{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DURGAPHAXDQR4AMDKMVKOHQFID","short_pith_number":"pith:DURGAPHA","canonical_record":{"source":{"id":"1103.1416","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-08T02:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"d6cd20e85467a6b327360e7403b4028df12d04fbc52dd2814fe8837b7d206ee5","abstract_canon_sha256":"92c92a141a9bf1e3caa5edf6f09c562f0ab9c9c9ce433c93f774e975ab7a27fa"},"schema_version":"1.0"},"canonical_sha256":"1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742","source":{"kind":"arxiv","id":"1103.1416","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1416","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1416v5","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1416","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"DURGAPHAXDQR","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DURGAPHAXDQR4AMD","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DURGAPHA","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DURGAPHAXDQR4AMDKMVKOHQFID","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1416","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-08T02:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"d6cd20e85467a6b327360e7403b4028df12d04fbc52dd2814fe8837b7d206ee5","abstract_canon_sha256":"92c92a141a9bf1e3caa5edf6f09c562f0ab9c9c9ce433c93f774e975ab7a27fa"},"schema_version":"1.0"},"canonical_sha256":"1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.703795Z","signature_b64":"PDPrIsW17DJYmojgxHcX+kqZbxaWw2XBZClSGfhJUIWFlmC0l3F58uVoxiHNPDbnc595pwOzW1cACAfaDEAqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742","last_reissued_at":"2026-05-17T23:53:36.703035Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.703035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1416","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tl5bV2Q9qCqSd/Ujcf7/Ii6fY4imiXwcqvhJZTtUtRcDv3Pt93XQ3eouKi88P059HmulPD8SkEUbqHcdZCipAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:06:13.149511Z"},"content_sha256":"36cb13f9cbdd16d18f8d49ef44423e032567ec22504510b8f52489737e840784","schema_version":"1.0","event_id":"sha256:36cb13f9cbdd16d18f8d49ef44423e032567ec22504510b8f52489737e840784"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DURGAPHAXDQR4AMDKMVKOHQFID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Chromatic Thresholds of Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dhruv Mubayi, Jane Butterfield, John Lenz, J\\'ozsef Balogh, Ping Hu","submitted_at":"2011-03-08T02:24:40Z","abstract_excerpt":"Let F be a family of r-uniform hypergraphs. The chromatic threshold of F is the infimum of all non-negative reals c such that the subfamily of F comprising hypergraphs H with minimum degree at least $c \\binom{|V(H)|}{r-1}$ has bounded chromatic number. This parameter has a long history for graphs (r=2), and in this paper we begin its systematic study for hypergraphs.\n  {\\L}uczak and Thomass\\'e recently proved that the chromatic threshold of the so-called near bipartite graphs is zero, and our main contribution is to generalize this result to r-uniform hypergraphs. For this class of hypergraphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1416","kind":"arxiv","version":5},"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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3LFx6RpbcOCzlAOtRiJ8cRtaeOtddXYiZa7Lk1JCUcCIm7iw9VRdqB/ihnQlcVCX3eKTq8gcX/0a52KNHboACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:06:13.150216Z"},"content_sha256":"75daa4a7cc157f77012bedae384edfb55c83a6e3a762669fbedaa0c6853b6139","schema_version":"1.0","event_id":"sha256:75daa4a7cc157f77012bedae384edfb55c83a6e3a762669fbedaa0c6853b6139"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DURGAPHAXDQR4AMDKMVKOHQFID/bundle.json","state_url":"https://pith.science/pith/DURGAPHAXDQR4AMDKMVKOHQFID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DURGAPHAXDQR4AMDKMVKOHQFID/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":"2026-05-31T21:06:13Z","links":{"resolver":"https://pith.science/pith/DURGAPHAXDQR4AMDKMVKOHQFID","bundle":"https://pith.science/pith/DURGAPHAXDQR4AMDKMVKOHQFID/bundle.json","state":"https://pith.science/pith/DURGAPHAXDQR4AMDKMVKOHQFID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DURGAPHAXDQR4AMDKMVKOHQFID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DURGAPHAXDQR4AMDKMVKOHQFID","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":"92c92a141a9bf1e3caa5edf6f09c562f0ab9c9c9ce433c93f774e975ab7a27fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-08T02:24:40Z","title_canon_sha256":"d6cd20e85467a6b327360e7403b4028df12d04fbc52dd2814fe8837b7d206ee5"},"schema_version":"1.0","source":{"id":"1103.1416","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1416","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1416v5","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1416","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"DURGAPHAXDQR","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DURGAPHAXDQR4AMD","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DURGAPHA","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:75daa4a7cc157f77012bedae384edfb55c83a6e3a762669fbedaa0c6853b6139","target":"graph","created_at":"2026-05-17T23:53:36Z","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 a family of r-uniform hypergraphs. The chromatic threshold of F is the infimum of all non-negative reals c such that the subfamily of F comprising hypergraphs H with minimum degree at least $c \\binom{|V(H)|}{r-1}$ has bounded chromatic number. This parameter has a long history for graphs (r=2), and in this paper we begin its systematic study for hypergraphs.\n  {\\L}uczak and Thomass\\'e recently proved that the chromatic threshold of the so-called near bipartite graphs is zero, and our main contribution is to generalize this result to r-uniform hypergraphs. For this class of hypergraphs","authors_text":"Dhruv Mubayi, Jane Butterfield, John Lenz, J\\'ozsef Balogh, Ping Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-08T02:24:40Z","title":"On the Chromatic Thresholds of Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1416","kind":"arxiv","version":5},"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":"sha256:36cb13f9cbdd16d18f8d49ef44423e032567ec22504510b8f52489737e840784","target":"record","created_at":"2026-05-17T23:53:36Z","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":"92c92a141a9bf1e3caa5edf6f09c562f0ab9c9c9ce433c93f774e975ab7a27fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-08T02:24:40Z","title_canon_sha256":"d6cd20e85467a6b327360e7403b4028df12d04fbc52dd2814fe8837b7d206ee5"},"schema_version":"1.0","source":{"id":"1103.1416","kind":"arxiv","version":5}},"canonical_sha256":"1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d22603ce0b8e11e0183532aa71e0540fc2acf63f8c877560dca765d0fa72742","first_computed_at":"2026-05-17T23:53:36.703035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.703035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PDPrIsW17DJYmojgxHcX+kqZbxaWw2XBZClSGfhJUIWFlmC0l3F58uVoxiHNPDbnc595pwOzW1cACAfaDEAqBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.703795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1416","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36cb13f9cbdd16d18f8d49ef44423e032567ec22504510b8f52489737e840784","sha256:75daa4a7cc157f77012bedae384edfb55c83a6e3a762669fbedaa0c6853b6139"],"state_sha256":"14c6b1de079b885a7224a3d291d24ffa6dbb51e160621d9ee9c3930332b4872e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0jnQa/5qihquBDY4iHYkFeaTHbOKCdJb5FJrDCJAAk1qVjN97ShETrhKNHLYT6xDiZXNu8GXwBwNcMBO2EnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:06:13.154368Z","bundle_sha256":"8a4f3525ae2bf16fec30019549127d1473182440ed7ea3d30b047aa6a4c926f0"}}