{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KTYW6YC3EKV6BVDFQEZJM5TJ24","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":"360740dac8cec659aa1a3b53472185d123bbb2edf08db96fa4b39fe3189ecd18","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-13T05:26:54Z","title_canon_sha256":"367e17cfe44bd26897bf3032bcb211d2bc38c928ef5999f1df262ee0354a8773"},"schema_version":"1.0","source":{"id":"2411.08345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.08345","created_at":"2026-07-05T09:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"2411.08345v1","created_at":"2026-07-05T09:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.08345","created_at":"2026-07-05T09:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"KTYW6YC3EKV6","created_at":"2026-07-05T09:34:45Z"},{"alias_kind":"pith_short_16","alias_value":"KTYW6YC3EKV6BVDF","created_at":"2026-07-05T09:34:45Z"},{"alias_kind":"pith_short_8","alias_value":"KTYW6YC3","created_at":"2026-07-05T09:34:45Z"}],"graph_snapshots":[{"event_id":"sha256:cce92d8d5a1aa93957708f12650156edcdce1b63057dba0f015a76c3d7331b70","target":"graph","created_at":"2026-07-05T09:34:45Z","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/2411.08345/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph is said to be $F$-free if it does not contain $F$ as a subgraph. Brualdi-Hoffman-Tur\\'{a}n problem seeks to determine the maximum spectral radius of an $F$-free graph with given size. The gem consists of a path on $4$ vertices, along with an additional vertex that is adjacent to every vertex of the path. Concerning Brualdi-Hoffman-Tur\\'{a}n problem of the gem, when the size is odd, Zhang and Wang [Discrete Math. 347 (2024) 114171] and Yu, Li and Peng [arXiv:2404. 03423] solved it. In this paper, we completely solve the Brualdi-Hoffman-Tur\\'{a}n problem type problem of the gem.","authors_text":"Fan Chen, Xiying Yuan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-13T05:26:54Z","title":"Brualdi-Hoffman-Tur\\'{a}n problem of the gem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.08345","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":"sha256:56b48002ac0dbf7aebfea3c8bb7f59405db0eca71150d74d5a5969b7d64f1998","target":"record","created_at":"2026-07-05T09:34:45Z","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":"360740dac8cec659aa1a3b53472185d123bbb2edf08db96fa4b39fe3189ecd18","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-13T05:26:54Z","title_canon_sha256":"367e17cfe44bd26897bf3032bcb211d2bc38c928ef5999f1df262ee0354a8773"},"schema_version":"1.0","source":{"id":"2411.08345","kind":"arxiv","version":1}},"canonical_sha256":"54f16f605b22abe0d4658132967669d715e8448a4caf36a5fa8add3ef56a355c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54f16f605b22abe0d4658132967669d715e8448a4caf36a5fa8add3ef56a355c","first_computed_at":"2026-07-05T09:34:45.696421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:34:45.696421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SEIx6CJl6/MBXt2r3OWFZKhccgn/BSlkgEz49dg+/xGHp0nvPN0NEOUIpl8siHhZhFpehCPvvQOAMboA63HNDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:34:45.696908Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.08345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56b48002ac0dbf7aebfea3c8bb7f59405db0eca71150d74d5a5969b7d64f1998","sha256:cce92d8d5a1aa93957708f12650156edcdce1b63057dba0f015a76c3d7331b70"],"state_sha256":"eea68db8f4edb57cdc43d67f37bb82876bc91812e64eea18cac355607215e1e1"}