Jeanne d\u2019Arc Avenue de Grande Bretagne, 63000 Clermont-Ferrand, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8460-444X","authenticated-orcid":false,"given":"Enrique G.","family":"Reyes","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica y Ciencia de la Computaci\u00f3n, Universidad de Santiago de Chile (USACH), Casilla 307 Correo 2, Santiago 9170020, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1090\/conm\/132\/1188434","article-title":"Introduction to the variational bicomplex","volume":"132","author":"Anderson","year":"1992","journal-title":"Contemp. 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