{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VYIOU4SCENSG7KA2GGHCJSMUYD","short_pith_number":"pith:VYIOU4SC","canonical_record":{"source":{"id":"1705.04840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-05-13T14:49:23Z","cross_cats_sorted":[],"title_canon_sha256":"1931af2ab4c9f93d6d6526a90b56f78e4e63043352ed952d890ae45112753dcb","abstract_canon_sha256":"c54bcbc541bbe536d516ec7e33278f7dec724f46ba82385276c070cba5bb9a04"},"schema_version":"1.0"},"canonical_sha256":"ae10ea724223646fa81a318e24c994c0c84c991f9a5a8d1d444c253052ecb6cb","source":{"kind":"arxiv","id":"1705.04840","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04840","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04840v2","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04840","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"VYIOU4SCENSG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VYIOU4SCENSG7KA2","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VYIOU4SC","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VYIOU4SCENSG7KA2GGHCJSMUYD","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-05-13T14:49:23Z","cross_cats_sorted":[],"title_canon_sha256":"1931af2ab4c9f93d6d6526a90b56f78e4e63043352ed952d890ae45112753dcb","abstract_canon_sha256":"c54bcbc541bbe536d516ec7e33278f7dec724f46ba82385276c070cba5bb9a04"},"schema_version":"1.0"},"canonical_sha256":"ae10ea724223646fa81a318e24c994c0c84c991f9a5a8d1d444c253052ecb6cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:22.888614Z","signature_b64":"OQORIZlXYV2GUOm5GLbDA5aQh4BnHOSmFGAxkYZEMgYQljvQHg1frBpHHhFajuRHPk6euK5xVA/PO5dAN/2YAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae10ea724223646fa81a318e24c994c0c84c991f9a5a8d1d444c253052ecb6cb","last_reissued_at":"2026-05-18T00:44:22.888018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:22.888018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04840","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2t/7iKVdzYGzTADkVEoNFwujTfjXCPckN7RaTbCUlhD8U5/Uw2A+KUEV7vV1YJ74KUAYn98mn0tT0zUgtZQxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:17:13.044387Z"},"content_sha256":"557cb980f6a02e04d40f458ae654e34f17e6276e925bc4e2b805532c5e07e66e","schema_version":"1.0","event_id":"sha256:557cb980f6a02e04d40f458ae654e34f17e6276e925bc4e2b805532c5e07e66e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VYIOU4SCENSG7KA2GGHCJSMUYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sublogarithmic Distributed Algorithms for Lov\\'asz Local lemma, and the Complexity Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Manuela Fischer, Mohsen Ghaffari","submitted_at":"2017-05-13T14:49:23Z","abstract_excerpt":"Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded degree graphs) that has an $o(\\log n)$-round randomized algorithm can be solved in $T_{LLL}(n)$ rounds, which is the randomized complexity of solving (a relaxed variant of) the Lov\\'asz Local Lemma (LLL) on bounded degree $n$-node graphs. Currently, the best known upper bound on $T_{LLL}(n)$ is $O(\\log n)$, by Chung, Pettie, and Su [PODC'14], while the best know"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04840","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jCTnrV2Y2ihFHfn035wO++EyC0XzN6pzfp0/x54Cr39u5cs7O82rpJmCxoA2v6aDg4Cplu5jSa+ghPc9nOSfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:17:13.045033Z"},"content_sha256":"4c1370a3012a94ea8cc080b4eee1626d0a9c4b26b1eb86d56216d92af4d24d20","schema_version":"1.0","event_id":"sha256:4c1370a3012a94ea8cc080b4eee1626d0a9c4b26b1eb86d56216d92af4d24d20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYIOU4SCENSG7KA2GGHCJSMUYD/bundle.json","state_url":"https://pith.science/pith/VYIOU4SCENSG7KA2GGHCJSMUYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYIOU4SCENSG7KA2GGHCJSMUYD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T21:17:13Z","links":{"resolver":"https://pith.science/pith/VYIOU4SCENSG7KA2GGHCJSMUYD","bundle":"https://pith.science/pith/VYIOU4SCENSG7KA2GGHCJSMUYD/bundle.json","state":"https://pith.science/pith/VYIOU4SCENSG7KA2GGHCJSMUYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYIOU4SCENSG7KA2GGHCJSMUYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VYIOU4SCENSG7KA2GGHCJSMUYD","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":"c54bcbc541bbe536d516ec7e33278f7dec724f46ba82385276c070cba5bb9a04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-05-13T14:49:23Z","title_canon_sha256":"1931af2ab4c9f93d6d6526a90b56f78e4e63043352ed952d890ae45112753dcb"},"schema_version":"1.0","source":{"id":"1705.04840","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04840","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04840v2","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04840","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"VYIOU4SCENSG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VYIOU4SCENSG7KA2","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VYIOU4SC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:4c1370a3012a94ea8cc080b4eee1626d0a9c4b26b1eb86d56216d92af4d24d20","target":"graph","created_at":"2026-05-18T00:44:22Z","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":"Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded degree graphs) that has an $o(\\log n)$-round randomized algorithm can be solved in $T_{LLL}(n)$ rounds, which is the randomized complexity of solving (a relaxed variant of) the Lov\\'asz Local Lemma (LLL) on bounded degree $n$-node graphs. Currently, the best known upper bound on $T_{LLL}(n)$ is $O(\\log n)$, by Chung, Pettie, and Su [PODC'14], while the best know","authors_text":"Manuela Fischer, Mohsen Ghaffari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-05-13T14:49:23Z","title":"Sublogarithmic Distributed Algorithms for Lov\\'asz Local lemma, and the Complexity Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04840","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":"sha256:557cb980f6a02e04d40f458ae654e34f17e6276e925bc4e2b805532c5e07e66e","target":"record","created_at":"2026-05-18T00:44:22Z","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":"c54bcbc541bbe536d516ec7e33278f7dec724f46ba82385276c070cba5bb9a04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-05-13T14:49:23Z","title_canon_sha256":"1931af2ab4c9f93d6d6526a90b56f78e4e63043352ed952d890ae45112753dcb"},"schema_version":"1.0","source":{"id":"1705.04840","kind":"arxiv","version":2}},"canonical_sha256":"ae10ea724223646fa81a318e24c994c0c84c991f9a5a8d1d444c253052ecb6cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae10ea724223646fa81a318e24c994c0c84c991f9a5a8d1d444c253052ecb6cb","first_computed_at":"2026-05-18T00:44:22.888018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:22.888018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OQORIZlXYV2GUOm5GLbDA5aQh4BnHOSmFGAxkYZEMgYQljvQHg1frBpHHhFajuRHPk6euK5xVA/PO5dAN/2YAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:22.888614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04840","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:557cb980f6a02e04d40f458ae654e34f17e6276e925bc4e2b805532c5e07e66e","sha256:4c1370a3012a94ea8cc080b4eee1626d0a9c4b26b1eb86d56216d92af4d24d20"],"state_sha256":"a6a7e0e39bb90192beb815519bcc2725b606fd257d05a68691f623178d726321"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDlnIk7pCp6wSsHx7W41QABjTJcXSBeWxijZgsr1olUOkPw4M1kyA3fKx4kR6c/2X3r4a1RUkmdWoVkZMxaBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:17:13.047858Z","bundle_sha256":"278dea045a6095e0b9b97db4802b10dd0d1049140cfb132d8a2499df93924938"}}