{"paper":{"title":"Underlying Stokes and de Rham structures for Arnold-type invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hiroki Mizuno, Noboru Ito","submitted_at":"2026-05-13T00:04:50Z","abstract_excerpt":"We introduce a framework on dual complexes for studying Arnold-type invariants of immersed curves and immersed surfaces via local finite-difference structures associated with Alexander numberings. For generic immersed plane curves and generic immersed surfaces, we define locally normalized maps $d^k \\phi$ on dual skeleta and show that suitable evaluations recover the Arnold-type invariants $St_{(1)}$ and $St_{(2)}$. In particular, we establish normalized discrete Stokes-type compatibilities between adjacent dual skeleta and derive corresponding Shumakovitch-type identities for curves and surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.12834","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}