{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6B7BLP4XNC2LHQ2C5NJUEOSBMC","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":"9445ccc9caddfcfd755c61a58f103b341768c9cf421b180c66c9d5e4b45fcd38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-18T10:48:27Z","title_canon_sha256":"56c3949522d6759e00d6731a395e85e4bcc78ed5c116b6e1b65bd77f7cde2b66"},"schema_version":"1.0","source":{"id":"1302.4219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4219","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4219v1","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4219","created_at":"2026-05-18T03:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"6B7BLP4XNC2L","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6B7BLP4XNC2LHQ2C","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6B7BLP4X","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:6c9b6f2ec91234aabf08058ad15420204ffbfa4f2c65f6e2f68278caabdd5d22","target":"graph","created_at":"2026-05-18T03:33:23Z","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":"In this paper we prove that we can find a labeled packing of a non star tree $T$ into $T^6$ with $m_T+\\lceil\\frac{n-m_T}{5}\\rceil$ labels, where $n$ is the number of vertices of $T$ and $m_T$ is the maximum number of leaves that can be removed from $T$ in such a way that the obtained graph is a non star tree. Also, we prove that we can find a labeled packing of a non star tree $T$ into $T^5$ with $m_T+1$ labels and a labeled packing of a path $P_n$, $n\\geq 4$, into $P_n^4$ with $\\lceil \\frac{n}{4}\\rceil$ labels.","authors_text":"Amine El Sahili, Hamamache Kheddouci, Maidoun Mortada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-18T10:48:27Z","title":"Labeled Packing of Non Star Tree into its Fifth Power and Sixth Power"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4219","kind":"arxiv","version":1},"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":"sha256:7edfc6f0a9b0924ef52119ea47ada27ede7622f93804382afdeb1992a3a0c562","target":"record","created_at":"2026-05-18T03:33:23Z","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":"9445ccc9caddfcfd755c61a58f103b341768c9cf421b180c66c9d5e4b45fcd38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-18T10:48:27Z","title_canon_sha256":"56c3949522d6759e00d6731a395e85e4bcc78ed5c116b6e1b65bd77f7cde2b66"},"schema_version":"1.0","source":{"id":"1302.4219","kind":"arxiv","version":1}},"canonical_sha256":"f07e15bf9768b4b3c342eb53423a416096be42e2521df904a393283017d447a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f07e15bf9768b4b3c342eb53423a416096be42e2521df904a393283017d447a3","first_computed_at":"2026-05-18T03:33:23.682674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:23.682674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90+uFcYeH1PuELYNdwJjxLw7px/YqAXGbgn9FTOetUVaof6a5GAb3NhtZkrCoyk4sXgorO2vu6iItTED3eWnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:23.683408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7edfc6f0a9b0924ef52119ea47ada27ede7622f93804382afdeb1992a3a0c562","sha256:6c9b6f2ec91234aabf08058ad15420204ffbfa4f2c65f6e2f68278caabdd5d22"],"state_sha256":"e923657be6b78d131a956bf511e803f870664fca74c1e1a2a47cd6bd2f8b9470"}