{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SOCFTDY3E4G3IIMAPFRU4XEHK5","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":"44e386ca82188bfaebdae981e9f58ab786a102f998e1a85fc938f167a21deab3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T07:37:34Z","title_canon_sha256":"f95abbacc12a7a0f2a5726e6f10091077809fdfa16df38f3c92933383fba068c"},"schema_version":"1.0","source":{"id":"2506.00878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00878","created_at":"2026-07-05T11:13:42Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00878v1","created_at":"2026-07-05T11:13:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00878","created_at":"2026-07-05T11:13:42Z"},{"alias_kind":"pith_short_12","alias_value":"SOCFTDY3E4G3","created_at":"2026-07-05T11:13:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOCFTDY3E4G3IIMA","created_at":"2026-07-05T11:13:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOCFTDY3","created_at":"2026-07-05T11:13:42Z"}],"graph_snapshots":[{"event_id":"sha256:4a7b639eca7eea05cb4052fc9249e99634d696abb5d16fbf6ae8f14aa94d20f5","target":"graph","created_at":"2026-07-05T11:13:42Z","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/2506.00878/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, the problem of establishing bounds on the edge density of 1-planar graphs, including their subclass IC-planar graphs, has received considerable attention. In 2018, Angelini et al. showed that any n-vertex bipartite IC-planar graph has at most 2.25n-4 edges, which implies that bipartite IC-planar graphs have vertex-connectivity at most 4. In this paper, we prove that any n-vertex maximal bipartite IC-plane graph with connectivity 2 has at least 3/2n-2 edges, and those with connectivity 3 has at least 2n-3 edges. All the above lower bounds are tight. For 4-connected maximal bipartite I","authors_text":"Guiping Wang, Licheng Zhang, Yuanqiu Huang, Zhangdong Ouyang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T07:37:34Z","title":"The minimum size of maximal bipartite IC-plane graphs with given connectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00878","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:ffea528d0308e34efb5caab8200c3da31f27bf45acde98abb218cb406406e5cc","target":"record","created_at":"2026-07-05T11:13:42Z","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":"44e386ca82188bfaebdae981e9f58ab786a102f998e1a85fc938f167a21deab3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-01T07:37:34Z","title_canon_sha256":"f95abbacc12a7a0f2a5726e6f10091077809fdfa16df38f3c92933383fba068c"},"schema_version":"1.0","source":{"id":"2506.00878","kind":"arxiv","version":1}},"canonical_sha256":"9384598f1b270db4218079634e5c875740af2105c778e20f2e8547b57d0baec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9384598f1b270db4218079634e5c875740af2105c778e20f2e8547b57d0baec7","first_computed_at":"2026-07-05T11:13:42.155245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:42.155245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Egc/HPhBSyN8StOZPRRNg+0qm/BZp/IDkYgRTG9K8+EBHKoR25EcyMVgtWR6BfuBJrF+5zOSk/KVzrSw5fAIAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:42.155746Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.00878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffea528d0308e34efb5caab8200c3da31f27bf45acde98abb218cb406406e5cc","sha256:4a7b639eca7eea05cb4052fc9249e99634d696abb5d16fbf6ae8f14aa94d20f5"],"state_sha256":"5cb8336af1cf7d0618a434923fdf4dedad07e3b188aabd75aaca05b79b38cc9e"}