{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JAKVQ4Z7Q2L457HDVWGD5PZYW2","short_pith_number":"pith:JAKVQ4Z7","schema_version":"1.0","canonical_sha256":"481558733f8697cefce3ad8c3ebf38b689098a3272e41498ff8edcf02a8670cd","source":{"kind":"arxiv","id":"1905.12151","version":1},"attestation_state":"computed","paper":{"title":"Leaves for packings with block size four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter J. Dukes, Tao Feng, Yanxun Chang","submitted_at":"2019-05-29T00:55:39Z","abstract_excerpt":"We consider maximum packings of edge-disjoint $4$-cliques in the complete graph $K_n$. When $n \\equiv 1$ or $4 \\pmod{12}$, these are simply block designs. In other congruence classes, there are necessarily uncovered edges; we examine the possible `leave' graphs induced by those edges. We give particular emphasis to the case $n \\equiv 0$ or $3 \\pmod{12}$, when the leave is $2$-regular. Colbourn and Ling settled the case of Hamiltonian leaves in this case. We extend their construction and use several additional direct and recursive constructions to realize a variety of $2$-regular leaves. For va"},"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":"1905.12151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-29T00:55:39Z","cross_cats_sorted":[],"title_canon_sha256":"bb2b90741421bda83ecde4fa5ade1a30f80b7e53f8affc51417c8430376e10f1","abstract_canon_sha256":"1d8a6e07e8d7a28add5a79a6956f49fdc32898f81576e72a5d844e2bac741fef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:47.012347Z","signature_b64":"nwDSQtnxpEs2HW2+cVyhUDCpvxPxMgA4IdfsHVehTlVey+Em32JMAJAPpavnBLy3iaE7fImbVQdxUUdiKGGeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"481558733f8697cefce3ad8c3ebf38b689098a3272e41498ff8edcf02a8670cd","last_reissued_at":"2026-05-17T23:44:47.011794Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:47.011794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Leaves for packings with block size four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter J. Dukes, Tao Feng, Yanxun Chang","submitted_at":"2019-05-29T00:55:39Z","abstract_excerpt":"We consider maximum packings of edge-disjoint $4$-cliques in the complete graph $K_n$. When $n \\equiv 1$ or $4 \\pmod{12}$, these are simply block designs. In other congruence classes, there are necessarily uncovered edges; we examine the possible `leave' graphs induced by those edges. We give particular emphasis to the case $n \\equiv 0$ or $3 \\pmod{12}$, when the leave is $2$-regular. Colbourn and Ling settled the case of Hamiltonian leaves in this case. We extend their construction and use several additional direct and recursive constructions to realize a variety of $2$-regular leaves. For va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12151","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":"1905.12151","created_at":"2026-05-17T23:44:47.011871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12151v1","created_at":"2026-05-17T23:44:47.011871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12151","created_at":"2026-05-17T23:44:47.011871+00:00"},{"alias_kind":"pith_short_12","alias_value":"JAKVQ4Z7Q2L4","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"JAKVQ4Z7Q2L457HD","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"JAKVQ4Z7","created_at":"2026-05-18T12:33:18.533446+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/JAKVQ4Z7Q2L457HDVWGD5PZYW2","json":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2.json","graph_json":"https://pith.science/api/pith-number/JAKVQ4Z7Q2L457HDVWGD5PZYW2/graph.json","events_json":"https://pith.science/api/pith-number/JAKVQ4Z7Q2L457HDVWGD5PZYW2/events.json","paper":"https://pith.science/paper/JAKVQ4Z7"},"agent_actions":{"view_html":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2","download_json":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2.json","view_paper":"https://pith.science/paper/JAKVQ4Z7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12151&json=true","fetch_graph":"https://pith.science/api/pith-number/JAKVQ4Z7Q2L457HDVWGD5PZYW2/graph.json","fetch_events":"https://pith.science/api/pith-number/JAKVQ4Z7Q2L457HDVWGD5PZYW2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2/action/storage_attestation","attest_author":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2/action/author_attestation","sign_citation":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2/action/citation_signature","submit_replication":"https://pith.science/pith/JAKVQ4Z7Q2L457HDVWGD5PZYW2/action/replication_record"}},"created_at":"2026-05-17T23:44:47.011871+00:00","updated_at":"2026-05-17T23:44:47.011871+00:00"}