{"paper":{"title":"Gibbons-Tsarev type systems and Eventual identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist, proven via a generalized Gibbons-Tsarev system defined by eventual identities.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alessandro Arsie, Karoline van Gemst, Paolo Lorenzoni, Sara Perletti","submitted_at":"2026-05-13T13:26:36Z","abstract_excerpt":"We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple $F$-manifolds cannot exist. The proof is based on the derivation and study of a generalised Gibbons--Tsarev system (gGT system) in the non-semisimple/non-diagonalisable setting. Remarkably, a class of solutions of the gGT system is defined by eventual identities of the underlying regular $F$-manifold structure. Furthermore, we use these vector fields to construct integrable reductions of Pavlov's hydrodynamic chain. In this case, the corresponding solutions are defined for any choice of Jordan"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The underlying F-manifold is regular and non-semisimple, with the reductions defined via the standard association to the multiplication operator and eventual identities.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist, proven via a generalized Gibbons-Tsarev system defined by eventual identities.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"12da932f7435f3bde2f16f4aef7b4244a5c8657662eb43116b324712e5d6d313"},"source":{"id":"2605.13505","kind":"arxiv","version":1},"verdict":{"id":"7ec3d7db-375f-4b5a-9d10-a3aaa5fa3126","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:01:16.957371Z","strongest_claim":"We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist.","one_line_summary":"Non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist, proven via a generalized Gibbons-Tsarev system defined by eventual identities.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The underlying F-manifold is regular and non-semisimple, with the reductions defined via the standard association to the multiplication operator and eventual identities.","pith_extraction_headline":""},"references":{"count":20,"sample":[{"doi":"","year":2013,"title":"A. 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Strachan,Dubrovin’s duality forF-manifolds with eventual identities, Adv. Math. Volume 226, Issue 5, 20 March 2011, Pages 4031–4060","work_id":"7efef116-06b0-494f-81ec-05915ba59303","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"C. Hertling and Yu. I. Manin,Weak Frobenius manifolds, International Mathematics Research Notices, Vol. 1999, No. 6, 277–286 (1999)","work_id":"9533d542-00fc-48f7-8bbc-3ec7b0c04fcb","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":20,"snapshot_sha256":"7466baa45d4d3433acfad96405dc75fb4c4b270151bcecef8447dccaf59e6fcb","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"1e00b5ff03e810c01c08ee989fae992f8e31335e9989e9049ba1fc57da19c989"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}