{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NLUF365U45QYKFH3PI4RDCSIXN","short_pith_number":"pith:NLUF365U","canonical_record":{"source":{"id":"1903.00245","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-01T11:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"e0f5242344cb35208de8e27880724242baa1b1a303b294dad852114ada20aae0","abstract_canon_sha256":"3c21fa12498357f371c30e36e67ee5a197de50f3f7604dd3335ade1e51db606f"},"schema_version":"1.0"},"canonical_sha256":"6ae85dfbb4e7618514fb7a39118a48bb7a30644a6469ae49be87ba8fdc26765d","source":{"kind":"arxiv","id":"1903.00245","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00245","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00245v4","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00245","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"NLUF365U45QY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NLUF365U45QYKFH3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NLUF365U","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NLUF365U45QYKFH3PI4RDCSIXN","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00245","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-01T11:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"e0f5242344cb35208de8e27880724242baa1b1a303b294dad852114ada20aae0","abstract_canon_sha256":"3c21fa12498357f371c30e36e67ee5a197de50f3f7604dd3335ade1e51db606f"},"schema_version":"1.0"},"canonical_sha256":"6ae85dfbb4e7618514fb7a39118a48bb7a30644a6469ae49be87ba8fdc26765d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:54.876107Z","signature_b64":"Y7OQAHX9tjpd2L2Aso7/W2yJTiF/LausHQ66Nj1HejiyVfBkoRfZl6ZsWCh8P3jF0B5LRbIxuyb7OYZarw9PDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ae85dfbb4e7618514fb7a39118a48bb7a30644a6469ae49be87ba8fdc26765d","last_reissued_at":"2026-05-17T23:48:54.875693Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:54.875693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00245","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"woXPZ1dZBHOnYyFh3r64n4ZCE/dM7yPY8/erL2wP5QGDgDvJG0WvyukXFd5Patu0R9yqti5ZKLdHzIpzcvbJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:28:51.222455Z"},"content_sha256":"762d57758266ea643ff330ed53e72cbb4388aa9dad3b0e1f2c5d3e8176292d05","schema_version":"1.0","event_id":"sha256:762d57758266ea643ff330ed53e72cbb4388aa9dad3b0e1f2c5d3e8176292d05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NLUF365U45QYKFH3PI4RDCSIXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large cliques in hypergraphs with forbidden substructures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andreas F. Holmsen","submitted_at":"2019-03-01T11:01:43Z","abstract_excerpt":"A result due to Gy\\'arf\\'as, Hubenko, and Solymosi (answering a question of Erd\\\"os) states that if a graph $G$ on $n$ vertices does not contain $K_{2,2}$ as an induced subgraph yet has at least $c\\binom{n}{2}$ edges, then $G$ has a complete subgraph on at least $\\frac{c^2}{10}n$ vertices. In this paper we suggest a \"higher-dimensional\" analogue of the notion of an induced $K_{2,2}$ which allows us to generalize their result to $k$-uniform hypergraphs. Our result also has an interesting consequence in discrete geometry. In particular, it implies that the fractional Helly theorem can be derived"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00245","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u7KRZG/V+MWC5LZL46qgi8TDqaduXcm5jS+dXTtZ3aLrdOjBNUrUuSHhGoaTsZs8Wk1dgQzJ9NKC0xp4If4uCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:28:51.222809Z"},"content_sha256":"7b03f3cf6d5b9530ca48edd74cbfdece6c34a7febf06a94d2059a29abb4470ab","schema_version":"1.0","event_id":"sha256:7b03f3cf6d5b9530ca48edd74cbfdece6c34a7febf06a94d2059a29abb4470ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NLUF365U45QYKFH3PI4RDCSIXN/bundle.json","state_url":"https://pith.science/pith/NLUF365U45QYKFH3PI4RDCSIXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NLUF365U45QYKFH3PI4RDCSIXN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T20:28:51Z","links":{"resolver":"https://pith.science/pith/NLUF365U45QYKFH3PI4RDCSIXN","bundle":"https://pith.science/pith/NLUF365U45QYKFH3PI4RDCSIXN/bundle.json","state":"https://pith.science/pith/NLUF365U45QYKFH3PI4RDCSIXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NLUF365U45QYKFH3PI4RDCSIXN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NLUF365U45QYKFH3PI4RDCSIXN","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":"3c21fa12498357f371c30e36e67ee5a197de50f3f7604dd3335ade1e51db606f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-01T11:01:43Z","title_canon_sha256":"e0f5242344cb35208de8e27880724242baa1b1a303b294dad852114ada20aae0"},"schema_version":"1.0","source":{"id":"1903.00245","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00245","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00245v4","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00245","created_at":"2026-05-17T23:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"NLUF365U45QY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NLUF365U45QYKFH3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NLUF365U","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:7b03f3cf6d5b9530ca48edd74cbfdece6c34a7febf06a94d2059a29abb4470ab","target":"graph","created_at":"2026-05-17T23:48:54Z","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":"A result due to Gy\\'arf\\'as, Hubenko, and Solymosi (answering a question of Erd\\\"os) states that if a graph $G$ on $n$ vertices does not contain $K_{2,2}$ as an induced subgraph yet has at least $c\\binom{n}{2}$ edges, then $G$ has a complete subgraph on at least $\\frac{c^2}{10}n$ vertices. In this paper we suggest a \"higher-dimensional\" analogue of the notion of an induced $K_{2,2}$ which allows us to generalize their result to $k$-uniform hypergraphs. Our result also has an interesting consequence in discrete geometry. In particular, it implies that the fractional Helly theorem can be derived","authors_text":"Andreas F. Holmsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-01T11:01:43Z","title":"Large cliques in hypergraphs with forbidden substructures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00245","kind":"arxiv","version":4},"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":"sha256:762d57758266ea643ff330ed53e72cbb4388aa9dad3b0e1f2c5d3e8176292d05","target":"record","created_at":"2026-05-17T23:48:54Z","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":"3c21fa12498357f371c30e36e67ee5a197de50f3f7604dd3335ade1e51db606f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-01T11:01:43Z","title_canon_sha256":"e0f5242344cb35208de8e27880724242baa1b1a303b294dad852114ada20aae0"},"schema_version":"1.0","source":{"id":"1903.00245","kind":"arxiv","version":4}},"canonical_sha256":"6ae85dfbb4e7618514fb7a39118a48bb7a30644a6469ae49be87ba8fdc26765d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ae85dfbb4e7618514fb7a39118a48bb7a30644a6469ae49be87ba8fdc26765d","first_computed_at":"2026-05-17T23:48:54.875693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:54.875693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y7OQAHX9tjpd2L2Aso7/W2yJTiF/LausHQ66Nj1HejiyVfBkoRfZl6ZsWCh8P3jF0B5LRbIxuyb7OYZarw9PDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:54.876107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00245","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:762d57758266ea643ff330ed53e72cbb4388aa9dad3b0e1f2c5d3e8176292d05","sha256:7b03f3cf6d5b9530ca48edd74cbfdece6c34a7febf06a94d2059a29abb4470ab"],"state_sha256":"3f47c845bf03be110bf50bff032a9d0a9a33f9cb2631146488454bcf9c10e20d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q85Her0VM0jVEljIRXDds2cPxkvfHBqfDW4u66f5SyIsvsSzEOrpd3IaEOeKmjdFBUN85LfQ+IiwZuvUg3+tCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:28:51.224866Z","bundle_sha256":"8b28c293034a6d29353f908486bca746eb2fc6f40e389a641271da43c1f6379b"}}