{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WGLKJACWRKPWRLJJTQ264EOPAG","short_pith_number":"pith:WGLKJACW","schema_version":"1.0","canonical_sha256":"b196a480568a9f68ad299c35ee11cf01b63db9b79731ccc18e1e8f713c2d869b","source":{"kind":"arxiv","id":"1307.4724","version":1},"attestation_state":"computed","paper":{"title":"On the strong metric generators of strong product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dorota Kuziak, Ismael G. Yero, Juan A. Rodr\\'iguez-Vel\\'azquez","submitted_at":"2013-07-17T18:45:30Z","abstract_excerpt":"Let $G$ be a connected graph. A vertex $w\\in V(G)$ strongly resolves two vertices $u,v\\in V(G)$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $S$ of vertices is a strong metric generator for $G$ if every pair of vertices of $G$ is strongly resolved by some vertex of $S$. The smallest cardinality of a strong metric generator for $G$ is called the strong metric dimension of $G$. It is well known that the problem of computing this invariant is NP-hard. In this paper we study the problem of finding exact values or sharp bounds for the str"},"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":"1307.4724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-17T18:45:30Z","cross_cats_sorted":[],"title_canon_sha256":"cb46a7a72a7e6dad9340b0b3ad43b29d005a940dc12437b0a063f405ab1b8fb3","abstract_canon_sha256":"8dde77187fc29cd171cca30aef6bc45a7fd6c69b239f6db8679781263d308794"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:17.305704Z","signature_b64":"jWB6Fooy4Mfwy/wogew+PPdKiMPvLESfYx/qBrRHT9ffNklJ2iRyQlwgrMm/NA4MvuB77N/QRQiwLlU7oFCSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b196a480568a9f68ad299c35ee11cf01b63db9b79731ccc18e1e8f713c2d869b","last_reissued_at":"2026-05-18T03:18:17.305099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:17.305099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the strong metric generators of strong product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dorota Kuziak, Ismael G. Yero, Juan A. Rodr\\'iguez-Vel\\'azquez","submitted_at":"2013-07-17T18:45:30Z","abstract_excerpt":"Let $G$ be a connected graph. A vertex $w\\in V(G)$ strongly resolves two vertices $u,v\\in V(G)$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $S$ of vertices is a strong metric generator for $G$ if every pair of vertices of $G$ is strongly resolved by some vertex of $S$. The smallest cardinality of a strong metric generator for $G$ is called the strong metric dimension of $G$. It is well known that the problem of computing this invariant is NP-hard. In this paper we study the problem of finding exact values or sharp bounds for the str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4724","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1307.4724","created_at":"2026-05-18T03:18:17.305198+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4724v1","created_at":"2026-05-18T03:18:17.305198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4724","created_at":"2026-05-18T03:18:17.305198+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGLKJACWRKPW","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGLKJACWRKPWRLJJ","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGLKJACW","created_at":"2026-05-18T12:28:04.890932+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/WGLKJACWRKPWRLJJTQ264EOPAG","json":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG.json","graph_json":"https://pith.science/api/pith-number/WGLKJACWRKPWRLJJTQ264EOPAG/graph.json","events_json":"https://pith.science/api/pith-number/WGLKJACWRKPWRLJJTQ264EOPAG/events.json","paper":"https://pith.science/paper/WGLKJACW"},"agent_actions":{"view_html":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG","download_json":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG.json","view_paper":"https://pith.science/paper/WGLKJACW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4724&json=true","fetch_graph":"https://pith.science/api/pith-number/WGLKJACWRKPWRLJJTQ264EOPAG/graph.json","fetch_events":"https://pith.science/api/pith-number/WGLKJACWRKPWRLJJTQ264EOPAG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG/action/storage_attestation","attest_author":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG/action/author_attestation","sign_citation":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG/action/citation_signature","submit_replication":"https://pith.science/pith/WGLKJACWRKPWRLJJTQ264EOPAG/action/replication_record"}},"created_at":"2026-05-18T03:18:17.305198+00:00","updated_at":"2026-05-18T03:18:17.305198+00:00"}