{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CBKZU26A5HABJ5OB6B4NTKEQWM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bc1ac787a678569130cd58840505e68c57e31ab77c4829c84d3dc40a515c2555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T17:11:25Z","title_canon_sha256":"57612fc76b0dbb92e800035409a27decd24e33df668e2eef2d9de9ada0c31d7a"},"schema_version":"1.0","source":{"id":"1906.04134","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04134","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04134v2","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04134","created_at":"2026-05-17T23:42:58Z"},{"alias_kind":"pith_short_12","alias_value":"CBKZU26A5HAB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CBKZU26A5HABJ5OB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CBKZU26A","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:be5cd861031c9b24f26fbde27b9827175a975cc9f046a9034ae3e5988d7997f0","target":"graph","created_at":"2026-05-17T23:42:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Afshin Goodarzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T17:11:25Z","title":"A note on Lefschetz spheres and their relatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04134","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8de27cb58c14457a5958152cf9f84586a6a1b0cdd06a11f03bed94aea0016159","target":"record","created_at":"2026-05-17T23:42:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bc1ac787a678569130cd58840505e68c57e31ab77c4829c84d3dc40a515c2555","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-10T17:11:25Z","title_canon_sha256":"57612fc76b0dbb92e800035409a27decd24e33df668e2eef2d9de9ada0c31d7a"},"schema_version":"1.0","source":{"id":"1906.04134","kind":"arxiv","version":2}},"canonical_sha256":"10559a6bc0e9c014f5c1f078d9a890b3008bbe211290bb7969ed5d65c1be2b8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10559a6bc0e9c014f5c1f078d9a890b3008bbe211290bb7969ed5d65c1be2b8a","first_computed_at":"2026-05-17T23:42:58.047042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:58.047042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y/s+2hORd/whwrqpA7ckq4LdzJQvPTyHaWRGhSf1AmRV+qQsbIEwoe/ybpzRv0U9W/e1rKNCrm+zFXRmDJZiBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:58.047591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.04134","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8de27cb58c14457a5958152cf9f84586a6a1b0cdd06a11f03bed94aea0016159","sha256:be5cd861031c9b24f26fbde27b9827175a975cc9f046a9034ae3e5988d7997f0"],"state_sha256":"9677a4c3642e3f5852ba0c69bca82c2df5e75bc3955b7faa6fc56d045e52cc9a"}