{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Z3MQC4FOP3CPP7PD7H3CX5ZBDM","short_pith_number":"pith:Z3MQC4FO","canonical_record":{"source":{"id":"1805.04195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-10T22:18:57Z","cross_cats_sorted":[],"title_canon_sha256":"5d946051ccf770d80afdd39e458b11ecdeea0dcadf333470fe06718e9cf0a971","abstract_canon_sha256":"de0edfa2c1b18156ae33d0e739af6d03983f094b69075c52a550378cef037e6f"},"schema_version":"1.0"},"canonical_sha256":"ced90170ae7ec4f7fde3f9f62bf7211b355591f8a7822642c71e07ca37b8825c","source":{"kind":"arxiv","id":"1805.04195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04195","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04195v2","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04195","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"Z3MQC4FOP3CP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z3MQC4FOP3CPP7PD","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z3MQC4FO","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Z3MQC4FOP3CPP7PD7H3CX5ZBDM","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-10T22:18:57Z","cross_cats_sorted":[],"title_canon_sha256":"5d946051ccf770d80afdd39e458b11ecdeea0dcadf333470fe06718e9cf0a971","abstract_canon_sha256":"de0edfa2c1b18156ae33d0e739af6d03983f094b69075c52a550378cef037e6f"},"schema_version":"1.0"},"canonical_sha256":"ced90170ae7ec4f7fde3f9f62bf7211b355591f8a7822642c71e07ca37b8825c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:07.242109Z","signature_b64":"mUucjnFhAnb4s5qe3WLI1XoLLGMD7quklknfbqHHA5NU1r4+dslinntCayMnCLl6qmUWzlCELujybL9A0t9UAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced90170ae7ec4f7fde3f9f62bf7211b355591f8a7822642c71e07ca37b8825c","last_reissued_at":"2026-05-18T00:16:07.241396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:07.241396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04195","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":"2026-05-18T00:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1ceXqu7VlIPfMF8EOgXYNz4KBsr/1jwij96DxOCaCBvig6VxRpiusiZP5ovcIoQ7W8Cta8RyqmUZuYPnxSeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T18:50:33.082881Z"},"content_sha256":"503f822a7388bbda7751863cae4cfdf9c6005a083bd21d6e3cbcbdf4dbc7fef9","schema_version":"1.0","event_id":"sha256:503f822a7388bbda7751863cae4cfdf9c6005a083bd21d6e3cbcbdf4dbc7fef9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Z3MQC4FOP3CPP7PD7H3CX5ZBDM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Avoiding long Berge cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Ruth Luo, Zoltan Furedi","submitted_at":"2018-05-10T22:18:57Z","abstract_excerpt":"Let $n\\geq k\\geq r+3$ and $\\mathcal H$ be an $n$-vertex $r$-uniform hypergraph. We show that if $|\\mathcal H|> \\frac{n-1}{k-2}\\binom{k-1}{r}$ then $\\mathcal H$ contains a Berge cycle of length at least $k$. This bound is tight when $k-2$ divides $n-1$. We also show that the bound is attained only for connected $r$-uniform hypergraphs in which every block is the complete hypergraph $K^{(r)}_{k-1}$. We conjecture that our bound also holds in the case $k=r+2$, but the case of short cycles, $k\\leq r+1$, is different."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04195","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":"2026-05-18T00:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"APa/TEAcGG0Z8JQrTmVrYynSqgQPoJL46LoCkmF67k6pfqdS0ZjOPL+w/Vd9iLsPH17zAkQ23aXo0jJSI5jZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T18:50:33.083574Z"},"content_sha256":"70cc0cd99dd1c908bd88ebfc77fafe4c6e2f2b9e6dedf9bd12757a8cd14f8012","schema_version":"1.0","event_id":"sha256:70cc0cd99dd1c908bd88ebfc77fafe4c6e2f2b9e6dedf9bd12757a8cd14f8012"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM/bundle.json","state_url":"https://pith.science/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM/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":"2026-05-18T18:50:33Z","links":{"resolver":"https://pith.science/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM","bundle":"https://pith.science/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM/bundle.json","state":"https://pith.science/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3MQC4FOP3CPP7PD7H3CX5ZBDM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z3MQC4FOP3CPP7PD7H3CX5ZBDM","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":"de0edfa2c1b18156ae33d0e739af6d03983f094b69075c52a550378cef037e6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-10T22:18:57Z","title_canon_sha256":"5d946051ccf770d80afdd39e458b11ecdeea0dcadf333470fe06718e9cf0a971"},"schema_version":"1.0","source":{"id":"1805.04195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04195","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04195v2","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04195","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"Z3MQC4FOP3CP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z3MQC4FOP3CPP7PD","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z3MQC4FO","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:70cc0cd99dd1c908bd88ebfc77fafe4c6e2f2b9e6dedf9bd12757a8cd14f8012","target":"graph","created_at":"2026-05-18T00:16:07Z","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":"Let $n\\geq k\\geq r+3$ and $\\mathcal H$ be an $n$-vertex $r$-uniform hypergraph. We show that if $|\\mathcal H|> \\frac{n-1}{k-2}\\binom{k-1}{r}$ then $\\mathcal H$ contains a Berge cycle of length at least $k$. This bound is tight when $k-2$ divides $n-1$. We also show that the bound is attained only for connected $r$-uniform hypergraphs in which every block is the complete hypergraph $K^{(r)}_{k-1}$. We conjecture that our bound also holds in the case $k=r+2$, but the case of short cycles, $k\\leq r+1$, is different.","authors_text":"Alexandr Kostochka, Ruth Luo, Zoltan Furedi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-10T22:18:57Z","title":"Avoiding long Berge cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04195","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":"sha256:503f822a7388bbda7751863cae4cfdf9c6005a083bd21d6e3cbcbdf4dbc7fef9","target":"record","created_at":"2026-05-18T00:16:07Z","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":"de0edfa2c1b18156ae33d0e739af6d03983f094b69075c52a550378cef037e6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-10T22:18:57Z","title_canon_sha256":"5d946051ccf770d80afdd39e458b11ecdeea0dcadf333470fe06718e9cf0a971"},"schema_version":"1.0","source":{"id":"1805.04195","kind":"arxiv","version":2}},"canonical_sha256":"ced90170ae7ec4f7fde3f9f62bf7211b355591f8a7822642c71e07ca37b8825c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ced90170ae7ec4f7fde3f9f62bf7211b355591f8a7822642c71e07ca37b8825c","first_computed_at":"2026-05-18T00:16:07.241396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:07.241396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mUucjnFhAnb4s5qe3WLI1XoLLGMD7quklknfbqHHA5NU1r4+dslinntCayMnCLl6qmUWzlCELujybL9A0t9UAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:07.242109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:503f822a7388bbda7751863cae4cfdf9c6005a083bd21d6e3cbcbdf4dbc7fef9","sha256:70cc0cd99dd1c908bd88ebfc77fafe4c6e2f2b9e6dedf9bd12757a8cd14f8012"],"state_sha256":"9b22c711d39b69ef3574d27f83109c2008769153431ed0d048c0db11c5586cbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T1VRmkGNhsMTIVOVanm4+1M/X9ggWOFmN8LLyWRFOG61bt+r8g8BZ+XVKGTTy7Aqh6sRKmAu0L7ZrvRKXQ1GAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T18:50:33.085627Z","bundle_sha256":"598a89599d1c87a5811e3482fa57e1eca35ba5284793cf725c7db89b7b190bca"}}