{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:42QZDE6JB7ZHYJPAHBYRHFCGZI","short_pith_number":"pith:42QZDE6J","canonical_record":{"source":{"id":"1010.4495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-21T15:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"0d81f3598a268d97f13160a24e2ddfd793d1b9c16fbb097afff736554d283096","abstract_canon_sha256":"cbb4bdb333fcdd9ec2f8f10bf20b6ce222a5fda02a06bbc27b7794f9fa28ba3e"},"schema_version":"1.0"},"canonical_sha256":"e6a19193c90ff27c25e03871139446ca12390f83cae6fed31bdd2ee2fd9c67bb","source":{"kind":"arxiv","id":"1010.4495","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:42QZDE6JB7ZHYJPAHBYRHFCGZI","target":"record","payload":{"canonical_record":{"source":{"id":"1010.4495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-21T15:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"0d81f3598a268d97f13160a24e2ddfd793d1b9c16fbb097afff736554d283096","abstract_canon_sha256":"cbb4bdb333fcdd9ec2f8f10bf20b6ce222a5fda02a06bbc27b7794f9fa28ba3e"},"schema_version":"1.0"},"canonical_sha256":"e6a19193c90ff27c25e03871139446ca12390f83cae6fed31bdd2ee2fd9c67bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:43.186411Z","signature_b64":"37W8YYZzPt8f0X/VylxUcA0D7oFiEL+Ng1bdr6U96k6b1iJBCIvuzwrpOcQW75KIJJLp03PP7dZGXbEg9RVuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6a19193c90ff27c25e03871139446ca12390f83cae6fed31bdd2ee2fd9c67bb","last_reissued_at":"2026-05-18T04:07:43.185804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:43.185804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.4495","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dUbOL1pB8kFBhn3MknKutWyfmM81xk4TZSr7L72ntPJOQfdp28XCWlCWGC9mr8jG1IEcZSC4MHKkV1laG/QFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:35:38.117642Z"},"content_sha256":"a6eb0905f616cae07b95bb02192822b2932280526e83b2a2259f28e7699822f7","schema_version":"1.0","event_id":"sha256:a6eb0905f616cae07b95bb02192822b2932280526e83b2a2259f28e7699822f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:42QZDE6JB7ZHYJPAHBYRHFCGZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the metric dimension of Grassmann graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Karen Meagher, Robert F. Bailey","submitted_at":"2010-10-21T15:25:32Z","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 $\\mathbb{F}_q^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4495","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEV1ScvOH+pKQ/CsJEb1JBRW15MnB2s63u4IIezlBzvtL47nLB/EuietsbbpOIoqTgpqQ0pNgkdPZt6A2IzuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:35:38.118002Z"},"content_sha256":"2d68d4aafceee4968cfb5f31463898bcf9e49244d0cf962620e56d2f5ec6bf53","schema_version":"1.0","event_id":"sha256:2d68d4aafceee4968cfb5f31463898bcf9e49244d0cf962620e56d2f5ec6bf53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI/bundle.json","state_url":"https://pith.science/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T06:35:38Z","links":{"resolver":"https://pith.science/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI","bundle":"https://pith.science/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI/bundle.json","state":"https://pith.science/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42QZDE6JB7ZHYJPAHBYRHFCGZI/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5NS0AZir96DsqO1YILAC27fAQzTbqF/mUGDWo6KXkO2okPDS0gG148JNwBPXp2iYNFWnb5ZeGAmQM+xr8KBWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T06:35:38.120043Z","bundle_sha256":"74054efde792dee3706d63b34fe06d0e1e8959bd14aaba01a9b3228d65e22879"}}