{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6GENF4F476DEIKZY7AA6RYIFPE","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":"0e8b83a7680028cb57808ec92dd72b62ca5b692b69af04e933d506bbecb8d00e","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-22T09:34:42Z","title_canon_sha256":"c86150190bc868a77e0bad06fedd4f5c3f0c98601c909ee8c1529f4941a945cf"},"schema_version":"1.0","source":{"id":"1410.5966","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5966","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5966v3","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5966","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"pith_short_12","alias_value":"6GENF4F476DE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6GENF4F476DEIKZY","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6GENF4F4","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:25c1b3d75dc39d5f8330f59ce47edf2a02a0f67a0fb0979d3b996c443f56bf96","target":"graph","created_at":"2026-05-18T01:10:38Z","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 prove a variant of the abstract probabilistic version of Szemer\\'edi's regularity lemma, due to Tao, which applies to a number of structures (including graphs, hypergraphs, hypercubes, graphons, and many more) and works for random variables in $L_p$ for any $p>1$. Our approach is based on martingale difference sequences.","authors_text":"Pandelis Dodos, Thodoris Karageorgos, Vassilis Kanellopoulos","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-22T09:34:42Z","title":"Szemer\\'edi's regularity lemma via martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5966","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":"sha256:989caef430371f7c856f72bea90e03ab9533bc85cd91cee857676f7541570e69","target":"record","created_at":"2026-05-18T01:10:38Z","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":"0e8b83a7680028cb57808ec92dd72b62ca5b692b69af04e933d506bbecb8d00e","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-22T09:34:42Z","title_canon_sha256":"c86150190bc868a77e0bad06fedd4f5c3f0c98601c909ee8c1529f4941a945cf"},"schema_version":"1.0","source":{"id":"1410.5966","kind":"arxiv","version":3}},"canonical_sha256":"f188d2f0bcff86442b38f801e8e1057900a1ca0abc4e0a26e2c4ef96ef2cb84e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f188d2f0bcff86442b38f801e8e1057900a1ca0abc4e0a26e2c4ef96ef2cb84e","first_computed_at":"2026-05-18T01:10:38.790509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:38.790509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SW0mu1RwljufGzLuFLDf4Y+Q50YrpCnUyNRppXoiKxLH1uG8HB8TqQvizlys0CRAblDlXc5Fr+3kvV8ArzNTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:38.791171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5966","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:989caef430371f7c856f72bea90e03ab9533bc85cd91cee857676f7541570e69","sha256:25c1b3d75dc39d5f8330f59ce47edf2a02a0f67a0fb0979d3b996c443f56bf96"],"state_sha256":"df09e1052b8bede0ba8a5526e6d3edc0d94ab960fd37b09dacf00e8c5eb5d898"}