{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:42QZDE6JB7ZHYJPAHBYRHFCGZI","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":"cbb4bdb333fcdd9ec2f8f10bf20b6ce222a5fda02a06bbc27b7794f9fa28ba3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-21T15:25:32Z","title_canon_sha256":"0d81f3598a268d97f13160a24e2ddfd793d1b9c16fbb097afff736554d283096"},"schema_version":"1.0","source":{"id":"1010.4495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4495","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4495v3","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4495","created_at":"2026-05-18T04:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"42QZDE6JB7ZH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"42QZDE6JB7ZHYJPA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"42QZDE6J","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:2d68d4aafceee4968cfb5f31463898bcf9e49244d0cf962620e56d2f5ec6bf53","target":"graph","created_at":"2026-05-18T04:07:43Z","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 {\\em metric dimension} of a graph $\\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph $G_q(n,k)$ (whose vertices are the $k$-subspaces of $\\mathbb{F}_q^n$, and are adjacent if they intersect in a $(k-1)$-subspace) for $k\\geq 2$, and find a constructive upper bound on its metric dimension. Our bound is equal to the number of 1-dimensional subspaces of $\\mathbb{F}_q^n$.","authors_text":"Karen Meagher, Robert F. Bailey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-21T15:25:32Z","title":"On the metric dimension of Grassmann graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4495","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:a6eb0905f616cae07b95bb02192822b2932280526e83b2a2259f28e7699822f7","target":"record","created_at":"2026-05-18T04:07:43Z","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":"cbb4bdb333fcdd9ec2f8f10bf20b6ce222a5fda02a06bbc27b7794f9fa28ba3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-21T15:25:32Z","title_canon_sha256":"0d81f3598a268d97f13160a24e2ddfd793d1b9c16fbb097afff736554d283096"},"schema_version":"1.0","source":{"id":"1010.4495","kind":"arxiv","version":3}},"canonical_sha256":"e6a19193c90ff27c25e03871139446ca12390f83cae6fed31bdd2ee2fd9c67bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6a19193c90ff27c25e03871139446ca12390f83cae6fed31bdd2ee2fd9c67bb","first_computed_at":"2026-05-18T04:07:43.185804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:43.185804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"37W8YYZzPt8f0X/VylxUcA0D7oFiEL+Ng1bdr6U96k6b1iJBCIvuzwrpOcQW75KIJJLp03PP7dZGXbEg9RVuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:43.186411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6eb0905f616cae07b95bb02192822b2932280526e83b2a2259f28e7699822f7","sha256:2d68d4aafceee4968cfb5f31463898bcf9e49244d0cf962620e56d2f5ec6bf53"],"state_sha256":"4fec91e169dbb7efc1e756a558480c57002ffbc3d640d077748249477707e605"}