{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:F5HPEZZTXGPRJPSQEMG2PWNEPG","short_pith_number":"pith:F5HPEZZT","schema_version":"1.0","canonical_sha256":"2f4ef26733b99f14be50230da7d9a4798710adb5bfc4b02e6d7f9915dd867266","source":{"kind":"arxiv","id":"2309.04334","version":1},"attestation_state":"computed","paper":{"title":"On Frobenius structures in symmetric cones","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Noemie C. Combe","submitted_at":"2023-09-08T14:02:42Z","abstract_excerpt":"We prove that in any strictly convex symmetric cone $\\Omega$ there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra (with a restriction to the rank 3 case if we consider the field $\\mathbb{O}$) but also on their linear combinations. This theorem holds as well in the case of pseudo-Riemannian geometry, in particular for a Lorentz symmetric cone of Anti-de-Sitter type. Our statement can be considered as a generalisation of a result by Ferapontov--Kruglikov--Novikov and Mokho"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2309.04334","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-09-08T14:02:42Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6ecb6afcabd39c5a4cf9610ed9af450fc980996fece62d14ffe23b853bf1c5e1","abstract_canon_sha256":"46f4142a485bdea353b9771af6e543e7bfd251eaf6a4c34c275b50d78fd6d0b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:58.358832Z","signature_b64":"vN/9WskeWcuweaTpKNE2NGaPFI/3KGCJAbAqSXiHQh7kv/DF2Qya9KIUt5t/fE4st+4SAarRlu+DUI6T5wE2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f4ef26733b99f14be50230da7d9a4798710adb5bfc4b02e6d7f9915dd867266","last_reissued_at":"2026-07-05T06:48:58.358327Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:58.358327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Frobenius structures in symmetric cones","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Noemie C. Combe","submitted_at":"2023-09-08T14:02:42Z","abstract_excerpt":"We prove that in any strictly convex symmetric cone $\\Omega$ there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra (with a restriction to the rank 3 case if we consider the field $\\mathbb{O}$) but also on their linear combinations. This theorem holds as well in the case of pseudo-Riemannian geometry, in particular for a Lorentz symmetric cone of Anti-de-Sitter type. Our statement can be considered as a generalisation of a result by Ferapontov--Kruglikov--Novikov and Mokho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04334","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.04334/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2309.04334","created_at":"2026-07-05T06:48:58.358389+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.04334v1","created_at":"2026-07-05T06:48:58.358389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.04334","created_at":"2026-07-05T06:48:58.358389+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5HPEZZTXGPR","created_at":"2026-07-05T06:48:58.358389+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5HPEZZTXGPRJPSQ","created_at":"2026-07-05T06:48:58.358389+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5HPEZZT","created_at":"2026-07-05T06:48:58.358389+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.01345","citing_title":"Maximum Likelihood, permutohedra and Associativity Equations","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG","json":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG.json","graph_json":"https://pith.science/api/pith-number/F5HPEZZTXGPRJPSQEMG2PWNEPG/graph.json","events_json":"https://pith.science/api/pith-number/F5HPEZZTXGPRJPSQEMG2PWNEPG/events.json","paper":"https://pith.science/paper/F5HPEZZT"},"agent_actions":{"view_html":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG","download_json":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG.json","view_paper":"https://pith.science/paper/F5HPEZZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.04334&json=true","fetch_graph":"https://pith.science/api/pith-number/F5HPEZZTXGPRJPSQEMG2PWNEPG/graph.json","fetch_events":"https://pith.science/api/pith-number/F5HPEZZTXGPRJPSQEMG2PWNEPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG/action/storage_attestation","attest_author":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG/action/author_attestation","sign_citation":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG/action/citation_signature","submit_replication":"https://pith.science/pith/F5HPEZZTXGPRJPSQEMG2PWNEPG/action/replication_record"}},"created_at":"2026-07-05T06:48:58.358389+00:00","updated_at":"2026-07-05T06:48:58.358389+00:00"}