{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3ZMSLWYRMDIEH7VVCQDOSAJDA3","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":"c3f6999c9457efee162e1f50ce87ca08f2763b48778368e243b42ddb2a60ff1e","cross_cats_sorted":["math.LO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-16T08:56:12Z","title_canon_sha256":"eeabadc274d7d6718d04a89ef2c44271dd07047e7508d0a2d8f75fb886963659"},"schema_version":"1.0","source":{"id":"2412.11571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11571","created_at":"2026-05-29T01:04:51Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11571v2","created_at":"2026-05-29T01:04:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11571","created_at":"2026-05-29T01:04:51Z"},{"alias_kind":"pith_short_12","alias_value":"3ZMSLWYRMDIE","created_at":"2026-05-29T01:04:51Z"},{"alias_kind":"pith_short_16","alias_value":"3ZMSLWYRMDIEH7VV","created_at":"2026-05-29T01:04:51Z"},{"alias_kind":"pith_short_8","alias_value":"3ZMSLWYR","created_at":"2026-05-29T01:04:51Z"}],"graph_snapshots":[{"event_id":"sha256:dd93c416641ef40d2b0d1e8c27067e1045c915064ad2644bdc9cadee2191de9f","target":"graph","created_at":"2026-05-29T01:04:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.11571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Lov\\'asz Local Lemma (the LLL for short) is a powerful tool in probabilistic combinatorics that is used to verify the existence of combinatorial objects with desirable properties. Recent years saw the development of various \"constructive\" versions of the LLL. A major success of this research direction is the Borel version of the LLL due to Cs\\'oka, Grabowski, M\\'ath\\'e, Pikhurko, and Tyros, which holds under a subexponential growth assumption. A drawback of their approach is that it only applies when the underlying random variables take values in a finite set. We present an alternative pro","authors_text":"Anton Bernshteyn, Jing Yu","cross_cats":["math.LO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-16T08:56:12Z","title":"Borel Local Lemma: arbitrary random variables and limited exponential growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11571","kind":"arxiv","version":2},"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":"sha256:17961a8fa8913cf9eac671bfcb6403225f6e766542fc888e1cde7b0935089f68","target":"record","created_at":"2026-05-29T01:04:51Z","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":"c3f6999c9457efee162e1f50ce87ca08f2763b48778368e243b42ddb2a60ff1e","cross_cats_sorted":["math.LO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-16T08:56:12Z","title_canon_sha256":"eeabadc274d7d6718d04a89ef2c44271dd07047e7508d0a2d8f75fb886963659"},"schema_version":"1.0","source":{"id":"2412.11571","kind":"arxiv","version":2}},"canonical_sha256":"de5925db1160d043feb51406e9012306dc36c9aad5880a5abe7069b5901bc420","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de5925db1160d043feb51406e9012306dc36c9aad5880a5abe7069b5901bc420","first_computed_at":"2026-05-29T01:04:51.779998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:04:51.779998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kC1rS/xnWIqJ1UOoIs2/0nVgJWW1SIoskvNPGIYEc9tef8vbsXt4py/idXp0PlghCTiShm1vPQExqc/niLQWDw==","signature_status":"signed_v1","signed_at":"2026-05-29T01:04:51.780507Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17961a8fa8913cf9eac671bfcb6403225f6e766542fc888e1cde7b0935089f68","sha256:dd93c416641ef40d2b0d1e8c27067e1045c915064ad2644bdc9cadee2191de9f"],"state_sha256":"9b5e968570fc48694b9bc71dbc53ba94ccc86952095e42d60c38d540fbf94e31"}