{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HWUZQCSGGGHQWIZCGTXT64UBHR","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":"f5f71dc0895de0d058199cdcdbf9921fc874476728994f57b8e194602a13390d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-15T06:56:13Z","title_canon_sha256":"60617ff51445f595d3bc92edd22e46758139cd2cb399500b5541855dbcaf95f7"},"schema_version":"1.0","source":{"id":"2507.11034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.11034","created_at":"2026-07-05T11:37:30Z"},{"alias_kind":"arxiv_version","alias_value":"2507.11034v1","created_at":"2026-07-05T11:37:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.11034","created_at":"2026-07-05T11:37:30Z"},{"alias_kind":"pith_short_12","alias_value":"HWUZQCSGGGHQ","created_at":"2026-07-05T11:37:30Z"},{"alias_kind":"pith_short_16","alias_value":"HWUZQCSGGGHQWIZC","created_at":"2026-07-05T11:37:30Z"},{"alias_kind":"pith_short_8","alias_value":"HWUZQCSG","created_at":"2026-07-05T11:37:30Z"}],"graph_snapshots":[{"event_id":"sha256:38332eeb8d4a100e4a36de248f7cdeb0e81e96a184075f774dc62d022b1f81fd","target":"graph","created_at":"2026-07-05T11:37:30Z","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/2507.11034/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathscr{F}$ be a family of graphs. A graph $G$ is $\\mathscr{F}$-free if $G$ does not contain any $F\\in \\mathscr{F}$ as a subgraph. The Tur\\'an number, denoted by $ex(n, \\mathscr{F})$, is the maximum number of edges in an $n$-vertex $\\mathscr{F}$-free graph. Let $F $ be a fixed graph with $ \\chi(F) \\geq 3 $. A forest $H$ is called a linear forest if all components of $H$ are paths. In this paper, we determined the exact value of $ex(n, \\{H, F\\}) $ for a fixed graph $F$ with $\\chi(F)\\geq 3$ and a linear forest $H$ with at least $2$ components and each component with size at least $3$.","authors_text":"Haixiang Zhang, Mei Lu, Xiamiao Zhao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-15T06:56:13Z","title":"Tur\\'an type problems for a fixed graph and a linear forest"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11034","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":"sha256:468ccf4ef55d4730b6b43d8855ea920065c8618716b198ced41ac41e2c58470f","target":"record","created_at":"2026-07-05T11:37:30Z","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":"f5f71dc0895de0d058199cdcdbf9921fc874476728994f57b8e194602a13390d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-15T06:56:13Z","title_canon_sha256":"60617ff51445f595d3bc92edd22e46758139cd2cb399500b5541855dbcaf95f7"},"schema_version":"1.0","source":{"id":"2507.11034","kind":"arxiv","version":1}},"canonical_sha256":"3da9980a46318f0b232234ef3f72813c7a13a314602b1c397b2d5c9f5ba3a1e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3da9980a46318f0b232234ef3f72813c7a13a314602b1c397b2d5c9f5ba3a1e8","first_computed_at":"2026-07-05T11:37:30.743862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:30.743862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2RiHBUGAXSh4XLjkVuc/8uhdMxvc2KSiFQfKVNbXTEMRUVITIq1DARKYpp0IK6c+CALeujHv9Vov9CI2iHAHDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:30.744436Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.11034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:468ccf4ef55d4730b6b43d8855ea920065c8618716b198ced41ac41e2c58470f","sha256:38332eeb8d4a100e4a36de248f7cdeb0e81e96a184075f774dc62d022b1f81fd"],"state_sha256":"007fd972ae98bceecaef03b063039037b62560a9c68ead9e3dc61200e593d3af"}