{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:JSWI74X4SILQDQYRZNW4UOOSI4","short_pith_number":"pith:JSWI74X4","schema_version":"1.0","canonical_sha256":"4cac8ff2fc921701c311cb6dca39d2470953c7707a482fe091ad38e5b9a14706","source":{"kind":"arxiv","id":"2305.16256","version":3},"attestation_state":"computed","paper":{"title":"On the $nk-attack Roman Dominating Number of a Graph","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Garrison Koch, Nathan Shank","submitted_at":"2023-05-25T17:11:32Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2305.16256","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-05-25T17:11:32Z","cross_cats_sorted":[],"title_canon_sha256":"e29ddd60317141d976657a5f67aab9b66eadd93dd427ce2872f85c6a6d6b708a","abstract_canon_sha256":"c36c7dd5e027fb55a5731dbc33a06e17cb5ddcd82998caa61445dfb7d7c8cb60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:59:58.667983Z","signature_b64":"5F9meGRgRzt+c4ZZHzcTPAz/GVWkIW1a/+gTzjBtsMpjxYUKZYKszsX7qWklbOJ+fp7FVp3OEr/X3Ua/aJNIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cac8ff2fc921701c311cb6dca39d2470953c7707a482fe091ad38e5b9a14706","last_reissued_at":"2026-07-05T08:59:58.667551Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:59:58.667551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $nk-attack Roman Dominating Number of a Graph","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Garrison Koch, Nathan Shank","submitted_at":"2023-05-25T17:11:32Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16256","kind":"arxiv","version":3},"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/2305.16256/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2305.16256","created_at":"2026-07-05T08:59:58.667613+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.16256v3","created_at":"2026-07-05T08:59:58.667613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16256","created_at":"2026-07-05T08:59:58.667613+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSWI74X4SILQ","created_at":"2026-07-05T08:59:58.667613+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSWI74X4SILQDQYR","created_at":"2026-07-05T08:59:58.667613+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSWI74X4","created_at":"2026-07-05T08:59:58.667613+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4","json":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4.json","graph_json":"https://pith.science/api/pith-number/JSWI74X4SILQDQYRZNW4UOOSI4/graph.json","events_json":"https://pith.science/api/pith-number/JSWI74X4SILQDQYRZNW4UOOSI4/events.json","paper":"https://pith.science/paper/JSWI74X4"},"agent_actions":{"view_html":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4","download_json":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4.json","view_paper":"https://pith.science/paper/JSWI74X4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.16256&json=true","fetch_graph":"https://pith.science/api/pith-number/JSWI74X4SILQDQYRZNW4UOOSI4/graph.json","fetch_events":"https://pith.science/api/pith-number/JSWI74X4SILQDQYRZNW4UOOSI4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4/action/storage_attestation","attest_author":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4/action/author_attestation","sign_citation":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4/action/citation_signature","submit_replication":"https://pith.science/pith/JSWI74X4SILQDQYRZNW4UOOSI4/action/replication_record"}},"created_at":"2026-07-05T08:59:58.667613+00:00","updated_at":"2026-07-05T08:59:58.667613+00:00"}