{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JBFMVHXBJB2U3PSDJR5YSMMVXK","short_pith_number":"pith:JBFMVHXB","schema_version":"1.0","canonical_sha256":"484aca9ee148754dbe434c7b893195bab9c4ea2267e61aa53821085143c21c46","source":{"kind":"arxiv","id":"1308.5437","version":1},"attestation_state":"computed","paper":{"title":"A Bound for the Locating Chromatic Numbers of Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Behtoei, Mahdi Anbarloei","submitted_at":"2013-08-25T19:22:18Z","abstract_excerpt":"Let $f$ be a proper $k$-coloring of a connected graph $G$ and $\\Pi=(V_1,V_2,\\ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $\\Pi$ is defined to be the ordered $k$-tuple $c_{{}_\\Pi}(v)=(d(v,V_1),d(v,V_2),\\ldots,d(v,V_k)),$ where $d(v,V_i)=\\min\\{d(v,x): x\\in V_i\\}, 1\\leq i\\leq k$. If distinct vertices have distinct color codes, then $f$ is called a locating coloring. The minimum number of colors needed in a locating coloring of $G$ is the locating chromatic number of $G$, denoted by $\\Cchi_{{}_L}(G)$."},"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":"1308.5437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-25T19:22:18Z","cross_cats_sorted":[],"title_canon_sha256":"10710351045b705f2379efe17b8749edf3d42e4ed37a9c441ad24f349626277a","abstract_canon_sha256":"ff27cf87ec3366dfb2aedf221eda2ea1d8e5b977087673fe5dceb15b69a64372"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:04.671018Z","signature_b64":"hsew0wResZZHjdmq6sskdltVDKVdeatAhXMEKSlRDqZdYQel1SgxKu8Hy3mB3Mgs73hGrVeyvL/gHbUoNx4TDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"484aca9ee148754dbe434c7b893195bab9c4ea2267e61aa53821085143c21c46","last_reissued_at":"2026-05-18T03:15:04.670049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:04.670049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bound for the Locating Chromatic Numbers of Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Behtoei, Mahdi Anbarloei","submitted_at":"2013-08-25T19:22:18Z","abstract_excerpt":"Let $f$ be a proper $k$-coloring of a connected graph $G$ and $\\Pi=(V_1,V_2,\\ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $\\Pi$ is defined to be the ordered $k$-tuple $c_{{}_\\Pi}(v)=(d(v,V_1),d(v,V_2),\\ldots,d(v,V_k)),$ where $d(v,V_i)=\\min\\{d(v,x): x\\in V_i\\}, 1\\leq i\\leq k$. If distinct vertices have distinct color codes, then $f$ is called a locating coloring. The minimum number of colors needed in a locating coloring of $G$ is the locating chromatic number of $G$, denoted by $\\Cchi_{{}_L}(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5437","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":"1308.5437","created_at":"2026-05-18T03:15:04.670189+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.5437v1","created_at":"2026-05-18T03:15:04.670189+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5437","created_at":"2026-05-18T03:15:04.670189+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBFMVHXBJB2U","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBFMVHXBJB2U3PSD","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBFMVHXB","created_at":"2026-05-18T12:27:49.015174+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/JBFMVHXBJB2U3PSDJR5YSMMVXK","json":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK.json","graph_json":"https://pith.science/api/pith-number/JBFMVHXBJB2U3PSDJR5YSMMVXK/graph.json","events_json":"https://pith.science/api/pith-number/JBFMVHXBJB2U3PSDJR5YSMMVXK/events.json","paper":"https://pith.science/paper/JBFMVHXB"},"agent_actions":{"view_html":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK","download_json":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK.json","view_paper":"https://pith.science/paper/JBFMVHXB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.5437&json=true","fetch_graph":"https://pith.science/api/pith-number/JBFMVHXBJB2U3PSDJR5YSMMVXK/graph.json","fetch_events":"https://pith.science/api/pith-number/JBFMVHXBJB2U3PSDJR5YSMMVXK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK/action/storage_attestation","attest_author":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK/action/author_attestation","sign_citation":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK/action/citation_signature","submit_replication":"https://pith.science/pith/JBFMVHXBJB2U3PSDJR5YSMMVXK/action/replication_record"}},"created_at":"2026-05-18T03:15:04.670189+00:00","updated_at":"2026-05-18T03:15:04.670189+00:00"}