{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O2NIRMJ4YSO6VKRYSII4MPYGWR","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":"a65bbbb327d9437bf7ee2fe1dc282dac294eec993e9d8cc716a33b9be4a681ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-12T00:49:54Z","title_canon_sha256":"f8d36d17e2f25a1ba3013fa541e98f25c56b5dc99644d8b5788c6064ff452460"},"schema_version":"1.0","source":{"id":"1406.3091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3091","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3091v2","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3091","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"O2NIRMJ4YSO6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O2NIRMJ4YSO6VKRY","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O2NIRMJ4","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:7b4d77b52d27f060939672f8f23116b2f36771cd91f2a237e2e0737954a55805","target":"graph","created_at":"2026-05-18T02:20:12Z","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":"We consider problems about packing and counting Hamilton $\\ell$-cycles in hypergraphs of large minimum degree. Given a hypergraph $\\mathcal H$, for a $d$-subset $A\\subseteq V(\\mathcal H)$, we denote by $d_{\\mathcal H}(A)$ the number of distinct \\emph{edges} $f\\in E(\\mathcal H)$ for which $A\\subseteq f$, and set $\\delta_d(\\mathcal H)$ to be the minimum $d_{\\mathcal H}(A)$ over all $A\\subseteq V(\\mathcal H)$ of size $d$. We show that if a $k$-uniform hypergraph on $n$ vertices $\\mathcal H$ satisfies $\\delta_{k-1}(\\mathcal H)\\geq \\alpha n$ for some $\\alpha>1/2$, then for every $\\ell<k/2$ $\\mathca","authors_text":"Asaf Ferber, Benny Sudakov, Michael Krivelevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-12T00:49:54Z","title":"Counting and packing Hamilton $\\ell$-cycles in dense hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3091","kind":"arxiv","version":2},"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":"sha256:8bd15f49f44b4b2b49e9dff895b615d3d4d833684147b419fdeee3246003900f","target":"record","created_at":"2026-05-18T02:20:12Z","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":"a65bbbb327d9437bf7ee2fe1dc282dac294eec993e9d8cc716a33b9be4a681ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-12T00:49:54Z","title_canon_sha256":"f8d36d17e2f25a1ba3013fa541e98f25c56b5dc99644d8b5788c6064ff452460"},"schema_version":"1.0","source":{"id":"1406.3091","kind":"arxiv","version":2}},"canonical_sha256":"769a88b13cc49deaaa389211c63f06b46c5bed3cb6be6af0efada48781071c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769a88b13cc49deaaa389211c63f06b46c5bed3cb6be6af0efada48781071c48","first_computed_at":"2026-05-18T02:20:12.587732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:12.587732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9P1XEPGItLK1+ihoStKDJCFllBri6ZJp9DC7+Hl7IYiOnQpazHuosLh5Bao+r6si7LGYZocb6eXv0js+dHPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:12.588155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bd15f49f44b4b2b49e9dff895b615d3d4d833684147b419fdeee3246003900f","sha256:7b4d77b52d27f060939672f8f23116b2f36771cd91f2a237e2e0737954a55805"],"state_sha256":"df12b0ac35e9f46ece255118bd456b6417843f6f7ae61d76b32c7d9e0988d061"}