{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:254DYNOYFEK4IRM4NJWPQJ4BMR","short_pith_number":"pith:254DYNOY","canonical_record":{"source":{"id":"1311.0719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-04T14:54:28Z","cross_cats_sorted":[],"title_canon_sha256":"0785e83f844f9263f4e7b7f4c3c3845f242a95732c04845bab5f33cc75369f7f","abstract_canon_sha256":"b9dc80115f5f8011b21fb18e913b3a712e10d52183fe65e6f5ff9ad7258d968e"},"schema_version":"1.0"},"canonical_sha256":"d7783c35d82915c4459c6a6cf827816447c88a72646e8986a1bb155c0f32508a","source":{"kind":"arxiv","id":"1311.0719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0719","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0719v2","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0719","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"254DYNOYFEK4","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"254DYNOYFEK4IRM4","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"254DYNOY","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:254DYNOYFEK4IRM4NJWPQJ4BMR","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-04T14:54:28Z","cross_cats_sorted":[],"title_canon_sha256":"0785e83f844f9263f4e7b7f4c3c3845f242a95732c04845bab5f33cc75369f7f","abstract_canon_sha256":"b9dc80115f5f8011b21fb18e913b3a712e10d52183fe65e6f5ff9ad7258d968e"},"schema_version":"1.0"},"canonical_sha256":"d7783c35d82915c4459c6a6cf827816447c88a72646e8986a1bb155c0f32508a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:12.759694Z","signature_b64":"PFrwcuFCtq/pbFp3BVXC9Ik95LW86nMcjrPX9wc21zivsv+ubOce6nK0hdLEAWMbDmC7VKXvuyhWnw7I5ORlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7783c35d82915c4459c6a6cf827816447c88a72646e8986a1bb155c0f32508a","last_reissued_at":"2026-05-18T03:06:12.759263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:12.759263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0719","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4Nm1s7KzjqnfxZPFgkBQ4e0k9C8iujSEntnpJGgzWn0QoUOz8PIef6k2Upth9/26lCJfMp5o0fYzxc8K4gnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:23:17.744718Z"},"content_sha256":"172341b20d449c9777507d70c3419cab8a962103506f6ed3e8fe72f34ec93c54","schema_version":"1.0","event_id":"sha256:172341b20d449c9777507d70c3419cab8a962103506f6ed3e8fe72f34ec93c54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:254DYNOYFEK4IRM4NJWPQJ4BMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An extremal problem on Hilbert cubes and complete r-partite hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Javier Cilleruelo","submitted_at":"2013-11-04T14:54:28Z","abstract_excerpt":"We construct a set of positive integers A in {1,..., n} with |A|>> n^{2/3} that does not contain Hilbert cubes of dimension 3. As a consequence we prove that ex(n; K^(3)(2,2,2))>> n^{8/3} where K^(3)(2,2,2) is the simplest complete 3-partite hypergraph. This is the first case of an improvement on the trivial lower bound for ex(n; L) when L is a complete r-partite hypergraph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0719","kind":"arxiv","version":2},"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":"2026-05-18T03:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"87QNDB22h+NzLNLlrSlAS+T4xi8dfS6QfNuReqWkU6RDEBeYxMV3rmS6LT4N+eRHhAB2eLn9GpkBn9sIxes8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:23:17.745295Z"},"content_sha256":"ab82378720785409144069dee0ec783c00eea66e35238ab169e971422b00dda3","schema_version":"1.0","event_id":"sha256:ab82378720785409144069dee0ec783c00eea66e35238ab169e971422b00dda3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/254DYNOYFEK4IRM4NJWPQJ4BMR/bundle.json","state_url":"https://pith.science/pith/254DYNOYFEK4IRM4NJWPQJ4BMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/254DYNOYFEK4IRM4NJWPQJ4BMR/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":"2026-05-26T15:23:17Z","links":{"resolver":"https://pith.science/pith/254DYNOYFEK4IRM4NJWPQJ4BMR","bundle":"https://pith.science/pith/254DYNOYFEK4IRM4NJWPQJ4BMR/bundle.json","state":"https://pith.science/pith/254DYNOYFEK4IRM4NJWPQJ4BMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/254DYNOYFEK4IRM4NJWPQJ4BMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:254DYNOYFEK4IRM4NJWPQJ4BMR","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":"b9dc80115f5f8011b21fb18e913b3a712e10d52183fe65e6f5ff9ad7258d968e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-04T14:54:28Z","title_canon_sha256":"0785e83f844f9263f4e7b7f4c3c3845f242a95732c04845bab5f33cc75369f7f"},"schema_version":"1.0","source":{"id":"1311.0719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0719","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0719v2","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0719","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"254DYNOYFEK4","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"254DYNOYFEK4IRM4","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"254DYNOY","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:ab82378720785409144069dee0ec783c00eea66e35238ab169e971422b00dda3","target":"graph","created_at":"2026-05-18T03:06:12Z","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":"We construct a set of positive integers A in {1,..., n} with |A|>> n^{2/3} that does not contain Hilbert cubes of dimension 3. As a consequence we prove that ex(n; K^(3)(2,2,2))>> n^{8/3} where K^(3)(2,2,2) is the simplest complete 3-partite hypergraph. This is the first case of an improvement on the trivial lower bound for ex(n; L) when L is a complete r-partite hypergraph.","authors_text":"Javier Cilleruelo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-04T14:54:28Z","title":"An extremal problem on Hilbert cubes and complete r-partite hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0719","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":"sha256:172341b20d449c9777507d70c3419cab8a962103506f6ed3e8fe72f34ec93c54","target":"record","created_at":"2026-05-18T03:06:12Z","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":"b9dc80115f5f8011b21fb18e913b3a712e10d52183fe65e6f5ff9ad7258d968e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-04T14:54:28Z","title_canon_sha256":"0785e83f844f9263f4e7b7f4c3c3845f242a95732c04845bab5f33cc75369f7f"},"schema_version":"1.0","source":{"id":"1311.0719","kind":"arxiv","version":2}},"canonical_sha256":"d7783c35d82915c4459c6a6cf827816447c88a72646e8986a1bb155c0f32508a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7783c35d82915c4459c6a6cf827816447c88a72646e8986a1bb155c0f32508a","first_computed_at":"2026-05-18T03:06:12.759263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:12.759263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFrwcuFCtq/pbFp3BVXC9Ik95LW86nMcjrPX9wc21zivsv+ubOce6nK0hdLEAWMbDmC7VKXvuyhWnw7I5ORlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:12.759694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:172341b20d449c9777507d70c3419cab8a962103506f6ed3e8fe72f34ec93c54","sha256:ab82378720785409144069dee0ec783c00eea66e35238ab169e971422b00dda3"],"state_sha256":"9c9d28b03df5d37c1f8462d003218c6e535655e4690cfaa282b3e4650c163107"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CqPe6tweCD6j2OUJgfxhaXbofOMtKTBeN2SDKfiRTgyeDr0qEvdF5R5T9pI05n1RaBS0HySTkz8r/vEmWofAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:23:17.747654Z","bundle_sha256":"b4fe22f388c1cd1a1a6d48b35e2f4fe51df21a019adc5e212a122b851ab4d7ab"}}