{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OSU7UETAV3GKNRLKNA6WBSWXJA","short_pith_number":"pith:OSU7UETA","schema_version":"1.0","canonical_sha256":"74a9fa1260aecca6c56a683d60cad7481bf6802e6d44f16d83049356c0226e5c","source":{"kind":"arxiv","id":"1909.08065","version":6},"attestation_state":"computed","paper":{"title":"Deterministic algorithms for the Lovasz Local Lemma: simpler, more general, and more parallel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David G. Harris","submitted_at":"2019-09-17T20:02:39Z","abstract_excerpt":"The Lov\\'{a}sz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\\mathcal B$ of \"bad\" events which are mostly independent and have low probability. In its simplest \"symmetric\" form, it asserts that whenever a bad-event has probability $p$ and affects at most $d$ bad-events, and $e p d < 1$, then a configuration avoiding all $\\mathcal B$ exists.\n  A seminal algorithm of Moser & Tardos (2010) gives nearly-automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms "},"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":"1909.08065","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-09-17T20:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"a1ba8603472ea2112c2319351cf29ac66b358dfe1c472130a344519242021f3c","abstract_canon_sha256":"c0d9bb9a0b990490c85d6201157d19712b273d2667534bbaa0884119d091d938"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:59:49.391560Z","signature_b64":"rzCM3ZWB3uA6H6BkkzRbj1TjMRPjfVWjfZ06tEP5MKMR2bAlgpDCWl28XUOsbJKTvLN0RSYd7lCsEocXUEsyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74a9fa1260aecca6c56a683d60cad7481bf6802e6d44f16d83049356c0226e5c","last_reissued_at":"2026-07-05T06:59:49.391070Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:59:49.391070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deterministic algorithms for the Lovasz Local Lemma: simpler, more general, and more parallel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David G. Harris","submitted_at":"2019-09-17T20:02:39Z","abstract_excerpt":"The Lov\\'{a}sz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\\mathcal B$ of \"bad\" events which are mostly independent and have low probability. In its simplest \"symmetric\" form, it asserts that whenever a bad-event has probability $p$ and affects at most $d$ bad-events, and $e p d < 1$, then a configuration avoiding all $\\mathcal B$ exists.\n  A seminal algorithm of Moser & Tardos (2010) gives nearly-automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.08065","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.08065/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.08065","created_at":"2026-07-05T06:59:49.391127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.08065v6","created_at":"2026-07-05T06:59:49.391127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.08065","created_at":"2026-07-05T06:59:49.391127+00:00"},{"alias_kind":"pith_short_12","alias_value":"OSU7UETAV3GK","created_at":"2026-07-05T06:59:49.391127+00:00"},{"alias_kind":"pith_short_16","alias_value":"OSU7UETAV3GKNRLK","created_at":"2026-07-05T06:59:49.391127+00:00"},{"alias_kind":"pith_short_8","alias_value":"OSU7UETA","created_at":"2026-07-05T06:59:49.391127+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.08296","citing_title":"Truly Work-efficient Parallel Deterministic $(\\Delta+1)$-coloring and Maximal Independent Set","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA","json":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA.json","graph_json":"https://pith.science/api/pith-number/OSU7UETAV3GKNRLKNA6WBSWXJA/graph.json","events_json":"https://pith.science/api/pith-number/OSU7UETAV3GKNRLKNA6WBSWXJA/events.json","paper":"https://pith.science/paper/OSU7UETA"},"agent_actions":{"view_html":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA","download_json":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA.json","view_paper":"https://pith.science/paper/OSU7UETA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.08065&json=true","fetch_graph":"https://pith.science/api/pith-number/OSU7UETAV3GKNRLKNA6WBSWXJA/graph.json","fetch_events":"https://pith.science/api/pith-number/OSU7UETAV3GKNRLKNA6WBSWXJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA/action/storage_attestation","attest_author":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA/action/author_attestation","sign_citation":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA/action/citation_signature","submit_replication":"https://pith.science/pith/OSU7UETAV3GKNRLKNA6WBSWXJA/action/replication_record"}},"created_at":"2026-07-05T06:59:49.391127+00:00","updated_at":"2026-07-05T06:59:49.391127+00:00"}