{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:45CT4U6CUNVR6ZLI4DGB7XXCCW","short_pith_number":"pith:45CT4U6C","schema_version":"1.0","canonical_sha256":"e7453e53c2a36b1f6568e0cc1fdee2158c0a586b8658502c6f59540501ec2afc","source":{"kind":"arxiv","id":"1401.3665","version":4},"attestation_state":"computed","paper":{"title":"The existence of designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Keevash","submitted_at":"2014-01-15T16:56:37Z","abstract_excerpt":"We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition. As a further generalisation, we obtain the same conclusion only assuming an extendability property and the existence of a robust fractional clique decomposition."},"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":"1401.3665","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-15T16:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"33e3a0baf0af1ea55d7b25be9b06188c498a99341270a33c48cbd9eafeaee2e1","abstract_canon_sha256":"23decc1c604a8fe7b04c3d09e6483b6e4645e2ce4c979498da20c243616adfa0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:50.655748Z","signature_b64":"L9vfBvRQxCy6LHIPi8vm2idNzbZ6Zr/PPkhd7XruRs/WMqsBVBXQ7ePkA1KBvqtJ1IFmfy5lgEG/wRL0jDvyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7453e53c2a36b1f6568e0cc1fdee2158c0a586b8658502c6f59540501ec2afc","last_reissued_at":"2026-07-05T09:40:50.655152Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:50.655152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence of designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Keevash","submitted_at":"2014-01-15T16:56:37Z","abstract_excerpt":"We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition. As a further generalisation, we obtain the same conclusion only assuming an extendability property and the existence of a robust fractional clique decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3665","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1401.3665/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1401.3665","created_at":"2026-07-05T09:40:50.655223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3665v4","created_at":"2026-07-05T09:40:50.655223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3665","created_at":"2026-07-05T09:40:50.655223+00:00"},{"alias_kind":"pith_short_12","alias_value":"45CT4U6CUNVR","created_at":"2026-07-05T09:40:50.655223+00:00"},{"alias_kind":"pith_short_16","alias_value":"45CT4U6CUNVR6ZLI","created_at":"2026-07-05T09:40:50.655223+00:00"},{"alias_kind":"pith_short_8","alias_value":"45CT4U6C","created_at":"2026-07-05T09:40:50.655223+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":9,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11178","citing_title":"A Proof of Nash-Williams' Conjecture","ref_index":37,"is_internal_anchor":false},{"citing_arxiv_id":"2606.02110","citing_title":"On cliques in hypergraphs under bounded $(j,p)$-norm","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31398","citing_title":"Universality for rainbow oriented cycles in perturbed digraphs","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25206","citing_title":"Fractional clique decompositions of dense balanced multipartite graphs","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2605.30092","citing_title":"Short proofs of three combinatorial results in the Johnson scheme","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"1906.11558","citing_title":"Perfectly packing graphs with bounded degeneracy and many leaves","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"1907.09950","citing_title":"A rainbow blow-up lemma for almost optimally bounded edge-colourings","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2605.22397","citing_title":"On the Tur\\'an number of blow-ups of $\\mathcal{F}_5$","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25206","citing_title":"Fractional clique decompositions of dense balanced multipartite graphs","ref_index":18,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW","json":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW.json","graph_json":"https://pith.science/api/pith-number/45CT4U6CUNVR6ZLI4DGB7XXCCW/graph.json","events_json":"https://pith.science/api/pith-number/45CT4U6CUNVR6ZLI4DGB7XXCCW/events.json","paper":"https://pith.science/paper/45CT4U6C"},"agent_actions":{"view_html":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW","download_json":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW.json","view_paper":"https://pith.science/paper/45CT4U6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3665&json=true","fetch_graph":"https://pith.science/api/pith-number/45CT4U6CUNVR6ZLI4DGB7XXCCW/graph.json","fetch_events":"https://pith.science/api/pith-number/45CT4U6CUNVR6ZLI4DGB7XXCCW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW/action/storage_attestation","attest_author":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW/action/author_attestation","sign_citation":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW/action/citation_signature","submit_replication":"https://pith.science/pith/45CT4U6CUNVR6ZLI4DGB7XXCCW/action/replication_record"}},"created_at":"2026-07-05T09:40:50.655223+00:00","updated_at":"2026-07-05T09:40:50.655223+00:00"}