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We prove that for a semi-resolving set $S$ in the incidence graph of $\\mathrm{PG}(2,q)$, $|S|\\geq \\min \\{2q+q/4-3, \\tau_2-2\\}$ holds. In particular, if $q\\geq9$ is a square, then the smallest semi-resolving set in $\\mathrm{PG}(2,q)$ has size $2q+2\\sqrt{q}$."},"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":"1207.5469","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-23T18:11:10Z","cross_cats_sorted":[],"title_canon_sha256":"84f1b6aef4bffeeb0247c5cd6e2ed9cb8c4973b52476f949900c80cec7fd76b2","abstract_canon_sha256":"a34f77604a467cfe578eabddb0efa0d573c3400b9354b0dfc579d2e273e00258"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:58.606105Z","signature_b64":"mknZ1Kv7WXxktDoNbZYJxiNze+o1/6JFyvOmmYShPed5bZTRERCEI7WiCCDcTQRUi6igHXkecRiD9M6djIXeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cad9f087cdf3d8210aaf7700bb1b556d3d1d077ae4f3b966adde66bd6ba10348","last_reissued_at":"2026-05-18T00:51:58.605580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:58.605580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolving sets and semi-resolving sets in finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcella Tak\\'ats, Tam\\'as H\\'eger","submitted_at":"2012-07-23T18:11:10Z","abstract_excerpt":"We show that the metric dimension of a finite projective plane of order $q\\geq 23$ is $4q-4$, and describe all resolving sets of that size. Let $\\tau_2$ denote the size of the smallest double blocking set in $\\mathrm{PG}(2,q)$, the Desarguesian projective plane of order $q$. We prove that for a semi-resolving set $S$ in the incidence graph of $\\mathrm{PG}(2,q)$, $|S|\\geq \\min \\{2q+q/4-3, \\tau_2-2\\}$ holds. In particular, if $q\\geq9$ is a square, then the smallest semi-resolving set in $\\mathrm{PG}(2,q)$ has size $2q+2\\sqrt{q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5469","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.5469","created_at":"2026-05-18T00:51:58.605690+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5469v3","created_at":"2026-05-18T00:51:58.605690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5469","created_at":"2026-05-18T00:51:58.605690+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZLM7BB6N6PMC","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZLM7BB6N6PMCCCVP","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZLM7BB6N","created_at":"2026-05-18T12:27:30.460161+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/ZLM7BB6N6PMCCCVPO4ALWG2VNU","json":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU.json","graph_json":"https://pith.science/api/pith-number/ZLM7BB6N6PMCCCVPO4ALWG2VNU/graph.json","events_json":"https://pith.science/api/pith-number/ZLM7BB6N6PMCCCVPO4ALWG2VNU/events.json","paper":"https://pith.science/paper/ZLM7BB6N"},"agent_actions":{"view_html":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU","download_json":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU.json","view_paper":"https://pith.science/paper/ZLM7BB6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5469&json=true","fetch_graph":"https://pith.science/api/pith-number/ZLM7BB6N6PMCCCVPO4ALWG2VNU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZLM7BB6N6PMCCCVPO4ALWG2VNU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU/action/storage_attestation","attest_author":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU/action/author_attestation","sign_citation":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU/action/citation_signature","submit_replication":"https://pith.science/pith/ZLM7BB6N6PMCCCVPO4ALWG2VNU/action/replication_record"}},"created_at":"2026-05-18T00:51:58.605690+00:00","updated_at":"2026-05-18T00:51:58.605690+00:00"}