{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E5JAEXNQCK5NOEEO6GPXKDCWNF","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":"6e9ec61e2bd41c74490826fa10e5c691afcecd88a9de729781811fdc00bb691f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-07T07:51:12Z","title_canon_sha256":"9690bf3dbc57f8056fbcd76941fd949af6078ed890c5eb4b7a005475fccb90b0"},"schema_version":"1.0","source":{"id":"1607.01903","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01903","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01903v3","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01903","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"pith_short_12","alias_value":"E5JAEXNQCK5N","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5JAEXNQCK5NOEEO","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5JAEXNQ","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:76118d96e25dedc9e4e65e5db3966a1acf407c1d85f287a5557966a6f2f09e3f","target":"graph","created_at":"2026-05-18T00:43:30Z","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"},"paper":{"abstract_excerpt":"We prove that the set of long cycles has the edge-Erd\\H{o}s-P\\'osa property: for every fixed integer $\\ell\\ge 3$ and every $k\\in\\mathbb{N}$, every graph $G$ either contains $k$ edge-disjoint cycles of length at least $\\ell$ (long cycles) or an edge set $X$ of size $O(k^2\\log k + \\ell k)$ such that $G-X$ does not contain any long cycle. This answers a question of Birmel\\'e, Bondy, and Reed (Combinatorica 27 (2007), 135--145).","authors_text":"Felix Joos, Henning Bruhn, Matthias Heinlein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-07T07:51:12Z","title":"Long cycles have the edge-Erd\\H{o}s-P\\'osa property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01903","kind":"arxiv","version":3},"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":"sha256:9516bd3dda75ed38e07e3fc242d09293237d52ec3c0c5c7b8175fbae5ee17b7b","target":"record","created_at":"2026-05-18T00:43:30Z","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":"6e9ec61e2bd41c74490826fa10e5c691afcecd88a9de729781811fdc00bb691f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-07T07:51:12Z","title_canon_sha256":"9690bf3dbc57f8056fbcd76941fd949af6078ed890c5eb4b7a005475fccb90b0"},"schema_version":"1.0","source":{"id":"1607.01903","kind":"arxiv","version":3}},"canonical_sha256":"2752025db012bad7108ef19f750c56696c4df2fb6da2809d62c10f5089c6d2a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2752025db012bad7108ef19f750c56696c4df2fb6da2809d62c10f5089c6d2a9","first_computed_at":"2026-05-18T00:43:30.590632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:30.590632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LbpgU+cvLBqvzmpoGkI/8qvFDN4QyFEGvI4LSTPtTuEQPIsKUXCM/gnIDXmMh89vIk5l7nCnK5FVDW5z1jb5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:30.591099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01903","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9516bd3dda75ed38e07e3fc242d09293237d52ec3c0c5c7b8175fbae5ee17b7b","sha256:76118d96e25dedc9e4e65e5db3966a1acf407c1d85f287a5557966a6f2f09e3f"],"state_sha256":"3d67d5b1932b015c7e9873c36ece1b1cd3c95b8b94c6373c28efdb9096b30eec"}