{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QU7TOXS6NJ6H2F5TX57OMT4DOD","short_pith_number":"pith:QU7TOXS6","schema_version":"1.0","canonical_sha256":"853f375e5e6a7c7d17b3bf7ee64f8370c4125c35322bcdcbda4650675ce0d15a","source":{"kind":"arxiv","id":"2411.15134","version":4},"attestation_state":"computed","paper":{"title":"Toric invariance of vertically parametrized systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elisenda Feliu, Oskar Henriksson","submitted_at":"2024-11-22T18:57:46Z","abstract_excerpt":"We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where we allow linear dependencies between coefficients in front of the same monomial. We give a matroid-theoretic characterization of the maximal-dimensional torus for which all solution sets are invariant under componentwise multiplication. Building on this, we provide necessary conditions and sufficient conditions for when the solution sets are unions of finit"},"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":"2411.15134","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-11-22T18:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"470ecf3ca98132a259e2bf0f3c0a99f2dd193dc69268ad7c3bf17e3d36ac5c47","abstract_canon_sha256":"aff33465b77ceca782df9d934b97a03eed66e72f620b931f75d589398f31e94f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:01.654134Z","signature_b64":"uHyVdwxD25jeJP296+dv2oSRr+o+T3HvfQ/iLgjTg4h6NCh6jc3k2omeXB423OdQZweHrp76RTWPJE4TJZNkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"853f375e5e6a7c7d17b3bf7ee64f8370c4125c35322bcdcbda4650675ce0d15a","last_reissued_at":"2026-05-17T23:39:01.653407Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:01.653407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toric invariance of vertically parametrized systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elisenda Feliu, Oskar Henriksson","submitted_at":"2024-11-22T18:57:46Z","abstract_excerpt":"We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where we allow linear dependencies between coefficients in front of the same monomial. We give a matroid-theoretic characterization of the maximal-dimensional torus for which all solution sets are invariant under componentwise multiplication. Building on this, we provide necessary conditions and sufficient conditions for when the solution sets are unions of finit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15134","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":""},"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":"2411.15134","created_at":"2026-05-17T23:39:01.653526+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.15134v4","created_at":"2026-05-17T23:39:01.653526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15134","created_at":"2026-05-17T23:39:01.653526+00:00"},{"alias_kind":"pith_short_12","alias_value":"QU7TOXS6NJ6H","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"QU7TOXS6NJ6H2F5T","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"QU7TOXS6","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2409.06877","citing_title":"Positive equilibria in mass action networks: geometry and bounds","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD","json":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD.json","graph_json":"https://pith.science/api/pith-number/QU7TOXS6NJ6H2F5TX57OMT4DOD/graph.json","events_json":"https://pith.science/api/pith-number/QU7TOXS6NJ6H2F5TX57OMT4DOD/events.json","paper":"https://pith.science/paper/QU7TOXS6"},"agent_actions":{"view_html":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD","download_json":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD.json","view_paper":"https://pith.science/paper/QU7TOXS6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.15134&json=true","fetch_graph":"https://pith.science/api/pith-number/QU7TOXS6NJ6H2F5TX57OMT4DOD/graph.json","fetch_events":"https://pith.science/api/pith-number/QU7TOXS6NJ6H2F5TX57OMT4DOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD/action/storage_attestation","attest_author":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD/action/author_attestation","sign_citation":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD/action/citation_signature","submit_replication":"https://pith.science/pith/QU7TOXS6NJ6H2F5TX57OMT4DOD/action/replication_record"}},"created_at":"2026-05-17T23:39:01.653526+00:00","updated_at":"2026-05-17T23:39:01.653526+00:00"}