{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:K2RINVJ5QHHVYC6ZRPX2OQD5IQ","short_pith_number":"pith:K2RINVJ5","schema_version":"1.0","canonical_sha256":"56a286d53d81cf5c0bd98befa7407d44253f3f22fdda43504e1770939d19d3cd","source":{"kind":"arxiv","id":"2411.18264","version":4},"attestation_state":"computed","paper":{"title":"Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.SI","authors_text":"Peter H. van der Kamp","submitted_at":"2024-11-27T12:01:10Z","abstract_excerpt":"We associate parametric classes of $n$-component Lotka-Volterra systems which admit $k$ additional linear Darboux polynomials, with admissible loopless hypergraphs of order $n$ and size $k$. We study the equivalence relation on admissible hypergraphs induced by linear transformations of the associated LV-systems, for $n\\leq 5$. We present a new 13-parameter 5-component superintegrable Lotka-Volterra system, i.e. one that is not equivalent to a so-called tree-system. We conjecture that tree-systems associated with nonisomorphic trees are not equivalent, which we verified for $n<9$."},"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":"2411.18264","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2024-11-27T12:01:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f0f654b439296c9ece111885ba6a4ecb684465ea2698757fb5fe7f8b90d182b8","abstract_canon_sha256":"1cac76163a9264fa04bb6f1686b788e6e5da9dff9b2d5bf643461f85f4205c24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:16.172780Z","signature_b64":"NMw5ySd9zJvcGAI+zqehYekvW4fmMkkbHG1tclnv5XfNgqNn+PGB98dXuDnWYXjTo0eRPgmrVIkYbZ+fWSADAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56a286d53d81cf5c0bd98befa7407d44253f3f22fdda43504e1770939d19d3cd","last_reissued_at":"2026-07-05T11:18:16.172281Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:16.172281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.SI","authors_text":"Peter H. van der Kamp","submitted_at":"2024-11-27T12:01:10Z","abstract_excerpt":"We associate parametric classes of $n$-component Lotka-Volterra systems which admit $k$ additional linear Darboux polynomials, with admissible loopless hypergraphs of order $n$ and size $k$. We study the equivalence relation on admissible hypergraphs induced by linear transformations of the associated LV-systems, for $n\\leq 5$. We present a new 13-parameter 5-component superintegrable Lotka-Volterra system, i.e. one that is not equivalent to a so-called tree-system. We conjecture that tree-systems associated with nonisomorphic trees are not equivalent, which we verified for $n<9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18264","kind":"arxiv","version":4},"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/2411.18264/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":"2411.18264","created_at":"2026-07-05T11:18:16.172349+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.18264v4","created_at":"2026-07-05T11:18:16.172349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18264","created_at":"2026-07-05T11:18:16.172349+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2RINVJ5QHHV","created_at":"2026-07-05T11:18:16.172349+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2RINVJ5QHHVYC6Z","created_at":"2026-07-05T11:18:16.172349+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2RINVJ5","created_at":"2026-07-05T11:18:16.172349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ","json":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ.json","graph_json":"https://pith.science/api/pith-number/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/graph.json","events_json":"https://pith.science/api/pith-number/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/events.json","paper":"https://pith.science/paper/K2RINVJ5"},"agent_actions":{"view_html":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ","download_json":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ.json","view_paper":"https://pith.science/paper/K2RINVJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.18264&json=true","fetch_graph":"https://pith.science/api/pith-number/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/graph.json","fetch_events":"https://pith.science/api/pith-number/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/action/storage_attestation","attest_author":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/action/author_attestation","sign_citation":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/action/citation_signature","submit_replication":"https://pith.science/pith/K2RINVJ5QHHVYC6ZRPX2OQD5IQ/action/replication_record"}},"created_at":"2026-07-05T11:18:16.172349+00:00","updated_at":"2026-07-05T11:18:16.172349+00:00"}