{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6GENF4F476DEIKZY7AA6RYIFPE","short_pith_number":"pith:6GENF4F4","schema_version":"1.0","canonical_sha256":"f188d2f0bcff86442b38f801e8e1057900a1ca0abc4e0a26e2c4ef96ef2cb84e","source":{"kind":"arxiv","id":"1410.5966","version":3},"attestation_state":"computed","paper":{"title":"Szemer\\'edi's regularity lemma via martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.CO","authors_text":"Pandelis Dodos, Thodoris Karageorgos, Vassilis Kanellopoulos","submitted_at":"2014-10-22T09:34:42Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.5966","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-22T09:34:42Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"c86150190bc868a77e0bad06fedd4f5c3f0c98601c909ee8c1529f4941a945cf","abstract_canon_sha256":"0e8b83a7680028cb57808ec92dd72b62ca5b692b69af04e933d506bbecb8d00e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:38.791171Z","signature_b64":"SW0mu1RwljufGzLuFLDf4Y+Q50YrpCnUyNRppXoiKxLH1uG8HB8TqQvizlys0CRAblDlXc5Fr+3kvV8ArzNTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f188d2f0bcff86442b38f801e8e1057900a1ca0abc4e0a26e2c4ef96ef2cb84e","last_reissued_at":"2026-05-18T01:10:38.790509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:38.790509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Szemer\\'edi's regularity lemma via martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.CO","authors_text":"Pandelis Dodos, Thodoris Karageorgos, Vassilis Kanellopoulos","submitted_at":"2014-10-22T09:34:42Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5966","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.5966","created_at":"2026-05-18T01:10:38.790611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.5966v3","created_at":"2026-05-18T01:10:38.790611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5966","created_at":"2026-05-18T01:10:38.790611+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GENF4F476DE","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GENF4F476DEIKZY","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GENF4F4","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE","json":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE.json","graph_json":"https://pith.science/api/pith-number/6GENF4F476DEIKZY7AA6RYIFPE/graph.json","events_json":"https://pith.science/api/pith-number/6GENF4F476DEIKZY7AA6RYIFPE/events.json","paper":"https://pith.science/paper/6GENF4F4"},"agent_actions":{"view_html":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE","download_json":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE.json","view_paper":"https://pith.science/paper/6GENF4F4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.5966&json=true","fetch_graph":"https://pith.science/api/pith-number/6GENF4F476DEIKZY7AA6RYIFPE/graph.json","fetch_events":"https://pith.science/api/pith-number/6GENF4F476DEIKZY7AA6RYIFPE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE/action/storage_attestation","attest_author":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE/action/author_attestation","sign_citation":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE/action/citation_signature","submit_replication":"https://pith.science/pith/6GENF4F476DEIKZY7AA6RYIFPE/action/replication_record"}},"created_at":"2026-05-18T01:10:38.790611+00:00","updated_at":"2026-05-18T01:10:38.790611+00:00"}