{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K6I2UW7S6S6Q5QEZRVSHOQ32BI","short_pith_number":"pith:K6I2UW7S","canonical_record":{"source":{"id":"1910.09208","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-10-21T08:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"6305b960a437a34a0b6b25bdf55b827e543fa80c01b1f7ea3b81ee37f067576e","abstract_canon_sha256":"4b11668a11a32cb6ea66c0d8d47dfd029e983ae240907cf58329ec69832ffeb6"},"schema_version":"1.0"},"canonical_sha256":"5791aa5bf2f4bd0ec0998d6477437a0a23e8a022c69d869c4c195d29ff5532e3","source":{"kind":"arxiv","id":"1910.09208","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.09208","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"arxiv_version","alias_value":"1910.09208v2","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.09208","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"pith_short_12","alias_value":"K6I2UW7S6S6Q","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"pith_short_16","alias_value":"K6I2UW7S6S6Q5QEZ","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"pith_short_8","alias_value":"K6I2UW7S","created_at":"2026-07-05T01:58:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K6I2UW7S6S6Q5QEZRVSHOQ32BI","target":"record","payload":{"canonical_record":{"source":{"id":"1910.09208","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-10-21T08:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"6305b960a437a34a0b6b25bdf55b827e543fa80c01b1f7ea3b81ee37f067576e","abstract_canon_sha256":"4b11668a11a32cb6ea66c0d8d47dfd029e983ae240907cf58329ec69832ffeb6"},"schema_version":"1.0"},"canonical_sha256":"5791aa5bf2f4bd0ec0998d6477437a0a23e8a022c69d869c4c195d29ff5532e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:58:29.178737Z","signature_b64":"ssPAx3jpgg7dv1dc/zZ82T7+FrI/YN3zR2P6S5fa477MjZcvDHp7FjT3xGWUNL4CV0544zug/fpyB3N9mSvvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5791aa5bf2f4bd0ec0998d6477437a0a23e8a022c69d869c4c195d29ff5532e3","last_reissued_at":"2026-07-05T01:58:29.178342Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:58:29.178342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.09208","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":"2026-07-05T01:58:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Df52go/39SRYveFSqFZ4/5dz+1V6yuc6U/g/WtrZWLjdxt+yxXucxrMEMNfymtUWWXslq6bwnheRWvdSMvIKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:33:02.934513Z"},"content_sha256":"caddb542ce62b928f7b087c61864400fcdd4ef4ff574ea9da1289c6eb29cf01b","schema_version":"1.0","event_id":"sha256:caddb542ce62b928f7b087c61864400fcdd4ef4ff574ea9da1289c6eb29cf01b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K6I2UW7S6S6Q5QEZRVSHOQ32BI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient container lemma","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J\\'ozsef Balogh, Wojciech Samotij","submitted_at":"2019-10-21T08:39:18Z","abstract_excerpt":"We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional convex geometry. The existence of smaller families of containers for independent sets in such hypergraphs, which is guaranteed by the new theorem, allows us to improve upon the best currently known bounds for several problems in extremal graph theory, discrete geometry, and Ramsey theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09208","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.09208/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":"2026-07-05T01:58:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqmIX95Ll7ml0oAasWTSUAX/0yfs8fbkBszmF6h6Aa4wwIIRkrluR5YM4YOJWT5cLo+kGUeyVvKqfLEvIXS1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:33:02.935007Z"},"content_sha256":"00628adc62cc14fafb83a260d17aba31d284630cba608d659855cb3d6763589d","schema_version":"1.0","event_id":"sha256:00628adc62cc14fafb83a260d17aba31d284630cba608d659855cb3d6763589d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI/bundle.json","state_url":"https://pith.science/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI/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":"2026-08-22T11:33:02Z","links":{"resolver":"https://pith.science/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI","bundle":"https://pith.science/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI/bundle.json","state":"https://pith.science/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6I2UW7S6S6Q5QEZRVSHOQ32BI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K6I2UW7S6S6Q5QEZRVSHOQ32BI","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":"4b11668a11a32cb6ea66c0d8d47dfd029e983ae240907cf58329ec69832ffeb6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-10-21T08:39:18Z","title_canon_sha256":"6305b960a437a34a0b6b25bdf55b827e543fa80c01b1f7ea3b81ee37f067576e"},"schema_version":"1.0","source":{"id":"1910.09208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.09208","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"arxiv_version","alias_value":"1910.09208v2","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.09208","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"pith_short_12","alias_value":"K6I2UW7S6S6Q","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"pith_short_16","alias_value":"K6I2UW7S6S6Q5QEZ","created_at":"2026-07-05T01:58:29Z"},{"alias_kind":"pith_short_8","alias_value":"K6I2UW7S","created_at":"2026-07-05T01:58:29Z"}],"graph_snapshots":[{"event_id":"sha256:00628adc62cc14fafb83a260d17aba31d284630cba608d659855cb3d6763589d","target":"graph","created_at":"2026-07-05T01:58:29Z","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/1910.09208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional convex geometry. The existence of smaller families of containers for independent sets in such hypergraphs, which is guaranteed by the new theorem, allows us to improve upon the best currently known bounds for several problems in extremal graph theory, discrete geometry, and Ramsey theory.","authors_text":"J\\'ozsef Balogh, Wojciech Samotij","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-10-21T08:39:18Z","title":"An efficient container lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09208","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:caddb542ce62b928f7b087c61864400fcdd4ef4ff574ea9da1289c6eb29cf01b","target":"record","created_at":"2026-07-05T01:58:29Z","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":"4b11668a11a32cb6ea66c0d8d47dfd029e983ae240907cf58329ec69832ffeb6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-10-21T08:39:18Z","title_canon_sha256":"6305b960a437a34a0b6b25bdf55b827e543fa80c01b1f7ea3b81ee37f067576e"},"schema_version":"1.0","source":{"id":"1910.09208","kind":"arxiv","version":2}},"canonical_sha256":"5791aa5bf2f4bd0ec0998d6477437a0a23e8a022c69d869c4c195d29ff5532e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5791aa5bf2f4bd0ec0998d6477437a0a23e8a022c69d869c4c195d29ff5532e3","first_computed_at":"2026-07-05T01:58:29.178342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:58:29.178342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ssPAx3jpgg7dv1dc/zZ82T7+FrI/YN3zR2P6S5fa477MjZcvDHp7FjT3xGWUNL4CV0544zug/fpyB3N9mSvvAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:58:29.178737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.09208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caddb542ce62b928f7b087c61864400fcdd4ef4ff574ea9da1289c6eb29cf01b","sha256:00628adc62cc14fafb83a260d17aba31d284630cba608d659855cb3d6763589d"],"state_sha256":"f876af689d0f04e3bbcd83e62d760f586ab3ed80a3fcf38e8503e8b4380c9bb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSkLlEZSnvasm6p+MVmgKhrR1NwdeZlTBUFAxEdEu3FaC/YEOg9eDIvGZ1nimMoukWPB7dJPpa3kHNj1Jx6XAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:33:02.939614Z","bundle_sha256":"164814943fefc332ceb2e4de2da959c30d5dd6bfe5d2fbf4dbcfe3d6e47b7964"}}