{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4VNTF73PINTUA6RVJVB4CDY23K","short_pith_number":"pith:4VNTF73P","canonical_record":{"source":{"id":"1608.08954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T17:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"46950b5f7f186650fa2f35403f66d76c559518a7d686f50630986dbc9c8f7916","abstract_canon_sha256":"a121b6670c5c62ef27b0a53185edb4a45b7f9853c6e3e0c190c0da8c7b15fec7"},"schema_version":"1.0"},"canonical_sha256":"e55b32ff6f4367407a354d43c10f1ada9e2fe45912c0ca092e66bae81357c445","source":{"kind":"arxiv","id":"1608.08954","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08954","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08954v1","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08954","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"4VNTF73PINTU","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4VNTF73PINTUA6RV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4VNTF73P","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4VNTF73PINTUA6RVJVB4CDY23K","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T17:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"46950b5f7f186650fa2f35403f66d76c559518a7d686f50630986dbc9c8f7916","abstract_canon_sha256":"a121b6670c5c62ef27b0a53185edb4a45b7f9853c6e3e0c190c0da8c7b15fec7"},"schema_version":"1.0"},"canonical_sha256":"e55b32ff6f4367407a354d43c10f1ada9e2fe45912c0ca092e66bae81357c445","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:39.588584Z","signature_b64":"nI+Av6D03608E2jV6yvcR4jk3cVfPYk6IWJJyKABja8r8x0CnVnf6N4rkr6Ua8zqe7Z6rEx7NL/Tkfyzl2oYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e55b32ff6f4367407a354d43c10f1ada9e2fe45912c0ca092e66bae81357c445","last_reissued_at":"2026-05-18T01:06:39.587936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:39.587936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08954","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":"2026-05-18T01:06:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LpSlMo2n9AelW2qOmrAFul/+9JwcXLJJaYaDSQe6BdcYhC06PwNhP2F4LcbL8HgUFSUORSwIt1wZNIprpaXdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:30:55.284095Z"},"content_sha256":"9ff6c4475459e8f39a673c9acdc8b2e664c3493b8c0bd4cfcd501187fe46a67a","schema_version":"1.0","event_id":"sha256:9ff6c4475459e8f39a673c9acdc8b2e664c3493b8c0bd4cfcd501187fe46a67a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4VNTF73PINTUA6RVJVB4CDY23K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chv\\'{a}tal's Conjecture and Correlation Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ehud Friedgut, Gil Kalai, Jeff Kahn, Nathan Keller","submitted_at":"2016-08-31T17:21:57Z","abstract_excerpt":"Chv\\'{a}tal's conjecture in extremal combinatorics asserts that for any decreasing family $\\mathcal{F}$ of subsets of a finite set $S$, there is a largest intersecting subfamily of $\\mathcal{F}$ consisting of all members of $\\mathcal{F}$ that include a particular $x \\in S$. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants using tools from discrete Fourier analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08954","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":"2026-05-18T01:06:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xyz2icIGXqBbVkVt/5CByyVh8QmuqX5e84kDa7vIH+RWnuJdBm+76/JmIKWUqCu6p4R6sTa+GusEqGDDPx0NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:30:55.284453Z"},"content_sha256":"7902691716fd63115a3dc3b242972dd391ffc76d07a5035a26073ee18327a34a","schema_version":"1.0","event_id":"sha256:7902691716fd63115a3dc3b242972dd391ffc76d07a5035a26073ee18327a34a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VNTF73PINTUA6RVJVB4CDY23K/bundle.json","state_url":"https://pith.science/pith/4VNTF73PINTUA6RVJVB4CDY23K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VNTF73PINTUA6RVJVB4CDY23K/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":"2026-06-09T12:30:55Z","links":{"resolver":"https://pith.science/pith/4VNTF73PINTUA6RVJVB4CDY23K","bundle":"https://pith.science/pith/4VNTF73PINTUA6RVJVB4CDY23K/bundle.json","state":"https://pith.science/pith/4VNTF73PINTUA6RVJVB4CDY23K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VNTF73PINTUA6RVJVB4CDY23K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4VNTF73PINTUA6RVJVB4CDY23K","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":"a121b6670c5c62ef27b0a53185edb4a45b7f9853c6e3e0c190c0da8c7b15fec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T17:21:57Z","title_canon_sha256":"46950b5f7f186650fa2f35403f66d76c559518a7d686f50630986dbc9c8f7916"},"schema_version":"1.0","source":{"id":"1608.08954","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08954","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08954v1","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08954","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"4VNTF73PINTU","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4VNTF73PINTUA6RV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4VNTF73P","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:7902691716fd63115a3dc3b242972dd391ffc76d07a5035a26073ee18327a34a","target":"graph","created_at":"2026-05-18T01:06:39Z","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":"Chv\\'{a}tal's conjecture in extremal combinatorics asserts that for any decreasing family $\\mathcal{F}$ of subsets of a finite set $S$, there is a largest intersecting subfamily of $\\mathcal{F}$ consisting of all members of $\\mathcal{F}$ that include a particular $x \\in S$. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants using tools from discrete Fourier analysis.","authors_text":"Ehud Friedgut, Gil Kalai, Jeff Kahn, Nathan Keller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T17:21:57Z","title":"Chv\\'{a}tal's Conjecture and Correlation Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08954","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":"sha256:9ff6c4475459e8f39a673c9acdc8b2e664c3493b8c0bd4cfcd501187fe46a67a","target":"record","created_at":"2026-05-18T01:06:39Z","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":"a121b6670c5c62ef27b0a53185edb4a45b7f9853c6e3e0c190c0da8c7b15fec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T17:21:57Z","title_canon_sha256":"46950b5f7f186650fa2f35403f66d76c559518a7d686f50630986dbc9c8f7916"},"schema_version":"1.0","source":{"id":"1608.08954","kind":"arxiv","version":1}},"canonical_sha256":"e55b32ff6f4367407a354d43c10f1ada9e2fe45912c0ca092e66bae81357c445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e55b32ff6f4367407a354d43c10f1ada9e2fe45912c0ca092e66bae81357c445","first_computed_at":"2026-05-18T01:06:39.587936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:39.587936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nI+Av6D03608E2jV6yvcR4jk3cVfPYk6IWJJyKABja8r8x0CnVnf6N4rkr6Ua8zqe7Z6rEx7NL/Tkfyzl2oYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:39.588584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ff6c4475459e8f39a673c9acdc8b2e664c3493b8c0bd4cfcd501187fe46a67a","sha256:7902691716fd63115a3dc3b242972dd391ffc76d07a5035a26073ee18327a34a"],"state_sha256":"f12bf5d36a2a87f399852c9c155b63f64cfcea81f4b150f41d237f26569dc46c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YSQ9w46DfrLdhTrDRYjrBvYYue9OD3vgzcnJefqQ7rt+vqniyfWflY3n3euJ/bwLsL7mxHiioQIn2252WXwhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:30:55.286504Z","bundle_sha256":"6e5180438933736cd8d836fa26df42793af737f09e12c548f67c98e383ffbf48"}}