{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DAFMLM2S2XMFYXB4NJK3IFGLGO","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":"b12c016e70d57b66d92f4a9be846de4f2bd5ec63ed170992ca5db283f5bb689c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-09T12:24:11Z","title_canon_sha256":"0dd5cc76150e41ebf5972db70d12850d51d72c4744a29a5df7f0cd5fd6759370"},"schema_version":"1.0","source":{"id":"2406.05758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.05758","created_at":"2026-07-05T08:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"2406.05758v1","created_at":"2026-07-05T08:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.05758","created_at":"2026-07-05T08:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"DAFMLM2S2XMF","created_at":"2026-07-05T08:29:33Z"},{"alias_kind":"pith_short_16","alias_value":"DAFMLM2S2XMFYXB4","created_at":"2026-07-05T08:29:33Z"},{"alias_kind":"pith_short_8","alias_value":"DAFMLM2S","created_at":"2026-07-05T08:29:33Z"}],"graph_snapshots":[{"event_id":"sha256:f8849afc540f683e0899237ae23891be11b9ca9571926dfed9f77368b2a2df22","target":"graph","created_at":"2026-07-05T08:29:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.05758/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Planar Tur\\'an number, denoted by $ex_{\\mathcal{P}}(n,H)$, is the maximum number of edges in an $n$-vertex planar graph which does not contain $H$ as a subgraph. Ghosh, Gy\\H{o}ri, Paulos and Xiao initiated the topic of the planar Tur\\'an number for double stars. For balanced double star, $S_{3,3}$ is the only remaining graph need to be considered. In this paper, we give the exact value of $ex_{\\mathcal{P}}(n,S_{3,3})$, forcing the planar Tur\\'an number for all balanced double stars completely determined.","authors_text":"Guiying Yan, Qiang Zhou, Tong Li, Xin Xu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-09T12:24:11Z","title":"Planar Tur\\'an number for balanced double stars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05758","kind":"arxiv","version":1},"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":"sha256:79f42c2253338b7c74823faa6fc86ffe55b4cda7814f63af3835858b34124c1e","target":"record","created_at":"2026-07-05T08:29:33Z","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":"b12c016e70d57b66d92f4a9be846de4f2bd5ec63ed170992ca5db283f5bb689c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-09T12:24:11Z","title_canon_sha256":"0dd5cc76150e41ebf5972db70d12850d51d72c4744a29a5df7f0cd5fd6759370"},"schema_version":"1.0","source":{"id":"2406.05758","kind":"arxiv","version":1}},"canonical_sha256":"180ac5b352d5d85c5c3c6a55b414cb3384ba49a6d31a665a552468a821e60a7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"180ac5b352d5d85c5c3c6a55b414cb3384ba49a6d31a665a552468a821e60a7a","first_computed_at":"2026-07-05T08:29:33.328068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:29:33.328068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LVuqUTsdHzNmauFGavnklE67tjxKinQJm7z3Uhf+L60TmuiHZHyiXQfTPtIHWDPrySlC1PA/zDDOsrOPF+Q5CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:29:33.328486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.05758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79f42c2253338b7c74823faa6fc86ffe55b4cda7814f63af3835858b34124c1e","sha256:f8849afc540f683e0899237ae23891be11b9ca9571926dfed9f77368b2a2df22"],"state_sha256":"77c05abd5f34d700883876bc5eaa210f6ed594afe80ab03d256377eb2a726946"}