{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QYPFIT5JNYMIVMPZTZLLXZWCIA","short_pith_number":"pith:QYPFIT5J","schema_version":"1.0","canonical_sha256":"861e544fa96e188ab1f99e56bbe6c240073808c2052b6f76a7e35928eb27fec8","source":{"kind":"arxiv","id":"1711.02157","version":1},"attestation_state":"computed","paper":{"title":"On the Gauss-Lucas theorem in the quaternionic setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Irene Sabadini, J. Oscar Gonz\\'alez-Cervantes, Sorin G. Gal","submitted_at":"2017-11-06T20:21:47Z","abstract_excerpt":"In theory of one complex variable, Gauss-Lucas Theorem states that the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the polynomial. The exact analogue of this result cannot hold, in general, in the quaternionic case; instead, the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the so-called symmetrization of the given polynomial. An incomplete proof of this statement was given in [8]. In this paper we present a different but complete proof of this theorem and we discuss a consequence."},"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":"1711.02157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-11-06T20:21:47Z","cross_cats_sorted":[],"title_canon_sha256":"ec0c55e0ece491e0f48ec0c429d0a827cab6d5d7b2c30e5fd03a39d3a7e0e64d","abstract_canon_sha256":"07094ce9456c205df8a4344ddbc7434628bc3ec2e02e9378924839080d2c93a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:08.680815Z","signature_b64":"bTqIkSwedQTxZXUJvug/x/H0ExnSTY9nLrlIFdlOv67rjdQDcTfjRvqD4npPod6OXlW6kxNFmvF1XUDDQ/xRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"861e544fa96e188ab1f99e56bbe6c240073808c2052b6f76a7e35928eb27fec8","last_reissued_at":"2026-05-18T00:31:08.680064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:08.680064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Gauss-Lucas theorem in the quaternionic setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Irene Sabadini, J. Oscar Gonz\\'alez-Cervantes, Sorin G. Gal","submitted_at":"2017-11-06T20:21:47Z","abstract_excerpt":"In theory of one complex variable, Gauss-Lucas Theorem states that the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the polynomial. The exact analogue of this result cannot hold, in general, in the quaternionic case; instead, the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the so-called symmetrization of the given polynomial. An incomplete proof of this statement was given in [8]. In this paper we present a different but complete proof of this theorem and we discuss a consequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02157","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":""},"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":"1711.02157","created_at":"2026-05-18T00:31:08.680182+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.02157v1","created_at":"2026-05-18T00:31:08.680182+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02157","created_at":"2026-05-18T00:31:08.680182+00:00"},{"alias_kind":"pith_short_12","alias_value":"QYPFIT5JNYMI","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QYPFIT5JNYMIVMPZ","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QYPFIT5J","created_at":"2026-05-18T12:31:39.905425+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/QYPFIT5JNYMIVMPZTZLLXZWCIA","json":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA.json","graph_json":"https://pith.science/api/pith-number/QYPFIT5JNYMIVMPZTZLLXZWCIA/graph.json","events_json":"https://pith.science/api/pith-number/QYPFIT5JNYMIVMPZTZLLXZWCIA/events.json","paper":"https://pith.science/paper/QYPFIT5J"},"agent_actions":{"view_html":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA","download_json":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA.json","view_paper":"https://pith.science/paper/QYPFIT5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.02157&json=true","fetch_graph":"https://pith.science/api/pith-number/QYPFIT5JNYMIVMPZTZLLXZWCIA/graph.json","fetch_events":"https://pith.science/api/pith-number/QYPFIT5JNYMIVMPZTZLLXZWCIA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA/action/storage_attestation","attest_author":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA/action/author_attestation","sign_citation":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA/action/citation_signature","submit_replication":"https://pith.science/pith/QYPFIT5JNYMIVMPZTZLLXZWCIA/action/replication_record"}},"created_at":"2026-05-18T00:31:08.680182+00:00","updated_at":"2026-05-18T00:31:08.680182+00:00"}