{"paper":{"title":"Equivariant nonlinear partial differential operators on constant curvature spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Nonlinear equivariant differential operators on constant-curvature spaces are classified by a vector space of multigraph equivalence classes.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erlend Grong, Francesco Ballerin","submitted_at":"2026-05-16T07:09:45Z","abstract_excerpt":"Motivated by PDE-learning, we give a classifying space for nonlinear operators on simply connected spaces with constant curvature which are also equivariant under the action of the isometry group. The nonlinear operators we are considering are those that can be written as a polynomial in linear operators. We show that the classifying space for such operators can be realized as the vector space spanned by equivalence-classes of multigraphs. We also illustrate how this realization can help us discover non-trivial linear dependence relations between nonlinear differential operators relative to th"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the classifying space for such operators can be realized as the vector space spanned by equivalence-classes of multigraphs.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The nonlinear operators under consideration are precisely those that can be written as a polynomial in linear operators, as stated in the abstract; if this polynomial restriction does not capture the intended class of operators, the classifying space construction would not apply to the broader set of nonlinear equivariant operators.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The classifying space for polynomial nonlinear isometry-equivariant operators on simply connected constant curvature spaces is realized as the vector space spanned by equivalence classes of multigraphs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonlinear equivariant differential operators on constant-curvature spaces are classified by a vector space of multigraph equivalence classes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"164c1ecfdc7e894ed7317b96a8214b7487e83445b7d5ab1d5a5678bf6c5ed854"},"source":{"id":"2605.16847","kind":"arxiv","version":1},"verdict":{"id":"b5c963cb-1f08-4084-966e-80b6a2cc784d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:51:32.991127Z","strongest_claim":"We show that the classifying space for such operators can be realized as the vector space spanned by equivalence-classes of multigraphs.","one_line_summary":"The classifying space for polynomial nonlinear isometry-equivariant operators on simply connected constant curvature spaces is realized as the vector space spanned by equivalence classes of multigraphs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The nonlinear operators under consideration are precisely those that can be written as a polynomial in linear operators, as stated in the abstract; if this polynomial restriction does not capture the intended class of operators, the classifying space construction would not apply to the broader set of nonlinear equivariant operators.","pith_extraction_headline":"Nonlinear equivariant differential operators on constant-curvature spaces are classified by a vector space of multigraph equivalence classes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16847/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T21:01:25.113970Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T21:01:19.243629Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.317107Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.389990Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cc2989a9a7c46de93fe5153ae26233651b79e3f79c9d99148e035ef983b64cf1"},"references":{"count":20,"sample":[{"doi":"","year":2024,"title":"E. 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OnG2 and sub-riemannian model spaces of step and rank three.Mathematische Zeitschrift, 298(3):1853–1885, 2021","work_id":"4d25d6ea-a761-4231-b942-0655295d0e9a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"Bollob´ as.Modern Graph Theory, volume 184 ofGraduate Texts in Mathematics","work_id":"0b11e366-c90c-4a99-8bf9-9f5449d87e9f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"L. Gao, Y. Du, H. Li, and G. Lin. 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