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In magnetic systems, they characterize deformation\u2010resistant spin textures and endow non\u2010trivial configurations with exceptional stability; however, they also create inherent challenges in precise modulation of topological magnetic states. Here, we demonstrate the generation and programmable modulation of arbitrary topological numbers in a magnetic skyrmion bag system that is thermally stable in the 2D van der Waals (vdW) ferromagnet Fe\n                    <jats:sub>3<\/jats:sub>\n                    GaTe\n                    <jats:sub>2<\/jats:sub>\n                    (FGaT) at above room temperature. The surface\u2010interior energy\u2010landscape decoupling has been uncovered by exploiting unusual perpendicular magnetic anisotropy (PMA) and the thickness\u2010dependent demagnetization energy, which enables hierarchical reconstruction of surface branching domains while retaining the bulk topological backbone. The encoding of skyrmion bags with different topological structures is demonstrated to enable applications in binary and higher\u2010radix information storage. This work establishes a comprehensive strategy for generating, reconfiguring and operating high\u2010order topological states, which paves the way toward programmable, multi\u2010state spintronic technologies.\n                  <\/jats:p>","DOI":"10.1002\/advs.77160","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T08:35:28Z","timestamp":1789979728000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Programmable Topological Magnetic Textures in Above\u2010Room\u2010Temperature 2D Ferromagnet Fe\n                    <sub>3<\/sub>\n                    GaTe\n                    <sub>2<\/sub>"],"prefix":"10.1002","author":[{"given":"Hanqing","family":"Shi","sequence":"first","affiliation":[{"name":"School of Physics Beihang University  Beijing People's Republic of 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