{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:O7Z6QKUY52524Z7IL7ZOFKTRUF","short_pith_number":"pith:O7Z6QKUY","schema_version":"1.0","canonical_sha256":"77f3e82a98eebbae67e85ff2e2aa71a14772769d65f2cad647b15d4e4753de37","source":{"kind":"arxiv","id":"1811.05973","version":1},"attestation_state":"computed","paper":{"title":"Fault-Tolerant Metric Dimension of $P(n,2)$ with Prism Graph","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Q. Baig, M. Naeem, M. O. Ahmad, Z. Ahmad","submitted_at":"2018-11-14T05:59:36Z","abstract_excerpt":"Let $G$ be a connected graph and $d(a,b)$ be the distance between the vertices $a$ and $b$. A subset $U =\\{u_1,u_2,\\cdots,u_k\\}$ of the vertices is called a resolving set for $G$ if for every two distinct vertices $a,b \\in V(G)$, there is a vertex $u_\\xi \\in U$ such that $d(a,u_\\xi)\\neq d(b,u_\\xi)$. A resolving set containing a minimum number of vertices is called a metric basis for $G$ and the number of vertices in a metric basis is its metric dimension denoted by $dim(G)$. A resolving set $U$ for $G$ is fault-tolerant if $U \\setminus \\{u\\}$ is also a resolving set, for each $u \\in U$, and th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.05973","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-14T05:59:36Z","cross_cats_sorted":[],"title_canon_sha256":"40b74355dfe3b2eef387837403d2961d041466528f3fea44db11a9d3eaca328d","abstract_canon_sha256":"258b6073d4b33b5b86878c93dbbb4ae18e7dbd8e7fc980b1d94cda94e942ebde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:38.914779Z","signature_b64":"qUgAnyBakCiDzqdPT4+HZSFJ5eoaKAFHmnUZOQX21xQcQCg/zVuHCPoJi8MQZQJGyMIvit4dM7nf8+tjWn0cCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77f3e82a98eebbae67e85ff2e2aa71a14772769d65f2cad647b15d4e4753de37","last_reissued_at":"2026-05-18T00:00:38.914342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:38.914342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fault-Tolerant Metric Dimension of $P(n,2)$ with Prism Graph","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Q. Baig, M. Naeem, M. O. Ahmad, Z. Ahmad","submitted_at":"2018-11-14T05:59:36Z","abstract_excerpt":"Let $G$ be a connected graph and $d(a,b)$ be the distance between the vertices $a$ and $b$. A subset $U =\\{u_1,u_2,\\cdots,u_k\\}$ of the vertices is called a resolving set for $G$ if for every two distinct vertices $a,b \\in V(G)$, there is a vertex $u_\\xi \\in U$ such that $d(a,u_\\xi)\\neq d(b,u_\\xi)$. A resolving set containing a minimum number of vertices is called a metric basis for $G$ and the number of vertices in a metric basis is its metric dimension denoted by $dim(G)$. A resolving set $U$ for $G$ is fault-tolerant if $U \\setminus \\{u\\}$ is also a resolving set, for each $u \\in U$, and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05973","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.05973","created_at":"2026-05-18T00:00:38.914408+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.05973v1","created_at":"2026-05-18T00:00:38.914408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05973","created_at":"2026-05-18T00:00:38.914408+00:00"},{"alias_kind":"pith_short_12","alias_value":"O7Z6QKUY5252","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"O7Z6QKUY52524Z7I","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"O7Z6QKUY","created_at":"2026-05-18T12:32:43.782077+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF","json":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF.json","graph_json":"https://pith.science/api/pith-number/O7Z6QKUY52524Z7IL7ZOFKTRUF/graph.json","events_json":"https://pith.science/api/pith-number/O7Z6QKUY52524Z7IL7ZOFKTRUF/events.json","paper":"https://pith.science/paper/O7Z6QKUY"},"agent_actions":{"view_html":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF","download_json":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF.json","view_paper":"https://pith.science/paper/O7Z6QKUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.05973&json=true","fetch_graph":"https://pith.science/api/pith-number/O7Z6QKUY52524Z7IL7ZOFKTRUF/graph.json","fetch_events":"https://pith.science/api/pith-number/O7Z6QKUY52524Z7IL7ZOFKTRUF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF/action/storage_attestation","attest_author":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF/action/author_attestation","sign_citation":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF/action/citation_signature","submit_replication":"https://pith.science/pith/O7Z6QKUY52524Z7IL7ZOFKTRUF/action/replication_record"}},"created_at":"2026-05-18T00:00:38.914408+00:00","updated_at":"2026-05-18T00:00:38.914408+00:00"}