{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ATD7VUHSMV6BZSCFSDYMKUXBDK","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":"de1392de9d459a6df869e0c2b7b2d98fecb7c1617897c93074af1e95128d92cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-12T13:14:08Z","title_canon_sha256":"fd077c2b0c204b107acab9fda18990714b16b1efcbc99494bd59885c8bf8da66"},"schema_version":"1.0","source":{"id":"1602.04042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04042","created_at":"2026-05-18T01:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04042v2","created_at":"2026-05-18T01:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04042","created_at":"2026-05-18T01:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"ATD7VUHSMV6B","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ATD7VUHSMV6BZSCF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ATD7VUHS","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:c43522e4121ee6e216f99191fd999314767e4b2ea9eb94f9200b9e63a824eaa3","target":"graph","created_at":"2026-05-18T01:19:33Z","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"},"paper":{"abstract_excerpt":"A graph $H$ is an immersion of a graph $G$ if $H$ can be obtained by some sugraph $G$ after lifting incident edges. We prove that there is a polynomial function $f:\\Bbb{N}\\times\\Bbb{N}\\rightarrow\\Bbb{N}$, such that if $H$ is a connected planar subcubic graph on $h>0$ edges, $G$ is a graph, and $k$ is a non-negative integer, then either $G$ contains $k$ vertex/edge-disjoint subgraphs, each containing $H$ as an immersion, or $G$ contains a set $F$ of $f(k,h)$ vertices/edges such that $G\\setminus F$ does not contain $H$ as an immersion.","authors_text":"Archontia Giannopoulou, Dimitrios M. Thilikos, Jean-Florent Raymond, O-joung Kwon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-12T13:14:08Z","title":"Packing and Covering Immersion Models of Planar subcubic Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04042","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":"sha256:7bad1ffcf396381ceb0660a25993225f69a0f5e54461bbef2d2d5af831981d69","target":"record","created_at":"2026-05-18T01:19:33Z","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":"de1392de9d459a6df869e0c2b7b2d98fecb7c1617897c93074af1e95128d92cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-12T13:14:08Z","title_canon_sha256":"fd077c2b0c204b107acab9fda18990714b16b1efcbc99494bd59885c8bf8da66"},"schema_version":"1.0","source":{"id":"1602.04042","kind":"arxiv","version":2}},"canonical_sha256":"04c7fad0f2657c1cc84590f0c552e11aa1b9f89e3ac49c0f648491fc4ed9f0e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04c7fad0f2657c1cc84590f0c552e11aa1b9f89e3ac49c0f648491fc4ed9f0e0","first_computed_at":"2026-05-18T01:19:33.756282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:33.756282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nj05V3T4DU8jB2Q84HjK1pe4xkILW4zDG9hsBJLYHMWumqTUJ8YP9ZRBN9BcKeL/VeQEsEdSPkgF3RSOXRKkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:33.756706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bad1ffcf396381ceb0660a25993225f69a0f5e54461bbef2d2d5af831981d69","sha256:c43522e4121ee6e216f99191fd999314767e4b2ea9eb94f9200b9e63a824eaa3"],"state_sha256":"c304d6cfde6e43ec6f37b9bc07f8598da962ce300896414109deb0b6b6a11815"}