{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:WHPQRK2JFPTC7NG7C3YTUKEW4Y","short_pith_number":"pith:WHPQRK2J","canonical_record":{"source":{"id":"2212.05619","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-12-11T22:23:10Z","cross_cats_sorted":[],"title_canon_sha256":"ed1b1bfc857d8a60830cc6180e7c9d36cea5e7d91832b7615af28d607fea7a5b","abstract_canon_sha256":"769e13a928b699930fb7aa5f49862a6ec448db535e0614b6f4c78cba635b9844"},"schema_version":"1.0"},"canonical_sha256":"b1df08ab492be62fb4df16f13a2896e6085f4f40fcd3d5986bdb92630bbc7493","source":{"kind":"arxiv","id":"2212.05619","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.05619","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"2212.05619v2","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.05619","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"WHPQRK2JFPTC","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"pith_short_16","alias_value":"WHPQRK2JFPTC7NG7","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"pith_short_8","alias_value":"WHPQRK2J","created_at":"2026-07-05T06:17:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:WHPQRK2JFPTC7NG7C3YTUKEW4Y","target":"record","payload":{"canonical_record":{"source":{"id":"2212.05619","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-12-11T22:23:10Z","cross_cats_sorted":[],"title_canon_sha256":"ed1b1bfc857d8a60830cc6180e7c9d36cea5e7d91832b7615af28d607fea7a5b","abstract_canon_sha256":"769e13a928b699930fb7aa5f49862a6ec448db535e0614b6f4c78cba635b9844"},"schema_version":"1.0"},"canonical_sha256":"b1df08ab492be62fb4df16f13a2896e6085f4f40fcd3d5986bdb92630bbc7493","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:17:43.404776Z","signature_b64":"3LoFfO4JkfhYVfBA5DVfpkhM5PwLmgwiFpPZpagHZ/naghL8zIbPT6ectkputuPuov26F42X2x5EdCdRRESVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1df08ab492be62fb4df16f13a2896e6085f4f40fcd3d5986bdb92630bbc7493","last_reissued_at":"2026-07-05T06:17:43.404330Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:17:43.404330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.05619","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":"2026-07-05T06:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTOOLvksv5sLUADJuH6N8/VADTJVnP/MN8P0rOUkSxQn7MO/5zgMs3E58M3Nria1+XUCmfiQygmi0gTqjOhpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:04:47.697833Z"},"content_sha256":"b9e36ef947e932a7f223f39caf370099337ea36f3b2dd90397a310e99b3c026c","schema_version":"1.0","event_id":"sha256:b9e36ef947e932a7f223f39caf370099337ea36f3b2dd90397a310e99b3c026c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:WHPQRK2JFPTC7NG7C3YTUKEW4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms approaching the threshold for semi-random planted clique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Steurer, Pravesh K. Kothari, Rares-Darius Buhai","submitted_at":"2022-12-11T22:23:10Z","abstract_excerpt":"We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian 2001. The previous best algorithms for this model succeed if the planted clique has size at least $n^{2/3}$ in a graph with $n$ vertices (Mehta, Mckenzie, Trevisan 2019 and Charikar, Steinhardt, Valiant 2017). Our algorithms work for planted-clique sizes approaching $n^{1/2}$ -- the information-theoretic threshold in the semi-random model (Steinhardt 2017) and a conjectured computational threshold even in the easier fully-random model. This result comes close to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.05619","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/2212.05619/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":"2026-07-05T06:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZF1WCJYHQ+F5EYH6XTpZNr70a+izna6X/dNzNEST6jngeL7aenneiJ/NMttoJk05TmtqdHQ8N3y6rkgq6rTtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:04:47.698330Z"},"content_sha256":"23142cb338bec8d96eff902886502c3c5d2b0f75dafb78a9b52140114d85c2db","schema_version":"1.0","event_id":"sha256:23142cb338bec8d96eff902886502c3c5d2b0f75dafb78a9b52140114d85c2db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y/bundle.json","state_url":"https://pith.science/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y/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":"2026-08-19T11:04:47Z","links":{"resolver":"https://pith.science/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y","bundle":"https://pith.science/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y/bundle.json","state":"https://pith.science/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHPQRK2JFPTC7NG7C3YTUKEW4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:WHPQRK2JFPTC7NG7C3YTUKEW4Y","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":"769e13a928b699930fb7aa5f49862a6ec448db535e0614b6f4c78cba635b9844","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-12-11T22:23:10Z","title_canon_sha256":"ed1b1bfc857d8a60830cc6180e7c9d36cea5e7d91832b7615af28d607fea7a5b"},"schema_version":"1.0","source":{"id":"2212.05619","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.05619","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"2212.05619v2","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.05619","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"WHPQRK2JFPTC","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"pith_short_16","alias_value":"WHPQRK2JFPTC7NG7","created_at":"2026-07-05T06:17:43Z"},{"alias_kind":"pith_short_8","alias_value":"WHPQRK2J","created_at":"2026-07-05T06:17:43Z"}],"graph_snapshots":[{"event_id":"sha256:23142cb338bec8d96eff902886502c3c5d2b0f75dafb78a9b52140114d85c2db","target":"graph","created_at":"2026-07-05T06:17:43Z","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/2212.05619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian 2001. The previous best algorithms for this model succeed if the planted clique has size at least $n^{2/3}$ in a graph with $n$ vertices (Mehta, Mckenzie, Trevisan 2019 and Charikar, Steinhardt, Valiant 2017). Our algorithms work for planted-clique sizes approaching $n^{1/2}$ -- the information-theoretic threshold in the semi-random model (Steinhardt 2017) and a conjectured computational threshold even in the easier fully-random model. This result comes close to","authors_text":"David Steurer, Pravesh K. Kothari, Rares-Darius Buhai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-12-11T22:23:10Z","title":"Algorithms approaching the threshold for semi-random planted clique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.05619","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:b9e36ef947e932a7f223f39caf370099337ea36f3b2dd90397a310e99b3c026c","target":"record","created_at":"2026-07-05T06:17:43Z","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":"769e13a928b699930fb7aa5f49862a6ec448db535e0614b6f4c78cba635b9844","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-12-11T22:23:10Z","title_canon_sha256":"ed1b1bfc857d8a60830cc6180e7c9d36cea5e7d91832b7615af28d607fea7a5b"},"schema_version":"1.0","source":{"id":"2212.05619","kind":"arxiv","version":2}},"canonical_sha256":"b1df08ab492be62fb4df16f13a2896e6085f4f40fcd3d5986bdb92630bbc7493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1df08ab492be62fb4df16f13a2896e6085f4f40fcd3d5986bdb92630bbc7493","first_computed_at":"2026-07-05T06:17:43.404330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:17:43.404330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3LoFfO4JkfhYVfBA5DVfpkhM5PwLmgwiFpPZpagHZ/naghL8zIbPT6ectkputuPuov26F42X2x5EdCdRRESVBw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:17:43.404776Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.05619","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9e36ef947e932a7f223f39caf370099337ea36f3b2dd90397a310e99b3c026c","sha256:23142cb338bec8d96eff902886502c3c5d2b0f75dafb78a9b52140114d85c2db"],"state_sha256":"45635fc1239b98b58c9d652313857f0b528d29ad6420b046b77c916513e2a5f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wz5bxIvzGsAY+A3GU5qc/xdzf7pgchA5JU0yd+ybYGbpg2J0OD0V0t8KcOMZi2fBcvNa1aOHLgqyYOO3XeH1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T11:04:47.702632Z","bundle_sha256":"3bd510fdfb4e126857e28b5c828911b3907f55f49d4650700973e66dd7dceb0b"}}