{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:4NMVYV6W7CH2ESFXZMRQCWJISD","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":"39f736853351c219316589be1f253f7348dc146baafca7a21c186e6cf27120de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-03-23T05:49:15Z","title_canon_sha256":"3e6d726f59bfb9208a037ef9ec6ad65e6e78a3eb99345c60b90a91806d5a5962"},"schema_version":"1.0","source":{"id":"2203.12206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.12206","created_at":"2026-07-05T04:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"2203.12206v1","created_at":"2026-07-05T04:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.12206","created_at":"2026-07-05T04:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"4NMVYV6W7CH2","created_at":"2026-07-05T04:07:56Z"},{"alias_kind":"pith_short_16","alias_value":"4NMVYV6W7CH2ESFX","created_at":"2026-07-05T04:07:56Z"},{"alias_kind":"pith_short_8","alias_value":"4NMVYV6W","created_at":"2026-07-05T04:07:56Z"}],"graph_snapshots":[{"event_id":"sha256:7325a11a564264fcf623b5fdf2e921b4effc1abce5c20392884e6ae491a64025","target":"graph","created_at":"2026-07-05T04:07:56Z","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/2203.12206/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"After $2$-crossing-critical graphs were characterized in 2016, their most general subfamily, large $3$-connected $2$-crossing-critical graphs, has attracted separate attention. This paper presents sharp upper and lower bounds for their domination and independence number.","authors_text":"Martin Pra\\v{c}ek, Maru\\v{s}a Lek\\v{s}e, Mihael Pa\\v{c}nik, Petra Podlogar, Vesna Ir\\v{s}i\\v{c}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-03-23T05:49:15Z","title":"Domination and independence number of large $2$-crossing-critical graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12206","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":"sha256:19d7c500aa92e6fe325108c4f634b89f6adafbf26c11ada82fdb96e6c43f8c75","target":"record","created_at":"2026-07-05T04:07:56Z","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":"39f736853351c219316589be1f253f7348dc146baafca7a21c186e6cf27120de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-03-23T05:49:15Z","title_canon_sha256":"3e6d726f59bfb9208a037ef9ec6ad65e6e78a3eb99345c60b90a91806d5a5962"},"schema_version":"1.0","source":{"id":"2203.12206","kind":"arxiv","version":1}},"canonical_sha256":"e3595c57d6f88fa248b7cb2301592890d1cd9df2cba3944800242a90aa2595e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3595c57d6f88fa248b7cb2301592890d1cd9df2cba3944800242a90aa2595e1","first_computed_at":"2026-07-05T04:07:56.932853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:07:56.932853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5iEN3IHqVJ2i42tNhx2Osbrv0Crab6dHrf3wGiwI+MaPe/sBR8SblrgmnrFtcX3poflGxNzYLdAmNs6qh7uWDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:07:56.933267Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.12206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19d7c500aa92e6fe325108c4f634b89f6adafbf26c11ada82fdb96e6c43f8c75","sha256:7325a11a564264fcf623b5fdf2e921b4effc1abce5c20392884e6ae491a64025"],"state_sha256":"a2b9a45147708b235b743e6135665ba1bdfcd0ba5e5049f6da594a642806bea5"}