{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OBPHBHJAZQJ3TTQZWA7IZC2452","short_pith_number":"pith:OBPHBHJA","canonical_record":{"source":{"id":"1308.2166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2013-08-09T15:54:22Z","cross_cats_sorted":["cs.DC","cs.DS","cs.SI"],"title_canon_sha256":"5f290cad42dd3330eb0903f15ea13467a79e130ee69b684741532b74bbe1ae40","abstract_canon_sha256":"c3d3fdaeb3097e9b7ef86775824511b07d664c5bbc79f6daa1032c9bb202490e"},"schema_version":"1.0"},"canonical_sha256":"705e709d20cc13b9ce19b03e8c8b5cee93435328893b13ee60688a41ea20a268","source":{"kind":"arxiv","id":"1308.2166","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2166","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2166v1","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2166","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"pith_short_12","alias_value":"OBPHBHJAZQJ3","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OBPHBHJAZQJ3TTQZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OBPHBHJA","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OBPHBHJAZQJ3TTQZWA7IZC2452","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2013-08-09T15:54:22Z","cross_cats_sorted":["cs.DC","cs.DS","cs.SI"],"title_canon_sha256":"5f290cad42dd3330eb0903f15ea13467a79e130ee69b684741532b74bbe1ae40","abstract_canon_sha256":"c3d3fdaeb3097e9b7ef86775824511b07d664c5bbc79f6daa1032c9bb202490e"},"schema_version":"1.0"},"canonical_sha256":"705e709d20cc13b9ce19b03e8c8b5cee93435328893b13ee60688a41ea20a268","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:18.106450Z","signature_b64":"2ZkFagbrarPgSkCkN0VYwkzeObJjhkX0PEswvr26wAVZGrnimD6hOlaXGvcsY/A0sl0wmG4pyCKKut1ZULbtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"705e709d20cc13b9ce19b03e8c8b5cee93435328893b13ee60688a41ea20a268","last_reissued_at":"2026-05-18T03:16:18.105952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:18.105952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2166","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":"2026-05-18T03:16:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtJqYPZAs4zRCZdw0gBddostdYDGgnJ9KaqCPtM9n7MZO/4cNX2kZCyDXWIgalVhuWiLqs/EA4TxV+G2K3I+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:17:14.822477Z"},"content_sha256":"76b76faa2d156bf7e9e4f00930ad0d41d723c974a94e0671a00c26d763b46e49","schema_version":"1.0","event_id":"sha256:76b76faa2d156bf7e9e4f00930ad0d41d723c974a94e0671a00c26d763b46e49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OBPHBHJAZQJ3TTQZWA7IZC2452","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel Triangle Counting in Massive Streaming Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.DS","cs.SI"],"primary_cat":"cs.DB","authors_text":"A. Pavan, Kanat Tangwongsan, Srikanta Tirthapura","submitted_at":"2013-08-09T15:54:22Z","abstract_excerpt":"The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic, we present the design and implementation of a fast and cache-efficient parallel algorithm for estimating the number of triangles in a massive undirected graph whose edges arrive as a stream. It brings together the benefits of streaming algorithms and parallel algorithms. By building on the streaming algorithms framework, the algorithm has a small memory foo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2166","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":"2026-05-18T03:16:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AiiwnI4tVMLqzWKYNUkubbTevdtb6IQBCPn7u1MnK19IhYU2iaKh5ZfhYdbbzVpBZgOgrv1s5NBnXQavcRH0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:17:14.823126Z"},"content_sha256":"5a1569d93114d4ac8714dc77f29bd5b2709b0db2ae636bfea845e78e9e50e4c9","schema_version":"1.0","event_id":"sha256:5a1569d93114d4ac8714dc77f29bd5b2709b0db2ae636bfea845e78e9e50e4c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBPHBHJAZQJ3TTQZWA7IZC2452/bundle.json","state_url":"https://pith.science/pith/OBPHBHJAZQJ3TTQZWA7IZC2452/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBPHBHJAZQJ3TTQZWA7IZC2452/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":"2026-06-08T17:17:14Z","links":{"resolver":"https://pith.science/pith/OBPHBHJAZQJ3TTQZWA7IZC2452","bundle":"https://pith.science/pith/OBPHBHJAZQJ3TTQZWA7IZC2452/bundle.json","state":"https://pith.science/pith/OBPHBHJAZQJ3TTQZWA7IZC2452/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBPHBHJAZQJ3TTQZWA7IZC2452/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OBPHBHJAZQJ3TTQZWA7IZC2452","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":"c3d3fdaeb3097e9b7ef86775824511b07d664c5bbc79f6daa1032c9bb202490e","cross_cats_sorted":["cs.DC","cs.DS","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2013-08-09T15:54:22Z","title_canon_sha256":"5f290cad42dd3330eb0903f15ea13467a79e130ee69b684741532b74bbe1ae40"},"schema_version":"1.0","source":{"id":"1308.2166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2166","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2166v1","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2166","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"pith_short_12","alias_value":"OBPHBHJAZQJ3","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OBPHBHJAZQJ3TTQZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OBPHBHJA","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:5a1569d93114d4ac8714dc77f29bd5b2709b0db2ae636bfea845e78e9e50e4c9","target":"graph","created_at":"2026-05-18T03:16:18Z","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":"The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic, we present the design and implementation of a fast and cache-efficient parallel algorithm for estimating the number of triangles in a massive undirected graph whose edges arrive as a stream. It brings together the benefits of streaming algorithms and parallel algorithms. By building on the streaming algorithms framework, the algorithm has a small memory foo","authors_text":"A. Pavan, Kanat Tangwongsan, Srikanta Tirthapura","cross_cats":["cs.DC","cs.DS","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2013-08-09T15:54:22Z","title":"Parallel Triangle Counting in Massive Streaming Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2166","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":"sha256:76b76faa2d156bf7e9e4f00930ad0d41d723c974a94e0671a00c26d763b46e49","target":"record","created_at":"2026-05-18T03:16:18Z","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":"c3d3fdaeb3097e9b7ef86775824511b07d664c5bbc79f6daa1032c9bb202490e","cross_cats_sorted":["cs.DC","cs.DS","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2013-08-09T15:54:22Z","title_canon_sha256":"5f290cad42dd3330eb0903f15ea13467a79e130ee69b684741532b74bbe1ae40"},"schema_version":"1.0","source":{"id":"1308.2166","kind":"arxiv","version":1}},"canonical_sha256":"705e709d20cc13b9ce19b03e8c8b5cee93435328893b13ee60688a41ea20a268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"705e709d20cc13b9ce19b03e8c8b5cee93435328893b13ee60688a41ea20a268","first_computed_at":"2026-05-18T03:16:18.105952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:18.105952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ZkFagbrarPgSkCkN0VYwkzeObJjhkX0PEswvr26wAVZGrnimD6hOlaXGvcsY/A0sl0wmG4pyCKKut1ZULbtDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:18.106450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76b76faa2d156bf7e9e4f00930ad0d41d723c974a94e0671a00c26d763b46e49","sha256:5a1569d93114d4ac8714dc77f29bd5b2709b0db2ae636bfea845e78e9e50e4c9"],"state_sha256":"329641d44c91061ff71298afd63fdbde410a7944e509289c182d40b2da1dfd23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HA+Nj0JF9/8z7bgdOd90XzRYHzP1RXqyOqWjMLBT76Qun9mi/n5KcGHLDy1GWPYpnOKVFeD52DDE9naomNDaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:17:14.827930Z","bundle_sha256":"a6110b067421dadc8428b2333bf29f08672a5d61054e597eb53ba43659fc8bc7"}}