{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:C3FLIKM3I5WVPUON2NPN3CXPBB","short_pith_number":"pith:C3FLIKM3","schema_version":"1.0","canonical_sha256":"16cab4299b476d57d1cdd35edd8aef0876f075f9d96cf588e1edd38dcf85ab27","source":{"kind":"arxiv","id":"1410.6916","version":7},"attestation_state":"computed","paper":{"title":"Distance magic labeling in complete 4-partite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dani Kotlar","submitted_at":"2014-10-25T12:32:44Z","abstract_excerpt":"Let $G$ be a complete $k$-partite simple undirected graph with parts of sizes $p_1\\le p_2...\\le p_k$. Let $P_j=\\sum_{i=1}^jp_i$ for $j=1,...,k$. It is conjectured that $G$ has distance magic labeling if and only if $\\sum_{i=1}^{P_j} (n-i+1)\\ge j{{n+1}\\choose{2}}/k$ for all $j=1,...,k$. The conjecture is proved for $k=4$, extending earlier results for $k=2,3$."},"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":"1410.6916","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-25T12:32:44Z","cross_cats_sorted":[],"title_canon_sha256":"dfc99b13667da32e2924fbaf64d5d4567db5123c5d7cc3ef7680575358a57d72","abstract_canon_sha256":"7a93cd662329a055957a8b9ac3eafcad73c340aabb6bb399ac9709c3380b37d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:50.780293Z","signature_b64":"1BPUZALAgUjLRP5LK3Vc4TqANx8bYNRy6ILzLwzaYAbttlHxqLSoslyggM7vHpfv/KI3yTu4L8QwRd+mb9+/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16cab4299b476d57d1cdd35edd8aef0876f075f9d96cf588e1edd38dcf85ab27","last_reissued_at":"2026-05-18T01:34:50.779826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:50.779826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distance magic labeling in complete 4-partite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dani Kotlar","submitted_at":"2014-10-25T12:32:44Z","abstract_excerpt":"Let $G$ be a complete $k$-partite simple undirected graph with parts of sizes $p_1\\le p_2...\\le p_k$. Let $P_j=\\sum_{i=1}^jp_i$ for $j=1,...,k$. It is conjectured that $G$ has distance magic labeling if and only if $\\sum_{i=1}^{P_j} (n-i+1)\\ge j{{n+1}\\choose{2}}/k$ for all $j=1,...,k$. The conjecture is proved for $k=4$, extending earlier results for $k=2,3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6916","kind":"arxiv","version":7},"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":"1410.6916","created_at":"2026-05-18T01:34:50.779886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6916v7","created_at":"2026-05-18T01:34:50.779886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6916","created_at":"2026-05-18T01:34:50.779886+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3FLIKM3I5WV","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3FLIKM3I5WVPUON","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3FLIKM3","created_at":"2026-05-18T12:28:22.404517+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/C3FLIKM3I5WVPUON2NPN3CXPBB","json":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB.json","graph_json":"https://pith.science/api/pith-number/C3FLIKM3I5WVPUON2NPN3CXPBB/graph.json","events_json":"https://pith.science/api/pith-number/C3FLIKM3I5WVPUON2NPN3CXPBB/events.json","paper":"https://pith.science/paper/C3FLIKM3"},"agent_actions":{"view_html":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB","download_json":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB.json","view_paper":"https://pith.science/paper/C3FLIKM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6916&json=true","fetch_graph":"https://pith.science/api/pith-number/C3FLIKM3I5WVPUON2NPN3CXPBB/graph.json","fetch_events":"https://pith.science/api/pith-number/C3FLIKM3I5WVPUON2NPN3CXPBB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB/action/storage_attestation","attest_author":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB/action/author_attestation","sign_citation":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB/action/citation_signature","submit_replication":"https://pith.science/pith/C3FLIKM3I5WVPUON2NPN3CXPBB/action/replication_record"}},"created_at":"2026-05-18T01:34:50.779886+00:00","updated_at":"2026-05-18T01:34:50.779886+00:00"}