{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7OQCK5D5TFKHO2HUQLZED3PHO6","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":"88f6ecdb2ff703f2d3a25d5d157bab4fdf2ee5ff29e05ff5bc33c52a93600ff1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T09:16:52Z","title_canon_sha256":"4b036b2a8a928cb1a0b87a6c09518f69a2e4c94506c1fde9d1679f3c51a42a8b"},"schema_version":"1.0","source":{"id":"1708.02414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02414","created_at":"2026-05-18T00:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02414v1","created_at":"2026-05-18T00:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02414","created_at":"2026-05-18T00:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"7OQCK5D5TFKH","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7OQCK5D5TFKHO2HU","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7OQCK5D5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:fe4a18f8dd5e2112a8f61d991fced42798199db5f5ded8bd717e1de67764c7b6","target":"graph","created_at":"2026-05-18T00:38:24Z","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":"The strong geodetic problem is a recent variation of the geodetic problem. For a graph $G$, its strong geodetic number ${\\rm sg}(G)$ is the cardinality of a smallest vertex subset $S$, such that each vertex of $G$ lies on a fixed shortest path between a pair of vertices from $S$. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for ${\\rm sg}(G \\,\\square\\, H)$ is determined, as well as exact values for $K_m \\,\\square\\, K_n$, $K_{1, k} \\,\\square\\, P_l$, and certain prisms. Connections between the strong geodetic number of a graph and","authors_text":"Sandi Klav\\v{z}ar, 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":"2017-08-08T09:16:52Z","title":"Strong geodetic problem on Cartesian products of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02414","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:d7813d3fd8f26eb8d795070e746203481d2c4cd32cf792b2bf3e436ccc689723","target":"record","created_at":"2026-05-18T00:38:24Z","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":"88f6ecdb2ff703f2d3a25d5d157bab4fdf2ee5ff29e05ff5bc33c52a93600ff1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T09:16:52Z","title_canon_sha256":"4b036b2a8a928cb1a0b87a6c09518f69a2e4c94506c1fde9d1679f3c51a42a8b"},"schema_version":"1.0","source":{"id":"1708.02414","kind":"arxiv","version":1}},"canonical_sha256":"fba025747d99547768f482f241ede777b0003c8082feb27227b41aa1370f8ae8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fba025747d99547768f482f241ede777b0003c8082feb27227b41aa1370f8ae8","first_computed_at":"2026-05-18T00:38:24.340212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:24.340212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gLZoNMveiopdV2WVL8TrCC31yGp3fRY0KaR5kUO/7D2cReJ5WbmDaiehhBVvlE7n5doKmKa9Kfm9BzTTkp6eBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:24.340958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7813d3fd8f26eb8d795070e746203481d2c4cd32cf792b2bf3e436ccc689723","sha256:fe4a18f8dd5e2112a8f61d991fced42798199db5f5ded8bd717e1de67764c7b6"],"state_sha256":"1366e6af48486291c99cbf304ae071f0153ee63f21a7816dda8a81df4c0b5fa7"}