{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WGLKJACWRKPWRLJJTQ264EOPAG","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":"8dde77187fc29cd171cca30aef6bc45a7fd6c69b239f6db8679781263d308794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-17T18:45:30Z","title_canon_sha256":"cb46a7a72a7e6dad9340b0b3ad43b29d005a940dc12437b0a063f405ab1b8fb3"},"schema_version":"1.0","source":{"id":"1307.4724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4724","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4724v1","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4724","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"pith_short_12","alias_value":"WGLKJACWRKPW","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WGLKJACWRKPWRLJJ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WGLKJACW","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:82f7c4d61b28875bd1b465e6574b4490b4aa7f7589fcc5d3ee7a8259acbaf396","target":"graph","created_at":"2026-05-18T03:18:17Z","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"},"paper":{"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","authors_text":"Dorota Kuziak, Ismael G. Yero, Juan A. Rodr\\'iguez-Vel\\'azquez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-17T18:45:30Z","title":"On the strong metric generators of strong product graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4724","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:b6841cee8a686b9aa887f6c49f6e62637f71cf13c4a6a2c2aacf9976711e43b8","target":"record","created_at":"2026-05-18T03:18:17Z","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":"8dde77187fc29cd171cca30aef6bc45a7fd6c69b239f6db8679781263d308794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-17T18:45:30Z","title_canon_sha256":"cb46a7a72a7e6dad9340b0b3ad43b29d005a940dc12437b0a063f405ab1b8fb3"},"schema_version":"1.0","source":{"id":"1307.4724","kind":"arxiv","version":1}},"canonical_sha256":"b196a480568a9f68ad299c35ee11cf01b63db9b79731ccc18e1e8f713c2d869b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b196a480568a9f68ad299c35ee11cf01b63db9b79731ccc18e1e8f713c2d869b","first_computed_at":"2026-05-18T03:18:17.305099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:17.305099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jWB6Fooy4Mfwy/wogew+PPdKiMPvLESfYx/qBrRHT9ffNklJ2iRyQlwgrMm/NA4MvuB77N/QRQiwLlU7oFCSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:17.305704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6841cee8a686b9aa887f6c49f6e62637f71cf13c4a6a2c2aacf9976711e43b8","sha256:82f7c4d61b28875bd1b465e6574b4490b4aa7f7589fcc5d3ee7a8259acbaf396"],"state_sha256":"c43d441f321b52d2f2b86139c233e10daa70466b3e7cb2c54100f89d976a48dc"}