{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VYI4BILLTGSYCFRFHQ6GSIM6A6","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":"6afda7148062565e93891d25fcb4d1fe3772a57dc7e0cc7fd5308e9d17e6373f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-26T00:14:39Z","title_canon_sha256":"2d59728bf50bcef60ec78a47516f4a2cda7225dd0d2c1d073ce21ca4951946af"},"schema_version":"1.0","source":{"id":"1406.6738","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6738","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6738v3","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6738","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"VYI4BILLTGSY","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VYI4BILLTGSYCFRF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VYI4BILL","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:ae79a92d9e11e416ba26dab4833907f8f4de7bd7715d9db5ae4873e9e83c9ee8","target":"graph","created_at":"2026-05-18T02:28:41Z","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":"We investigate the famous conjecture by Erd\\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type conditions allow us to extend Sidorenko's conjecture to large families of $k$-uniform hypergraphs. This is somewhat unexpected since the conjecture fails for $k$ uniform hypergraphs in general.","authors_text":"Balazs Szegedy","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-26T00:14:39Z","title":"An information theoretic approach to Sidorenko's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6738","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:be5e06476fdd7850bf6aa7bcd15a27a44d1134ef63f4eebdd5e5445d2db1129a","target":"record","created_at":"2026-05-18T02:28:41Z","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":"6afda7148062565e93891d25fcb4d1fe3772a57dc7e0cc7fd5308e9d17e6373f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-26T00:14:39Z","title_canon_sha256":"2d59728bf50bcef60ec78a47516f4a2cda7225dd0d2c1d073ce21ca4951946af"},"schema_version":"1.0","source":{"id":"1406.6738","kind":"arxiv","version":3}},"canonical_sha256":"ae11c0a16b99a58116253c3c69219e079a56335f5cd2308ab52816462db49b9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae11c0a16b99a58116253c3c69219e079a56335f5cd2308ab52816462db49b9f","first_computed_at":"2026-05-18T02:28:41.217871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:41.217871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJkjbbgsjN/bVSMlLIBXrODvVPS25BgF2xaXRMLGj1hF4OyI2TiiGkCudsvvxBrovYOcDQ1FvCJg5pHf8bQYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:41.218376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6738","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5e06476fdd7850bf6aa7bcd15a27a44d1134ef63f4eebdd5e5445d2db1129a","sha256:ae79a92d9e11e416ba26dab4833907f8f4de7bd7715d9db5ae4873e9e83c9ee8"],"state_sha256":"4e99c347bdd4df6f47d7c2fc7fdd627dbdc060434d9a264d7824452cb5abbc22"}