{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7XT2NZ7OBTWPQI3OF2SON72W7U","short_pith_number":"pith:7XT2NZ7O","canonical_record":{"source":{"id":"1307.7363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-28T14:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"00b7f76ab30ef8ea3376ff27035833d8f9420512bb719745da6ce42648df70d3","abstract_canon_sha256":"4ec717d689c749c717b9bfa8c52ae9e458e4fe45e1b991164f4192bad6816f12"},"schema_version":"1.0"},"canonical_sha256":"fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6","source":{"kind":"arxiv","id":"1307.7363","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7363","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7363v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7363","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"7XT2NZ7OBTWP","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7XT2NZ7OBTWPQI3O","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7XT2NZ7O","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7XT2NZ7OBTWPQI3OF2SON72W7U","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-28T14:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"00b7f76ab30ef8ea3376ff27035833d8f9420512bb719745da6ce42648df70d3","abstract_canon_sha256":"4ec717d689c749c717b9bfa8c52ae9e458e4fe45e1b991164f4192bad6816f12"},"schema_version":"1.0"},"canonical_sha256":"fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:23.488333Z","signature_b64":"ReigFjnRAGsSnvsgokywU3le7szIFF0Uh/HthlZ4eoDABOoidCPqZU0xBn+iLM8PXqKcsytCIEpODp4+DFnjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6","last_reissued_at":"2026-05-18T03:17:23.487908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:23.487908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7363","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjeGChiyR5CTTrtsOmBtmv/ERtZW8sSjBeSq4K3Q/5U2OXmcfHWaQ40JvVInRlGHBQTh8qLOj68fCa3LUqDLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:15:51.050916Z"},"content_sha256":"3faa57901ba0e0aeaa04b230c60da173e85360a5426ba632af51149c64e0cf29","schema_version":"1.0","event_id":"sha256:3faa57901ba0e0aeaa04b230c60da173e85360a5426ba632af51149c64e0cf29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7XT2NZ7OBTWPQI3OF2SON72W7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypergraphs with Zero Chromatic Threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John Lenz, J\\'ozsef Balogh","submitted_at":"2013-07-28T14:00:58Z","abstract_excerpt":"Let F be an r-uniform hypergraph. The chromatic threshold of the family of F-free, r-uniform hypergraphs is the infimum of all non-negative reals c such that the subfamily of F-free, r-uniform hypergraphs H with minimum degree at least $c \\binom{|V(H)|}{r-1}$ has bounded chromatic number. The study of chromatic thresholds of various graphs has a long history, beginning with the early work of Erd\\H{o}s-Simonovits. One interesting question, first proposed by \\L{}uczak-Thomass\\'{e} and then solved by Allen-B\\\"{o}ttcher-Griffiths-Kohayakawa-Morris, is the characterization of graphs having zero chr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7363","kind":"arxiv","version":1},"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":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQkX46b8fgcDOwyLT2xJm27kYk5rRuCwWJFN08surQb4Xgsovaxn0tsX73+eStWddVWm4hN8fxisDuFRUrhfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:15:51.051589Z"},"content_sha256":"bf0a5761c7ee0ec97bc1686e6b9f66df3b53698cc69ce5cab32ca249973ec80d","schema_version":"1.0","event_id":"sha256:bf0a5761c7ee0ec97bc1686e6b9f66df3b53698cc69ce5cab32ca249973ec80d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XT2NZ7OBTWPQI3OF2SON72W7U/bundle.json","state_url":"https://pith.science/pith/7XT2NZ7OBTWPQI3OF2SON72W7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XT2NZ7OBTWPQI3OF2SON72W7U/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":"2026-05-31T22:15:51Z","links":{"resolver":"https://pith.science/pith/7XT2NZ7OBTWPQI3OF2SON72W7U","bundle":"https://pith.science/pith/7XT2NZ7OBTWPQI3OF2SON72W7U/bundle.json","state":"https://pith.science/pith/7XT2NZ7OBTWPQI3OF2SON72W7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XT2NZ7OBTWPQI3OF2SON72W7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7XT2NZ7OBTWPQI3OF2SON72W7U","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":"4ec717d689c749c717b9bfa8c52ae9e458e4fe45e1b991164f4192bad6816f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-28T14:00:58Z","title_canon_sha256":"00b7f76ab30ef8ea3376ff27035833d8f9420512bb719745da6ce42648df70d3"},"schema_version":"1.0","source":{"id":"1307.7363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7363","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7363v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7363","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"7XT2NZ7OBTWP","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7XT2NZ7OBTWPQI3O","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7XT2NZ7O","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:bf0a5761c7ee0ec97bc1686e6b9f66df3b53698cc69ce5cab32ca249973ec80d","target":"graph","created_at":"2026-05-18T03:17:23Z","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 F be an r-uniform hypergraph. The chromatic threshold of the family of F-free, r-uniform hypergraphs is the infimum of all non-negative reals c such that the subfamily of F-free, r-uniform hypergraphs H with minimum degree at least $c \\binom{|V(H)|}{r-1}$ has bounded chromatic number. The study of chromatic thresholds of various graphs has a long history, beginning with the early work of Erd\\H{o}s-Simonovits. One interesting question, first proposed by \\L{}uczak-Thomass\\'{e} and then solved by Allen-B\\\"{o}ttcher-Griffiths-Kohayakawa-Morris, is the characterization of graphs having zero chr","authors_text":"John Lenz, J\\'ozsef Balogh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-28T14:00:58Z","title":"Hypergraphs with Zero Chromatic Threshold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7363","kind":"arxiv","version":1},"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":"sha256:3faa57901ba0e0aeaa04b230c60da173e85360a5426ba632af51149c64e0cf29","target":"record","created_at":"2026-05-18T03:17:23Z","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":"4ec717d689c749c717b9bfa8c52ae9e458e4fe45e1b991164f4192bad6816f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-28T14:00:58Z","title_canon_sha256":"00b7f76ab30ef8ea3376ff27035833d8f9420512bb719745da6ce42648df70d3"},"schema_version":"1.0","source":{"id":"1307.7363","kind":"arxiv","version":1}},"canonical_sha256":"fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fde7a6e7ee0cecf8236e2ea4e6ff56fd03fd379fcea22ca53733e9e698498eb6","first_computed_at":"2026-05-18T03:17:23.487908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:23.487908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ReigFjnRAGsSnvsgokywU3le7szIFF0Uh/HthlZ4eoDABOoidCPqZU0xBn+iLM8PXqKcsytCIEpODp4+DFnjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:23.488333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3faa57901ba0e0aeaa04b230c60da173e85360a5426ba632af51149c64e0cf29","sha256:bf0a5761c7ee0ec97bc1686e6b9f66df3b53698cc69ce5cab32ca249973ec80d"],"state_sha256":"f60b2fc898915236ec7104914dec97e86b5f1ca0aafee987f0843702ab2574d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CazFnL2x0PI/EaI6PPfqiYtz7LkWrUAQV+GklPZqqKTt/P360YD2yroH9BO6I/c8+degscX4MHtJaTbdWcrrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:15:51.055664Z","bundle_sha256":"4b0d84f53a6896fb961fc10f0196e82fd1ed81ab3f81157743efbabac65ee4cf"}}