{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KVABIUL5A3CQRWHZHRAO7766MV","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":"1134042de95903e596290e5eeb283b993ffbce702776b440e045678ffa45fbf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-07T10:25:44Z","title_canon_sha256":"d58f08bee023eecef79d9e60b780c51f01ac89ddf1c00bd077edf52fd1a9801f"},"schema_version":"1.0","source":{"id":"1205.1334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1334","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1334v2","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1334","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"KVABIUL5A3CQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KVABIUL5A3CQRWHZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KVABIUL5","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:d88f16962c3a581a88fab2daf64ad3cc4ff6ce7272fa00332cf17dd9e4204f1a","target":"graph","created_at":"2026-05-18T03:56:10Z","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":"This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs with equal metric dimension and resolving number. We also solve in the affirmative a conjecture posed by Chartrand, Poisson and Zhang about the realization of the metric dimension and the upper dimension. Finally we prove that no integer $a\\geq 4$ is realizable as the resolving number of an infinite family of graphs.","authors_text":"Alberto M\\'arquez, Antonio Gonz\\'alez, Delia Garijo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-07T10:25:44Z","title":"On the metric dimension, the upper dimension and the resolving number of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1334","kind":"arxiv","version":2},"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":"sha256:94bc0458632fa0284034fae479ed4d1df1ef9d1d4ddb09e99b586cbc3543087b","target":"record","created_at":"2026-05-18T03:56:10Z","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":"1134042de95903e596290e5eeb283b993ffbce702776b440e045678ffa45fbf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-07T10:25:44Z","title_canon_sha256":"d58f08bee023eecef79d9e60b780c51f01ac89ddf1c00bd077edf52fd1a9801f"},"schema_version":"1.0","source":{"id":"1205.1334","kind":"arxiv","version":2}},"canonical_sha256":"554014517d06c508d8f93c40efffde656fa5fdad47c14c7c0f97bc8d0eb01de7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"554014517d06c508d8f93c40efffde656fa5fdad47c14c7c0f97bc8d0eb01de7","first_computed_at":"2026-05-18T03:56:10.082793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:10.082793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqSrAmOAeHLLHJmvrW3/VI6Et2ARWWWLNBoVnd19H17TRvLvu30TyVQ3EpEUVT65cAFtAbf+khBA9Ic6GihfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:10.083535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94bc0458632fa0284034fae479ed4d1df1ef9d1d4ddb09e99b586cbc3543087b","sha256:d88f16962c3a581a88fab2daf64ad3cc4ff6ce7272fa00332cf17dd9e4204f1a"],"state_sha256":"66f5fb1a38b39d007988d970d6583020688fbdc3e9d7ab529037cb3d749c3884"}