{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:ODMXM2YJY4P5RCYJMM7LCA33MU","short_pith_number":"pith:ODMXM2YJ","canonical_record":{"source":{"id":"2008.09593","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-21T17:39:52Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"183d9db0a0fca6e202882a9321ac28cf45c699c28c0e49c5c37db4527f9838f4","abstract_canon_sha256":"e6aa8ca4a299a15bfa76f13eb385cf61252d83c6f65a7f630f8dd02fa1e4c5c8"},"schema_version":"1.0"},"canonical_sha256":"70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc","source":{"kind":"arxiv","id":"2008.09593","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.09593","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"2008.09593v3","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.09593","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"ODMXM2YJY4P5","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"pith_short_16","alias_value":"ODMXM2YJY4P5RCYJ","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"pith_short_8","alias_value":"ODMXM2YJ","created_at":"2026-07-05T04:40:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:ODMXM2YJY4P5RCYJMM7LCA33MU","target":"record","payload":{"canonical_record":{"source":{"id":"2008.09593","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-21T17:39:52Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"183d9db0a0fca6e202882a9321ac28cf45c699c28c0e49c5c37db4527f9838f4","abstract_canon_sha256":"e6aa8ca4a299a15bfa76f13eb385cf61252d83c6f65a7f630f8dd02fa1e4c5c8"},"schema_version":"1.0"},"canonical_sha256":"70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:40:06.228364Z","signature_b64":"gdIqWnyqLXDvSNWEubRtALjCqwl9UzyIAcCpEf/dcris40n4B8q87XLnWglSZmPM/juEw0tkJbAKAbAAwvnYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc","last_reissued_at":"2026-07-05T04:40:06.227759Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:40:06.227759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.09593","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:40:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"orpsl0bjuJmd9ZcsdDMlB0gq8tL4w4vMWmRcj9iDiyIGJ4F1iC4MqkdToSF57c7G5/Tjs8WJdBKP/Hsd2g13Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T22:37:27.738761Z"},"content_sha256":"73a9b03991ea6f909af724872e6cc5b96384d69fdfc21dfc095613760e020f18","schema_version":"1.0","event_id":"sha256:73a9b03991ea6f909af724872e6cc5b96384d69fdfc21dfc095613760e020f18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:ODMXM2YJY4P5RCYJMM7LCA33MU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic Concentration, Anti-concentration, and Discrepancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.PR","authors_text":"Ruizhe Zhang, Zhao Song","submitted_at":"2020-08-21T17:39:52Z","abstract_excerpt":"Chernoff bound is a fundamental tool in theoretical computer science. It has been extensively used in randomized algorithm design and stochastic type analysis. Discrepancy theory, which deals with finding a bi-coloring of a set system such that the coloring of each set is balanced, has a huge number of applications in approximation algorithms design. Chernoff bound [Che52] implies that a random bi-coloring of any set system with $n$ sets and $n$ elements will have discrepancy $O(\\sqrt{n \\log n})$ with high probability, while the famous result by Spencer [Spe85] shows that there exists an $O(\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.09593","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.09593/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:40:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9NCZ+2dPDGr+yxYzH9CVDDCtjP42Zo2DdzBOvsMLZIQb7PpbaG0ZuYIzVjFp4dcyXmVj1jJ6EGTB+k4hJK+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T22:37:27.739354Z"},"content_sha256":"3c8062aa0f9c5030974cbabda1d423b648cf9319d4cb83576cd3d780be0d4300","schema_version":"1.0","event_id":"sha256:3c8062aa0f9c5030974cbabda1d423b648cf9319d4cb83576cd3d780be0d4300"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODMXM2YJY4P5RCYJMM7LCA33MU/bundle.json","state_url":"https://pith.science/pith/ODMXM2YJY4P5RCYJMM7LCA33MU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODMXM2YJY4P5RCYJMM7LCA33MU/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":"2026-08-07T22:37:27Z","links":{"resolver":"https://pith.science/pith/ODMXM2YJY4P5RCYJMM7LCA33MU","bundle":"https://pith.science/pith/ODMXM2YJY4P5RCYJMM7LCA33MU/bundle.json","state":"https://pith.science/pith/ODMXM2YJY4P5RCYJMM7LCA33MU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODMXM2YJY4P5RCYJMM7LCA33MU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ODMXM2YJY4P5RCYJMM7LCA33MU","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":"e6aa8ca4a299a15bfa76f13eb385cf61252d83c6f65a7f630f8dd02fa1e4c5c8","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-21T17:39:52Z","title_canon_sha256":"183d9db0a0fca6e202882a9321ac28cf45c699c28c0e49c5c37db4527f9838f4"},"schema_version":"1.0","source":{"id":"2008.09593","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.09593","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"2008.09593v3","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.09593","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"ODMXM2YJY4P5","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"pith_short_16","alias_value":"ODMXM2YJY4P5RCYJ","created_at":"2026-07-05T04:40:06Z"},{"alias_kind":"pith_short_8","alias_value":"ODMXM2YJ","created_at":"2026-07-05T04:40:06Z"}],"graph_snapshots":[{"event_id":"sha256:3c8062aa0f9c5030974cbabda1d423b648cf9319d4cb83576cd3d780be0d4300","target":"graph","created_at":"2026-07-05T04:40:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.09593/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Chernoff bound is a fundamental tool in theoretical computer science. It has been extensively used in randomized algorithm design and stochastic type analysis. Discrepancy theory, which deals with finding a bi-coloring of a set system such that the coloring of each set is balanced, has a huge number of applications in approximation algorithms design. Chernoff bound [Che52] implies that a random bi-coloring of any set system with $n$ sets and $n$ elements will have discrepancy $O(\\sqrt{n \\log n})$ with high probability, while the famous result by Spencer [Spe85] shows that there exists an $O(\\s","authors_text":"Ruizhe Zhang, Zhao Song","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-21T17:39:52Z","title":"Hyperbolic Concentration, Anti-concentration, and Discrepancy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.09593","kind":"arxiv","version":3},"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":"sha256:73a9b03991ea6f909af724872e6cc5b96384d69fdfc21dfc095613760e020f18","target":"record","created_at":"2026-07-05T04:40:06Z","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":"e6aa8ca4a299a15bfa76f13eb385cf61252d83c6f65a7f630f8dd02fa1e4c5c8","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-21T17:39:52Z","title_canon_sha256":"183d9db0a0fca6e202882a9321ac28cf45c699c28c0e49c5c37db4527f9838f4"},"schema_version":"1.0","source":{"id":"2008.09593","kind":"arxiv","version":3}},"canonical_sha256":"70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc","first_computed_at":"2026-07-05T04:40:06.227759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:40:06.227759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gdIqWnyqLXDvSNWEubRtALjCqwl9UzyIAcCpEf/dcris40n4B8q87XLnWglSZmPM/juEw0tkJbAKAbAAwvnYBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:40:06.228364Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.09593","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73a9b03991ea6f909af724872e6cc5b96384d69fdfc21dfc095613760e020f18","sha256:3c8062aa0f9c5030974cbabda1d423b648cf9319d4cb83576cd3d780be0d4300"],"state_sha256":"186767282c037d8989a468b881a59c210971bd5682a427fe245718da4e19618f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1NbYTerYiIZEOUShwDbTU8f8NcMvlcjDNIXC2Cc+SmQ4tDMj8+45Df+CFt17LBFaj2tQYWGYzuMR6iDJ0wexBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T22:37:27.743528Z","bundle_sha256":"6b4203d2ea86cf76e286b1a1532f5475816b7a15dcc01fb5e747a62b706d95ee"}}