{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C3FLIKM3I5WVPUON2NPN3CXPBB","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":"7a93cd662329a055957a8b9ac3eafcad73c340aabb6bb399ac9709c3380b37d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-25T12:32:44Z","title_canon_sha256":"dfc99b13667da32e2924fbaf64d5d4567db5123c5d7cc3ef7680575358a57d72"},"schema_version":"1.0","source":{"id":"1410.6916","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6916","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6916v7","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6916","created_at":"2026-05-18T01:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"C3FLIKM3I5WV","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C3FLIKM3I5WVPUON","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C3FLIKM3","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:0911c7a775e9c131b5d3ffc2da96da89e6288a1863a5d348f6c00fbc08b4028b","target":"graph","created_at":"2026-05-18T01:34:50Z","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":"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 $k=2,3$.","authors_text":"Dani Kotlar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-25T12:32:44Z","title":"Distance magic labeling in complete 4-partite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6916","kind":"arxiv","version":7},"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":"sha256:664dbc6af8c84b6260e603652255cccdd7e81f6ae3132fc4269f0179df05864e","target":"record","created_at":"2026-05-18T01:34:50Z","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":"7a93cd662329a055957a8b9ac3eafcad73c340aabb6bb399ac9709c3380b37d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-25T12:32:44Z","title_canon_sha256":"dfc99b13667da32e2924fbaf64d5d4567db5123c5d7cc3ef7680575358a57d72"},"schema_version":"1.0","source":{"id":"1410.6916","kind":"arxiv","version":7}},"canonical_sha256":"16cab4299b476d57d1cdd35edd8aef0876f075f9d96cf588e1edd38dcf85ab27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16cab4299b476d57d1cdd35edd8aef0876f075f9d96cf588e1edd38dcf85ab27","first_computed_at":"2026-05-18T01:34:50.779826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:50.779826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1BPUZALAgUjLRP5LK3Vc4TqANx8bYNRy6ILzLwzaYAbttlHxqLSoslyggM7vHpfv/KI3yTu4L8QwRd+mb9+/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:50.780293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6916","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:664dbc6af8c84b6260e603652255cccdd7e81f6ae3132fc4269f0179df05864e","sha256:0911c7a775e9c131b5d3ffc2da96da89e6288a1863a5d348f6c00fbc08b4028b"],"state_sha256":"7274cc7bfcbe5b837b1a0e9ae795b2b335087be77191712d9ea2e0699e411b0f"}