{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CBKZU26A5HABJ5OB6B4NTKEQWM","short_pith_number":"pith:CBKZU26A","schema_version":"1.0","canonical_sha256":"10559a6bc0e9c014f5c1f078d9a890b3008bbe211290bb7969ed5d65c1be2b8a","source":{"kind":"arxiv","id":"1906.04134","version":2},"attestation_state":"computed","paper":{"title":"A note on Lefschetz spheres and their relatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Afshin Goodarzi","submitted_at":"2019-06-10T17:11:25Z","abstract_excerpt":"Inspired by the works of Adiprasito, Babson, Nevo, and Murai on the $g$-conjecture, we consider different classes of PL-spheres and the relations between them. We focus on a certain class of spheres that is in the intersection of vertex-decomposable spheres (a concept due to Provan and Billera) and strongly edge-decomposable spheres (a concept due to Eran Nevo). The spheres in this class are exactly those vertex-decomposable ones for which Adiprasito's recent proof method works."},"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":"1906.04134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T17:11:25Z","cross_cats_sorted":[],"title_canon_sha256":"57612fc76b0dbb92e800035409a27decd24e33df668e2eef2d9de9ada0c31d7a","abstract_canon_sha256":"bc1ac787a678569130cd58840505e68c57e31ab77c4829c84d3dc40a515c2555"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:58.047591Z","signature_b64":"y/s+2hORd/whwrqpA7ckq4LdzJQvPTyHaWRGhSf1AmRV+qQsbIEwoe/ybpzRv0U9W/e1rKNCrm+zFXRmDJZiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10559a6bc0e9c014f5c1f078d9a890b3008bbe211290bb7969ed5d65c1be2b8a","last_reissued_at":"2026-05-17T23:42:58.047042Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:58.047042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on Lefschetz spheres and their relatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Afshin Goodarzi","submitted_at":"2019-06-10T17:11:25Z","abstract_excerpt":"Inspired by the works of Adiprasito, Babson, Nevo, and Murai on the $g$-conjecture, we consider different classes of PL-spheres and the relations between them. We focus on a certain class of spheres that is in the intersection of vertex-decomposable spheres (a concept due to Provan and Billera) and strongly edge-decomposable spheres (a concept due to Eran Nevo). The spheres in this class are exactly those vertex-decomposable ones for which Adiprasito's recent proof method works."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04134","kind":"arxiv","version":2},"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":"1906.04134","created_at":"2026-05-17T23:42:58.047124+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.04134v2","created_at":"2026-05-17T23:42:58.047124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04134","created_at":"2026-05-17T23:42:58.047124+00:00"},{"alias_kind":"pith_short_12","alias_value":"CBKZU26A5HAB","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"CBKZU26A5HABJ5OB","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"CBKZU26A","created_at":"2026-05-18T12:33:12.712433+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/CBKZU26A5HABJ5OB6B4NTKEQWM","json":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM.json","graph_json":"https://pith.science/api/pith-number/CBKZU26A5HABJ5OB6B4NTKEQWM/graph.json","events_json":"https://pith.science/api/pith-number/CBKZU26A5HABJ5OB6B4NTKEQWM/events.json","paper":"https://pith.science/paper/CBKZU26A"},"agent_actions":{"view_html":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM","download_json":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM.json","view_paper":"https://pith.science/paper/CBKZU26A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.04134&json=true","fetch_graph":"https://pith.science/api/pith-number/CBKZU26A5HABJ5OB6B4NTKEQWM/graph.json","fetch_events":"https://pith.science/api/pith-number/CBKZU26A5HABJ5OB6B4NTKEQWM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM/action/storage_attestation","attest_author":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM/action/author_attestation","sign_citation":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM/action/citation_signature","submit_replication":"https://pith.science/pith/CBKZU26A5HABJ5OB6B4NTKEQWM/action/replication_record"}},"created_at":"2026-05-17T23:42:58.047124+00:00","updated_at":"2026-05-17T23:42:58.047124+00:00"}