{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VANJCF5J4DAMOTRBEAQPWQQIW7","short_pith_number":"pith:VANJCF5J","canonical_record":{"source":{"id":"1905.00850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-02T16:53:55Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"ff6c57dd3be617816fb02beb5b64ecd334788cc288a32d9cc3fabfc74b04d2f3","abstract_canon_sha256":"8447469cadcba0638c7f3003eac5e43aa76ba6e8826ec7b79da8d7171b627f94"},"schema_version":"1.0"},"canonical_sha256":"a81a9117a9e0c0c74e212020fb4208b7e3bd854004d8805ff2e864a91fa99e3e","source":{"kind":"arxiv","id":"1905.00850","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00850","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00850v1","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00850","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"VANJCF5J4DAM","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VANJCF5J4DAMOTRB","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VANJCF5J","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VANJCF5J4DAMOTRBEAQPWQQIW7","target":"record","payload":{"canonical_record":{"source":{"id":"1905.00850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-02T16:53:55Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"ff6c57dd3be617816fb02beb5b64ecd334788cc288a32d9cc3fabfc74b04d2f3","abstract_canon_sha256":"8447469cadcba0638c7f3003eac5e43aa76ba6e8826ec7b79da8d7171b627f94"},"schema_version":"1.0"},"canonical_sha256":"a81a9117a9e0c0c74e212020fb4208b7e3bd854004d8805ff2e864a91fa99e3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:09.100730Z","signature_b64":"MfmLku2THo8vCaCcpPdIETSd6b4KiT0HqDR5EgfFgA0CdX7LkC4mueJ9LmlHApHeEfdYl5HebXBkJWxUqpzeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a81a9117a9e0c0c74e212020fb4208b7e3bd854004d8805ff2e864a91fa99e3e","last_reissued_at":"2026-05-17T23:47:09.100112Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:09.100112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.00850","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRXmPKUUi/FYfE3tNYMwq6vApnc30HEBi/qfRFQo0oodtAFfnAkKTsh5fAwKs1IxtGcT0a2eNhIRHuPYcYgoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:14.848103Z"},"content_sha256":"bf282f0469803ee2310c43041c6424f03f147a4c7da7bffde97680eedb9381d5","schema_version":"1.0","event_id":"sha256:bf282f0469803ee2310c43041c6424f03f147a4c7da7bffde97680eedb9381d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VANJCF5J4DAMOTRBEAQPWQQIW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Log Diameter Rounds Algorithms for $2$-Vertex and $2$-Edge Connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Alexandr Andoni, Clifford Stein, Peilin Zhong","submitted_at":"2019-05-02T16:53:55Z","abstract_excerpt":"Many modern parallel systems, such as MapReduce, Hadoop and Spark, can be modeled well by the MPC model. The MPC model captures well coarse-grained computation on large data --- data is distributed to processors, each of which has a sublinear (in the input data) amount of memory and we alternate between rounds of computation and rounds of communication, where each machine can communicate an amount of data as large as the size of its memory. This model is stronger than the classical PRAM model, and it is an intriguing question to design algorithms whose running time is smaller than in the PRAM "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00850","kind":"arxiv","version":1},"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":"2026-05-17T23:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ifKmnPm24jBgqB/ZfqHgIIsaXTlyQn90f+vh4L6TqyDotjg5iwU6c2kohyuOyyRO1XnmfwRpdh493rMVdDNQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:14.848833Z"},"content_sha256":"64a966f3fbb23893962ba5995b6b293b66287920681b7c3bcaef7f3c5589dc96","schema_version":"1.0","event_id":"sha256:64a966f3fbb23893962ba5995b6b293b66287920681b7c3bcaef7f3c5589dc96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VANJCF5J4DAMOTRBEAQPWQQIW7/bundle.json","state_url":"https://pith.science/pith/VANJCF5J4DAMOTRBEAQPWQQIW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VANJCF5J4DAMOTRBEAQPWQQIW7/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":"2026-06-06T06:46:14Z","links":{"resolver":"https://pith.science/pith/VANJCF5J4DAMOTRBEAQPWQQIW7","bundle":"https://pith.science/pith/VANJCF5J4DAMOTRBEAQPWQQIW7/bundle.json","state":"https://pith.science/pith/VANJCF5J4DAMOTRBEAQPWQQIW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VANJCF5J4DAMOTRBEAQPWQQIW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VANJCF5J4DAMOTRBEAQPWQQIW7","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":"8447469cadcba0638c7f3003eac5e43aa76ba6e8826ec7b79da8d7171b627f94","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-02T16:53:55Z","title_canon_sha256":"ff6c57dd3be617816fb02beb5b64ecd334788cc288a32d9cc3fabfc74b04d2f3"},"schema_version":"1.0","source":{"id":"1905.00850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00850","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00850v1","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00850","created_at":"2026-05-17T23:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"VANJCF5J4DAM","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VANJCF5J4DAMOTRB","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VANJCF5J","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:64a966f3fbb23893962ba5995b6b293b66287920681b7c3bcaef7f3c5589dc96","target":"graph","created_at":"2026-05-17T23:47:09Z","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":"Many modern parallel systems, such as MapReduce, Hadoop and Spark, can be modeled well by the MPC model. The MPC model captures well coarse-grained computation on large data --- data is distributed to processors, each of which has a sublinear (in the input data) amount of memory and we alternate between rounds of computation and rounds of communication, where each machine can communicate an amount of data as large as the size of its memory. This model is stronger than the classical PRAM model, and it is an intriguing question to design algorithms whose running time is smaller than in the PRAM ","authors_text":"Alexandr Andoni, Clifford Stein, Peilin Zhong","cross_cats":["cs.DC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-02T16:53:55Z","title":"Log Diameter Rounds Algorithms for $2$-Vertex and $2$-Edge Connectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00850","kind":"arxiv","version":1},"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:bf282f0469803ee2310c43041c6424f03f147a4c7da7bffde97680eedb9381d5","target":"record","created_at":"2026-05-17T23:47:09Z","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":"8447469cadcba0638c7f3003eac5e43aa76ba6e8826ec7b79da8d7171b627f94","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-02T16:53:55Z","title_canon_sha256":"ff6c57dd3be617816fb02beb5b64ecd334788cc288a32d9cc3fabfc74b04d2f3"},"schema_version":"1.0","source":{"id":"1905.00850","kind":"arxiv","version":1}},"canonical_sha256":"a81a9117a9e0c0c74e212020fb4208b7e3bd854004d8805ff2e864a91fa99e3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a81a9117a9e0c0c74e212020fb4208b7e3bd854004d8805ff2e864a91fa99e3e","first_computed_at":"2026-05-17T23:47:09.100112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:09.100112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfmLku2THo8vCaCcpPdIETSd6b4KiT0HqDR5EgfFgA0CdX7LkC4mueJ9LmlHApHeEfdYl5HebXBkJWxUqpzeBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:09.100730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf282f0469803ee2310c43041c6424f03f147a4c7da7bffde97680eedb9381d5","sha256:64a966f3fbb23893962ba5995b6b293b66287920681b7c3bcaef7f3c5589dc96"],"state_sha256":"981b2ba333b4e48a4f7c05d1c9da3fca58c5bcf86f7e8dd85a990799fa31baee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmapz2G8P0mTRzAWGek7lTWErROgk/W4e1T7wtmp9aANV86jkZMgc/nhkk7fu+YquI9BOYAzKZKKj9ZACaitAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:46:14.852496Z","bundle_sha256":"74a9ca1634fad082e1d171be2635fa580df6aa9e41b03192422a71936e7f5c2d"}}