{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZRSHOHDFHUB57FOWT7V7K7ELYC","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":"67a51b6206de6a2e005b0516cd5b412d3deb98431497ace255bd8665456cb7e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T18:00:07Z","title_canon_sha256":"bb92241f68eebd45ac4f4cf0c70ea239439475c489f0502d28cce596ffbd514d"},"schema_version":"1.0","source":{"id":"2407.06275","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.06275","created_at":"2026-07-05T11:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"2407.06275v2","created_at":"2026-07-05T11:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.06275","created_at":"2026-07-05T11:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZRSHOHDFHUB5","created_at":"2026-07-05T11:21:34Z"},{"alias_kind":"pith_short_16","alias_value":"ZRSHOHDFHUB57FOW","created_at":"2026-07-05T11:21:34Z"},{"alias_kind":"pith_short_8","alias_value":"ZRSHOHDF","created_at":"2026-07-05T11:21:34Z"}],"graph_snapshots":[{"event_id":"sha256:f90b23671abd25d0e00f1059a5ce7f6f830a909ca349a604981a967bb3bba84c","target":"graph","created_at":"2026-07-05T11:21:34Z","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/2407.06275/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a $k$-uniform hypergraph on $n$ vertices has a spanning subgraph homeomorphic to the $(k - 1)$-dimensional sphere provided that $H$ has no isolated vertices and each set of $k - 1$ vertices supported by an edge is contained in at least $n/2 + o(n)$ edges. This gives a topological extension of Dirac's theorem and asymptotically confirms a conjecture of Georgakopoulos, Haslegrave, Montgomery, and Narayanan.\n  Unlike typical results in the area, our proof does not rely on the Absorption Method, the Regularity Lemma or the Blow-up Lemma. Instead, we use a recently introduced framework","authors_text":"Alp M\\\"uyesser, Amedeo Sgueglia, Freddie Illingworth, Olaf Parczyk, Richard Lang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T18:00:07Z","title":"Spanning spheres in Dirac hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06275","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:afcf0971762e9f628261bc33d12e9f386e466845e537dcfdaa41f93717254465","target":"record","created_at":"2026-07-05T11:21:34Z","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":"67a51b6206de6a2e005b0516cd5b412d3deb98431497ace255bd8665456cb7e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T18:00:07Z","title_canon_sha256":"bb92241f68eebd45ac4f4cf0c70ea239439475c489f0502d28cce596ffbd514d"},"schema_version":"1.0","source":{"id":"2407.06275","kind":"arxiv","version":2}},"canonical_sha256":"cc64771c653d03df95d69febf57c8bc093f34a6b514da06089afbc6554c4feb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc64771c653d03df95d69febf57c8bc093f34a6b514da06089afbc6554c4feb2","first_computed_at":"2026-07-05T11:21:34.053496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:34.053496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cerdj3bT6ZKaIax0r93mYXpAlgRQPH2VbiEW6SkJxZwqPNlx2vPEncQc3MjgruGQyCdPUe8p2OPqM0A/3sZvBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:34.053955Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.06275","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afcf0971762e9f628261bc33d12e9f386e466845e537dcfdaa41f93717254465","sha256:f90b23671abd25d0e00f1059a5ce7f6f830a909ca349a604981a967bb3bba84c"],"state_sha256":"61f588ce632d3341f1bb5b415269fbea5fca206c282c1373faf79f1d091034eb"}