{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7TG4HKXFTFZ2VQVNH752BVXHXE","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":"24c7aa48696d4cb05f03663658cf5d504147e934cc5b02c4e531afac3a4d43c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:39Z","title_canon_sha256":"715711b70e47ed56f7e4626242c0d7cecc4d832e2629eb547fd7320e02540c58"},"schema_version":"1.0","source":{"id":"1403.7932","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7932","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7932v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7932","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"7TG4HKXFTFZ2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7TG4HKXFTFZ2VQVN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7TG4HKXF","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:85ed4bc964114c859059d2fc6ce90994c013fa95ea2040f66406fd12f8a164a3","target":"graph","created_at":"2026-05-18T02:55:12Z","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":"In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if $n$ divides $\\binom{n}{k}$, then the complete $k$-uniform hypergraph on $n$ vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence $v_1,e_1,v_2,\\dots,v_n,e_n$ of distinct vertices $v_i$ and distinct edges $e_i$ so that each $e_i$ contains $v_i$ and $v_{i+1}$. So the divisibility condition is clearly necessary. In this note, we prove that the conjecture holds whenever $k \\ge 4$ and $n \\ge 30$. Our argument is based on the Kruskal-Katona theorem. The case when $k=3$ was alre","authors_text":"Daniela K\\\"uhn, Deryk Osthus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:39Z","title":"Decompositions of complete uniform hypergraphs into Hamilton Berge cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7932","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":"sha256:69d28d91efa3c03a19bacf8abe18d243e12dfac8975a69e84f1cfef60009e649","target":"record","created_at":"2026-05-18T02:55:12Z","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":"24c7aa48696d4cb05f03663658cf5d504147e934cc5b02c4e531afac3a4d43c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:39Z","title_canon_sha256":"715711b70e47ed56f7e4626242c0d7cecc4d832e2629eb547fd7320e02540c58"},"schema_version":"1.0","source":{"id":"1403.7932","kind":"arxiv","version":1}},"canonical_sha256":"fccdc3aae59973aac2ad3ffba0d6e7b902528979abf7819e389d93f723be8fd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fccdc3aae59973aac2ad3ffba0d6e7b902528979abf7819e389d93f723be8fd2","first_computed_at":"2026-05-18T02:55:12.115818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:12.115818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xAFFzV8rqOhwm79L3fwvSGLJRTLg6EUdhhHT6rrtDVoYmCuG0QF7i2lzArApiOPchnLwOyK/T8eBGRbY2y9mBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:12.116264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7932","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69d28d91efa3c03a19bacf8abe18d243e12dfac8975a69e84f1cfef60009e649","sha256:85ed4bc964114c859059d2fc6ce90994c013fa95ea2040f66406fd12f8a164a3"],"state_sha256":"119b32e8119ce1eb208f0a488401f4422ddba03b8e6172e39bc52530553bb19d"}