{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JSWI74X4SILQDQYRZNW4UOOSI4","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":"c36c7dd5e027fb55a5731dbc33a06e17cb5ddcd82998caa61445dfb7d7c8cb60","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-05-25T17:11:32Z","title_canon_sha256":"e29ddd60317141d976657a5f67aab9b66eadd93dd427ce2872f85c6a6d6b708a"},"schema_version":"1.0","source":{"id":"2305.16256","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.16256","created_at":"2026-07-05T08:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"2305.16256v3","created_at":"2026-07-05T08:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16256","created_at":"2026-07-05T08:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"JSWI74X4SILQ","created_at":"2026-07-05T08:59:58Z"},{"alias_kind":"pith_short_16","alias_value":"JSWI74X4SILQDQYR","created_at":"2026-07-05T08:59:58Z"},{"alias_kind":"pith_short_8","alias_value":"JSWI74X4","created_at":"2026-07-05T08:59:58Z"}],"graph_snapshots":[{"event_id":"sha256:f15e3a04b70967d807d502ad279b630727bee89b7765a5fe60c1e04fe7fc2533","target":"graph","created_at":"2026-07-05T08:59:58Z","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/2305.16256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph $G=(V,E)$, the dominating number of a graph is the minimum size of a vertex set, $V' \\subseteq V$, so that every vertex in the graph is either in $V'$ or is adjacent to a vertex in $V'$. A Roman Dominating function of $G$ is defined as $f:V \\rightarrow \\{0,1,2\\}$ such that every vertex with a label of 0 in $G$ is adjacent to a vertex with a label of 2. The Roman Dominating number of a graph is the minimum total weight over all possible Roman Dominating functions. We consider the $k$-attack Roman Domination, particularly focusing on 2-attack Roman Domination. A Roman Dominating fu","authors_text":"Garrison Koch, Nathan Shank","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-05-25T17:11:32Z","title":"On the $nk-attack Roman Dominating Number of a Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16256","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":"sha256:573535ce5d3e94cb5de0b569267061fd2cf359f44026ce8192ddbfe54a231115","target":"record","created_at":"2026-07-05T08:59:58Z","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":"c36c7dd5e027fb55a5731dbc33a06e17cb5ddcd82998caa61445dfb7d7c8cb60","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-05-25T17:11:32Z","title_canon_sha256":"e29ddd60317141d976657a5f67aab9b66eadd93dd427ce2872f85c6a6d6b708a"},"schema_version":"1.0","source":{"id":"2305.16256","kind":"arxiv","version":3}},"canonical_sha256":"4cac8ff2fc921701c311cb6dca39d2470953c7707a482fe091ad38e5b9a14706","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cac8ff2fc921701c311cb6dca39d2470953c7707a482fe091ad38e5b9a14706","first_computed_at":"2026-07-05T08:59:58.667551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:59:58.667551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5F9meGRgRzt+c4ZZHzcTPAz/GVWkIW1a/+gTzjBtsMpjxYUKZYKszsX7qWklbOJ+fp7FVp3OEr/X3Ua/aJNIAA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:59:58.667983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.16256","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:573535ce5d3e94cb5de0b569267061fd2cf359f44026ce8192ddbfe54a231115","sha256:f15e3a04b70967d807d502ad279b630727bee89b7765a5fe60c1e04fe7fc2533"],"state_sha256":"a57289e70563d49e0615b2bece50d8a621fcc403d05f14fe7e16bfd37d3a14b3"}