{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AH7TSUV2P3B2HM7QOB5ASFIG3W","short_pith_number":"pith:AH7TSUV2","canonical_record":{"source":{"id":"2009.09645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-21T07:07:55Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"c981ae19709049eeb579fe5581d6c07250012642cac9dd9b2c8792c910ad41cd","abstract_canon_sha256":"04c17fe1c4d6961a6beec80f7d368aa5bcbfcc231f1c95fedbcab3185eb05358"},"schema_version":"1.0"},"canonical_sha256":"01ff3952ba7ec3a3b3f0707a091506dd85697f29e45b1bb2b12f2f6a44f9381a","source":{"kind":"arxiv","id":"2009.09645","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.09645","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"arxiv_version","alias_value":"2009.09645v2","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.09645","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"pith_short_12","alias_value":"AH7TSUV2P3B2","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"pith_short_16","alias_value":"AH7TSUV2P3B2HM7Q","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"pith_short_8","alias_value":"AH7TSUV2","created_at":"2026-06-23T02:12:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AH7TSUV2P3B2HM7QOB5ASFIG3W","target":"record","payload":{"canonical_record":{"source":{"id":"2009.09645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-21T07:07:55Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"c981ae19709049eeb579fe5581d6c07250012642cac9dd9b2c8792c910ad41cd","abstract_canon_sha256":"04c17fe1c4d6961a6beec80f7d368aa5bcbfcc231f1c95fedbcab3185eb05358"},"schema_version":"1.0"},"canonical_sha256":"01ff3952ba7ec3a3b3f0707a091506dd85697f29e45b1bb2b12f2f6a44f9381a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:12:29.398839Z","signature_b64":"j6lnyrkoQb2DXfLRdguTxtofQQxyZ2jqHryOk70LYsqPujF+rume0NEl7kCe//aHB7caC9RsfCnbwCbgd/xlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01ff3952ba7ec3a3b3f0707a091506dd85697f29e45b1bb2b12f2f6a44f9381a","last_reissued_at":"2026-06-23T02:12:29.397394Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:12:29.397394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.09645","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":"2026-06-23T02:12:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iFYTX2Xa6CZd+c0ayPNLKXZ8eo07z+sCZRmcVyKD5OYogoHFFA6dPOPlwjvmFpSES1RkF2BMF0ZT0mujwIUtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:23:39.684370Z"},"content_sha256":"c84bbbef3510e1639b4daf6711d858f434af7b5f03d22bb2763bd2c1119bab68","schema_version":"1.0","event_id":"sha256:c84bbbef3510e1639b4daf6711d858f434af7b5f03d22bb2763bd2c1119bab68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AH7TSUV2P3B2HM7QOB5ASFIG3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complexity Landscape of Distributed Locally Checkable Problems on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Yi-Jun Chang","submitted_at":"2020-09-21T07:07:55Z","abstract_excerpt":"Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on bounded-degree graphs is either $O(\\log^\\ast n)$ or $\\Omega(\\log n)$ [Chang, Kopelowitz, and Pettie, FOCS 2016]. The complexity landscape of LCL problems is now quite well-understood, but a few questions remain open.\n  For bounded-degree trees, there is an LCL problem with round complexity $\\Theta(n^{1/k})$ for each positive integer $k$ [Chang and Pettie, FOCS 20"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.09645","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.09645/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T02:12:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MZsDHF6Hou3/zjllnceDyFgp2hekzJdZuoX3sHYXo9frs2TfxqUjL0zk5g00p72FQ1Z3ARu7e1zmI/QYvkKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:23:39.684876Z"},"content_sha256":"b071b5083240b8d31becded07aeb441c89062693f0d68e83cc402b56d9d25689","schema_version":"1.0","event_id":"sha256:b071b5083240b8d31becded07aeb441c89062693f0d68e83cc402b56d9d25689"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W/bundle.json","state_url":"https://pith.science/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W/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":"2026-08-12T13:23:39Z","links":{"resolver":"https://pith.science/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W","bundle":"https://pith.science/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W/bundle.json","state":"https://pith.science/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AH7TSUV2P3B2HM7QOB5ASFIG3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AH7TSUV2P3B2HM7QOB5ASFIG3W","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":"04c17fe1c4d6961a6beec80f7d368aa5bcbfcc231f1c95fedbcab3185eb05358","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-21T07:07:55Z","title_canon_sha256":"c981ae19709049eeb579fe5581d6c07250012642cac9dd9b2c8792c910ad41cd"},"schema_version":"1.0","source":{"id":"2009.09645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.09645","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"arxiv_version","alias_value":"2009.09645v2","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.09645","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"pith_short_12","alias_value":"AH7TSUV2P3B2","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"pith_short_16","alias_value":"AH7TSUV2P3B2HM7Q","created_at":"2026-06-23T02:12:29Z"},{"alias_kind":"pith_short_8","alias_value":"AH7TSUV2","created_at":"2026-06-23T02:12:29Z"}],"graph_snapshots":[{"event_id":"sha256:b071b5083240b8d31becded07aeb441c89062693f0d68e83cc402b56d9d25689","target":"graph","created_at":"2026-06-23T02:12:29Z","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/2009.09645/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on bounded-degree graphs is either $O(\\log^\\ast n)$ or $\\Omega(\\log n)$ [Chang, Kopelowitz, and Pettie, FOCS 2016]. The complexity landscape of LCL problems is now quite well-understood, but a few questions remain open.\n  For bounded-degree trees, there is an LCL problem with round complexity $\\Theta(n^{1/k})$ for each positive integer $k$ [Chang and Pettie, FOCS 20","authors_text":"Yi-Jun Chang","cross_cats":["cs.DC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-21T07:07:55Z","title":"The Complexity Landscape of Distributed Locally Checkable Problems on Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.09645","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:c84bbbef3510e1639b4daf6711d858f434af7b5f03d22bb2763bd2c1119bab68","target":"record","created_at":"2026-06-23T02:12:29Z","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":"04c17fe1c4d6961a6beec80f7d368aa5bcbfcc231f1c95fedbcab3185eb05358","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-09-21T07:07:55Z","title_canon_sha256":"c981ae19709049eeb579fe5581d6c07250012642cac9dd9b2c8792c910ad41cd"},"schema_version":"1.0","source":{"id":"2009.09645","kind":"arxiv","version":2}},"canonical_sha256":"01ff3952ba7ec3a3b3f0707a091506dd85697f29e45b1bb2b12f2f6a44f9381a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01ff3952ba7ec3a3b3f0707a091506dd85697f29e45b1bb2b12f2f6a44f9381a","first_computed_at":"2026-06-23T02:12:29.397394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:12:29.397394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j6lnyrkoQb2DXfLRdguTxtofQQxyZ2jqHryOk70LYsqPujF+rume0NEl7kCe//aHB7caC9RsfCnbwCbgd/xlCQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:12:29.398839Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.09645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c84bbbef3510e1639b4daf6711d858f434af7b5f03d22bb2763bd2c1119bab68","sha256:b071b5083240b8d31becded07aeb441c89062693f0d68e83cc402b56d9d25689"],"state_sha256":"ef9aa2fa8a4d342e8adb38f7c5036b0d62f51a3314829e195a7e3d65e95f8e8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p3dU2/LCxoHH27lVmfif/4ABQljjCjSVXZ77usy2MHRajaLyf89eC0KmzN0dKNBuiPG6kxqex44CVS+GjojMDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T13:23:39.689109Z","bundle_sha256":"cf50f03545cce2e653a980c7f2c855ae2b5e56e32da88efb598aa796c04251b9"}}