{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MH4PW5LKH62U4LEXBJOPKYDP7A","short_pith_number":"pith:MH4PW5LK","canonical_record":{"source":{"id":"2407.05883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T12:44:18Z","cross_cats_sorted":[],"title_canon_sha256":"214f5700245049354d04bdbfe292d0c92b82d3ceb811e1c0fa802ac13ebd0caa","abstract_canon_sha256":"47b9b79e3a1ab98ae9d7241e237d222957f2fbc4e105d8d4f90cf3a9070c4e22"},"schema_version":"1.0"},"canonical_sha256":"61f8fb756a3fb54e2c970a5cf5606ff817e340be4ae43c24d35024df9b793f16","source":{"kind":"arxiv","id":"2407.05883","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.05883","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"2407.05883v2","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05883","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"MH4PW5LKH62U","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"pith_short_16","alias_value":"MH4PW5LKH62U4LEX","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"pith_short_8","alias_value":"MH4PW5LK","created_at":"2026-07-05T09:59:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MH4PW5LKH62U4LEXBJOPKYDP7A","target":"record","payload":{"canonical_record":{"source":{"id":"2407.05883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T12:44:18Z","cross_cats_sorted":[],"title_canon_sha256":"214f5700245049354d04bdbfe292d0c92b82d3ceb811e1c0fa802ac13ebd0caa","abstract_canon_sha256":"47b9b79e3a1ab98ae9d7241e237d222957f2fbc4e105d8d4f90cf3a9070c4e22"},"schema_version":"1.0"},"canonical_sha256":"61f8fb756a3fb54e2c970a5cf5606ff817e340be4ae43c24d35024df9b793f16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:17.266956Z","signature_b64":"77UVvAbDgkeZ3AkxlJDdvq8BP7IiJ7bqvNcLy2mGEhkjJ1KG6uabFH9pgANFK/vW8iGZDWIFbBGwYBMUJgKUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61f8fb756a3fb54e2c970a5cf5606ff817e340be4ae43c24d35024df9b793f16","last_reissued_at":"2026-07-05T09:59:17.266428Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:17.266428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.05883","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"euzW75urSfW9/OFd45nu41Fq6lTRVLWztoUOvkarEl5Tsg41A+Rc/DpVEByyssKvPpiutnlhtImu3f9tXWAJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:13:01.032691Z"},"content_sha256":"2d8a15c006e7f178d9b1e04d5964392655c2a17844877a680e988869b10610c2","schema_version":"1.0","event_id":"sha256:2d8a15c006e7f178d9b1e04d5964392655c2a17844877a680e988869b10610c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MH4PW5LKH62U4LEXBJOPKYDP7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A coarse Erd\\H{o}s-P\\'{o}sa theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. Pascal Gollin, Jungho Ahn, O-joung Kwon, Tony Huynh","submitted_at":"2024-07-08T12:44:18Z","abstract_excerpt":"An induced packing of cycles in a graph is a set of vertex-disjoint cycles with no edges between them. We generalise the classic Erd\\H{o}s-P\\'osa theorem to induced packings of cycles. More specifically, we show that there exist functions $f(k,\\ell)=\\mathcal{O}(\\ell k\\log k)$ and $g(k)=\\mathcal{O}(k\\log k)$ such that for all integers $k\\geq1$ and $\\ell\\geq3$, every graph $G$ contains either an induced packing of $k$ cycles of length at least $\\ell$, not necessarily induced cycles, or sets $X_1$ and $X_2$ of vertices with $|X_1|\\leq f(k,\\ell)$ and $|X_2|\\leq g(k)$ such that, after removing the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05883","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.05883/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bI673yPHTe/Mi5Ks14Te1obpodu9s8xfd0OCf1KqyNlhWYpo8cruaeucK2C3Pcj7SUa0R2Ru0E2WbNNyw8/rDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:13:01.033741Z"},"content_sha256":"73b36840191d6d4c1269784dd2f9cebd98886139d3dbbdb771bd95adec1d4b64","schema_version":"1.0","event_id":"sha256:73b36840191d6d4c1269784dd2f9cebd98886139d3dbbdb771bd95adec1d4b64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MH4PW5LKH62U4LEXBJOPKYDP7A/bundle.json","state_url":"https://pith.science/pith/MH4PW5LKH62U4LEXBJOPKYDP7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MH4PW5LKH62U4LEXBJOPKYDP7A/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T17:13:01Z","links":{"resolver":"https://pith.science/pith/MH4PW5LKH62U4LEXBJOPKYDP7A","bundle":"https://pith.science/pith/MH4PW5LKH62U4LEXBJOPKYDP7A/bundle.json","state":"https://pith.science/pith/MH4PW5LKH62U4LEXBJOPKYDP7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MH4PW5LKH62U4LEXBJOPKYDP7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MH4PW5LKH62U4LEXBJOPKYDP7A","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":"47b9b79e3a1ab98ae9d7241e237d222957f2fbc4e105d8d4f90cf3a9070c4e22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T12:44:18Z","title_canon_sha256":"214f5700245049354d04bdbfe292d0c92b82d3ceb811e1c0fa802ac13ebd0caa"},"schema_version":"1.0","source":{"id":"2407.05883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.05883","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"2407.05883v2","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05883","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"MH4PW5LKH62U","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"pith_short_16","alias_value":"MH4PW5LKH62U4LEX","created_at":"2026-07-05T09:59:17Z"},{"alias_kind":"pith_short_8","alias_value":"MH4PW5LK","created_at":"2026-07-05T09:59:17Z"}],"graph_snapshots":[{"event_id":"sha256:73b36840191d6d4c1269784dd2f9cebd98886139d3dbbdb771bd95adec1d4b64","target":"graph","created_at":"2026-07-05T09:59:17Z","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/2407.05883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An induced packing of cycles in a graph is a set of vertex-disjoint cycles with no edges between them. We generalise the classic Erd\\H{o}s-P\\'osa theorem to induced packings of cycles. More specifically, we show that there exist functions $f(k,\\ell)=\\mathcal{O}(\\ell k\\log k)$ and $g(k)=\\mathcal{O}(k\\log k)$ such that for all integers $k\\geq1$ and $\\ell\\geq3$, every graph $G$ contains either an induced packing of $k$ cycles of length at least $\\ell$, not necessarily induced cycles, or sets $X_1$ and $X_2$ of vertices with $|X_1|\\leq f(k,\\ell)$ and $|X_2|\\leq g(k)$ such that, after removing the ","authors_text":"J. Pascal Gollin, Jungho Ahn, O-joung Kwon, Tony Huynh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T12:44:18Z","title":"A coarse Erd\\H{o}s-P\\'{o}sa theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05883","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":"sha256:2d8a15c006e7f178d9b1e04d5964392655c2a17844877a680e988869b10610c2","target":"record","created_at":"2026-07-05T09:59:17Z","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":"47b9b79e3a1ab98ae9d7241e237d222957f2fbc4e105d8d4f90cf3a9070c4e22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T12:44:18Z","title_canon_sha256":"214f5700245049354d04bdbfe292d0c92b82d3ceb811e1c0fa802ac13ebd0caa"},"schema_version":"1.0","source":{"id":"2407.05883","kind":"arxiv","version":2}},"canonical_sha256":"61f8fb756a3fb54e2c970a5cf5606ff817e340be4ae43c24d35024df9b793f16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61f8fb756a3fb54e2c970a5cf5606ff817e340be4ae43c24d35024df9b793f16","first_computed_at":"2026-07-05T09:59:17.266428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:59:17.266428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"77UVvAbDgkeZ3AkxlJDdvq8BP7IiJ7bqvNcLy2mGEhkjJ1KG6uabFH9pgANFK/vW8iGZDWIFbBGwYBMUJgKUCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:59:17.266956Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.05883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d8a15c006e7f178d9b1e04d5964392655c2a17844877a680e988869b10610c2","sha256:73b36840191d6d4c1269784dd2f9cebd98886139d3dbbdb771bd95adec1d4b64"],"state_sha256":"c05068ea56d92e4dc2085c43770b1a2eb2497cb30fadce98e086287faac0d8fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqSmLwbq4pkSgyXf8qHXEB2yJqrJnopeoyNKdV2Fgfm42FR2BB+DgYoWFw/ImL/WxK3kT8X1bTPrDfFBRrk0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T17:13:01.040697Z","bundle_sha256":"624e0e06851c44a09f756fdad789c36faef159f44a5e4dc695c485a503839e58"}}