{"paper":{"title":"A Linear Structure from Magnetic-Dipole Systems and Its Geometry","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Bohuan Lin, Fengping Li, Zhengya Zhang","submitted_at":"2025-12-03T03:27:44Z","abstract_excerpt":"We investigate a class of algebras on $\\mathbb{R}^3$ arising and generalized from the algebraic structure of magnetic gradient fields induced by systems of synchronous magnets with identical dipole moments (i.e., $\\mathbf{M}_i=\\mathbf{M},\\,\\forall i$). We show that when there is a $2$ dimensional sub-algebra, the linear structure associated to such an algebra admits a certain type of decompositions, which allows the locating of the dipole moment $\\bar{\\mathbf{M}}$ that yields the strongest translational force(s) on a test magnet $\\mathfrak{m}$. Upper bounds to the strength of this magnetic for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.03408","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.03408/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}