{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CGYIRDQSF6FBKZNDTZ3IQDQT6E","short_pith_number":"pith:CGYIRDQS","schema_version":"1.0","canonical_sha256":"11b0888e122f8a1565a39e76880e13f101bed5b7a168562be430c2e7db411974","source":{"kind":"arxiv","id":"1102.3904","version":1},"attestation_state":"computed","paper":{"title":"Regularity lemmas for stable graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"M. Malliaris, S. Shelah","submitted_at":"2011-02-18T20:32:35Z","abstract_excerpt":"Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of Szemer\\'edi's regularity lemma for such graphs, Theorem 5.18, in which there are no irregular pairs, the bounds are significantly improved, and each component satisfies an indivisibility condition. Motivation for this work comes from a coincidence of model-theoretic and graph-theoretic ideas. Namely, it was known that the \"irregular pairs\" in the statement of Szemer\\'ed"},"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":"1102.3904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-02-18T20:32:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"80ee76fa8461c2d0c58c8a3cf9de5a79a1e426b2b3f7ae386581a3a988ef1aa0","abstract_canon_sha256":"dc16a381cd6c654c10b61b31a045166223ead81923f4d968461fcaa7567c5e97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.378660Z","signature_b64":"AhqGrLUgH33EEci+CuFh5v6W2sb4APyYzPqsYl5ULaESHnlldmwxpV52o9uan06D7rHuq9+rSFtEijGNLGc1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11b0888e122f8a1565a39e76880e13f101bed5b7a168562be430c2e7db411974","last_reissued_at":"2026-05-18T01:35:05.378040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.378040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity lemmas for stable graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"M. Malliaris, S. Shelah","submitted_at":"2011-02-18T20:32:35Z","abstract_excerpt":"Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of Szemer\\'edi's regularity lemma for such graphs, Theorem 5.18, in which there are no irregular pairs, the bounds are significantly improved, and each component satisfies an indivisibility condition. Motivation for this work comes from a coincidence of model-theoretic and graph-theoretic ideas. Namely, it was known that the \"irregular pairs\" in the statement of Szemer\\'ed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3904","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.3904","created_at":"2026-05-18T01:35:05.378129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.3904v1","created_at":"2026-05-18T01:35:05.378129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3904","created_at":"2026-05-18T01:35:05.378129+00:00"},{"alias_kind":"pith_short_12","alias_value":"CGYIRDQSF6FB","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CGYIRDQSF6FBKZND","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CGYIRDQS","created_at":"2026-05-18T12:26:26.731475+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/CGYIRDQSF6FBKZNDTZ3IQDQT6E","json":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E.json","graph_json":"https://pith.science/api/pith-number/CGYIRDQSF6FBKZNDTZ3IQDQT6E/graph.json","events_json":"https://pith.science/api/pith-number/CGYIRDQSF6FBKZNDTZ3IQDQT6E/events.json","paper":"https://pith.science/paper/CGYIRDQS"},"agent_actions":{"view_html":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E","download_json":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E.json","view_paper":"https://pith.science/paper/CGYIRDQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.3904&json=true","fetch_graph":"https://pith.science/api/pith-number/CGYIRDQSF6FBKZNDTZ3IQDQT6E/graph.json","fetch_events":"https://pith.science/api/pith-number/CGYIRDQSF6FBKZNDTZ3IQDQT6E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E/action/storage_attestation","attest_author":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E/action/author_attestation","sign_citation":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E/action/citation_signature","submit_replication":"https://pith.science/pith/CGYIRDQSF6FBKZNDTZ3IQDQT6E/action/replication_record"}},"created_at":"2026-05-18T01:35:05.378129+00:00","updated_at":"2026-05-18T01:35:05.378129+00:00"}