{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z5HA535QPVTEL4FSN33SXPFJCM","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":"44f94732362c0b64f457101f7e3f5ce9458da5d5316afafd351e35859c3bc09d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T15:12:33Z","title_canon_sha256":"4f23c7cb3783d95ca6139d6935c2008489b6a70fb9098b929eb595805e912aac"},"schema_version":"1.0","source":{"id":"1611.06827","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06827","created_at":"2026-07-05T00:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06827v3","created_at":"2026-07-05T00:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06827","created_at":"2026-07-05T00:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"Z5HA535QPVTE","created_at":"2026-07-05T00:44:23Z"},{"alias_kind":"pith_short_16","alias_value":"Z5HA535QPVTEL4FS","created_at":"2026-07-05T00:44:23Z"},{"alias_kind":"pith_short_8","alias_value":"Z5HA535Q","created_at":"2026-07-05T00:44:23Z"}],"graph_snapshots":[{"event_id":"sha256:20cb6272dc8f67eadba4579f02985cc8ad70561e934c13b347b02079727b8423","target":"graph","created_at":"2026-07-05T00:44:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1611.06827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We solve the existence problem for $F$-designs for arbitrary $r$-uniform hypergraphs~$F$. This implies that given any $r$-uniform hypergraph~$F$, the trivially necessary divisibility conditions are sufficient to guarantee a decomposition of any sufficiently large complete $r$-uniform hypergraph into edge-disjoint copies of~$F$, which answers a question asked e.g.~by Keevash. The graph case $r=2$ was proved by Wilson in 1975 and forms one of the cornerstones of design theory. The case when~$F$ is complete corresponds to the existence of block designs, a problem going back to the 19th century, w","authors_text":"Allan Lo, Daniela K\\\"uhn, Deryk Osthus, Stefan Glock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T15:12:33Z","title":"The existence of designs via iterative absorption: hypergraph $F$-designs for arbitrary $F$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06827","kind":"arxiv","version":3},"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:a6c7b7d18678b4c69fc84b379af1d55e7179f353388e9845b0be1fac1935120d","target":"record","created_at":"2026-07-05T00:44:23Z","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":"44f94732362c0b64f457101f7e3f5ce9458da5d5316afafd351e35859c3bc09d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T15:12:33Z","title_canon_sha256":"4f23c7cb3783d95ca6139d6935c2008489b6a70fb9098b929eb595805e912aac"},"schema_version":"1.0","source":{"id":"1611.06827","kind":"arxiv","version":3}},"canonical_sha256":"cf4e0eefb07d6645f0b26ef72bbca9132d43767ff0fc7aedf870fcc97c8b34db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf4e0eefb07d6645f0b26ef72bbca9132d43767ff0fc7aedf870fcc97c8b34db","first_computed_at":"2026-07-05T00:44:23.508234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:44:23.508234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y6aGa4eDfW1Bm5K29u30LetKsCl7QFnDAC8VA5TLhF2D8+zXPXVhjDgWf/hlhjSPww4AmYtezO+o7M/XdO8UDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:44:23.508760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06827","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6c7b7d18678b4c69fc84b379af1d55e7179f353388e9845b0be1fac1935120d","sha256:20cb6272dc8f67eadba4579f02985cc8ad70561e934c13b347b02079727b8423"],"state_sha256":"0d39888144a38c1d2c17439097b2114bb6c5c7644077cbce4119078c79047fad"}