{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:Q4K2OEKG4VXDUO6IYYFLR65VGT","short_pith_number":"pith:Q4K2OEKG","canonical_record":{"source":{"id":"1903.12165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-28T17:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"2180be53d6f1c8342a41ecdc2cd4d17d3a7e0f55eddf7e5e070e57348ac7d0b0","abstract_canon_sha256":"cff7b5be41fc65f22539c0c7ac47aea72bbbb4746e9fe4a3178238dd87bc46de"},"schema_version":"1.0"},"canonical_sha256":"8715a71146e56e3a3bc8c60ab8fbb534f7c25480c463c7165ebff876f56a52e3","source":{"kind":"arxiv","id":"1903.12165","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12165","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12165v1","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12165","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"Q4K2OEKG4VXD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q4K2OEKG4VXDUO6I","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q4K2OEKG","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:Q4K2OEKG4VXDUO6IYYFLR65VGT","target":"record","payload":{"canonical_record":{"source":{"id":"1903.12165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-28T17:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"2180be53d6f1c8342a41ecdc2cd4d17d3a7e0f55eddf7e5e070e57348ac7d0b0","abstract_canon_sha256":"cff7b5be41fc65f22539c0c7ac47aea72bbbb4746e9fe4a3178238dd87bc46de"},"schema_version":"1.0"},"canonical_sha256":"8715a71146e56e3a3bc8c60ab8fbb534f7c25480c463c7165ebff876f56a52e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:57.835631Z","signature_b64":"X5XtVxnIN6ty9X4+we3MPAGw9NmuyxZA1a4EYmOR+u2RRwXYwD2hyH4BiQI75TyEhQDP17Y114N2td1JLrm3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8715a71146e56e3a3bc8c60ab8fbb534f7c25480c463c7165ebff876f56a52e3","last_reissued_at":"2026-05-17T23:49:57.834988Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:57.834988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.12165","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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obQBqXRrHK7nxqG+2kj+TJdDWBay7tZVbxW6tis2uj+pJsf+t6/+Sia3vMzpck1UJ2N82s4Ebe8bWjKmK4d6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:59:14.443753Z"},"content_sha256":"c3bd6e4c94dc8507a2efb807895c0e0d4f036d0772351ed616a3527e39be89a1","schema_version":"1.0","event_id":"sha256:c3bd6e4c94dc8507a2efb807895c0e0d4f036d0772351ed616a3527e39be89a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:Q4K2OEKG4VXDUO6IYYFLR65VGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Spectral Sparsification in Dynamic Streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aida Mousavifar, Cameron Musco, Christopher Musco, Michael Kapralov, Navid Nouri","submitted_at":"2019-03-28T17:50:51Z","abstract_excerpt":"Graph sketching has emerged as a powerful technique for processing massive graphs that change over time (i.e., are presented as a dynamic stream of edge updates) over the past few years, starting with the work of Ahn, Guha and McGregor (SODA'12) on graph connectivity via sketching. In this paper we consider the problem of designing spectral approximations to graphs, or spectral sparsifiers, using a small number of linear measurements, with the additional constraint that the sketches admit an efficient recovery scheme.\n  Prior to our work, sketching algorithms were known with near optimal $\\til"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12165","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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5DOiW3xUDDwaA6E9E/vmZMV8f0jdVooiI89CCoe8lmIYtkoF+dHL17h25FcHMnme32Dkh7uqaCr2T40V5qVUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:59:14.444108Z"},"content_sha256":"3dacb95bd4d3de209e5d399133478d8ad8dd0ca88808e211386334e01d9f755e","schema_version":"1.0","event_id":"sha256:3dacb95bd4d3de209e5d399133478d8ad8dd0ca88808e211386334e01d9f755e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT/bundle.json","state_url":"https://pith.science/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT/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":"2026-05-31T21:59:14Z","links":{"resolver":"https://pith.science/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT","bundle":"https://pith.science/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT/bundle.json","state":"https://pith.science/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4K2OEKG4VXDUO6IYYFLR65VGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Q4K2OEKG4VXDUO6IYYFLR65VGT","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":"cff7b5be41fc65f22539c0c7ac47aea72bbbb4746e9fe4a3178238dd87bc46de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-28T17:50:51Z","title_canon_sha256":"2180be53d6f1c8342a41ecdc2cd4d17d3a7e0f55eddf7e5e070e57348ac7d0b0"},"schema_version":"1.0","source":{"id":"1903.12165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12165","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12165v1","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12165","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"Q4K2OEKG4VXD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q4K2OEKG4VXDUO6I","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q4K2OEKG","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:3dacb95bd4d3de209e5d399133478d8ad8dd0ca88808e211386334e01d9f755e","target":"graph","created_at":"2026-05-17T23:49:57Z","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":"Graph sketching has emerged as a powerful technique for processing massive graphs that change over time (i.e., are presented as a dynamic stream of edge updates) over the past few years, starting with the work of Ahn, Guha and McGregor (SODA'12) on graph connectivity via sketching. In this paper we consider the problem of designing spectral approximations to graphs, or spectral sparsifiers, using a small number of linear measurements, with the additional constraint that the sketches admit an efficient recovery scheme.\n  Prior to our work, sketching algorithms were known with near optimal $\\til","authors_text":"Aida Mousavifar, Cameron Musco, Christopher Musco, Michael Kapralov, Navid Nouri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-28T17:50:51Z","title":"Faster Spectral Sparsification in Dynamic Streams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12165","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:c3bd6e4c94dc8507a2efb807895c0e0d4f036d0772351ed616a3527e39be89a1","target":"record","created_at":"2026-05-17T23:49:57Z","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":"cff7b5be41fc65f22539c0c7ac47aea72bbbb4746e9fe4a3178238dd87bc46de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-28T17:50:51Z","title_canon_sha256":"2180be53d6f1c8342a41ecdc2cd4d17d3a7e0f55eddf7e5e070e57348ac7d0b0"},"schema_version":"1.0","source":{"id":"1903.12165","kind":"arxiv","version":1}},"canonical_sha256":"8715a71146e56e3a3bc8c60ab8fbb534f7c25480c463c7165ebff876f56a52e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8715a71146e56e3a3bc8c60ab8fbb534f7c25480c463c7165ebff876f56a52e3","first_computed_at":"2026-05-17T23:49:57.834988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:57.834988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X5XtVxnIN6ty9X4+we3MPAGw9NmuyxZA1a4EYmOR+u2RRwXYwD2hyH4BiQI75TyEhQDP17Y114N2td1JLrm3AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:57.835631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3bd6e4c94dc8507a2efb807895c0e0d4f036d0772351ed616a3527e39be89a1","sha256:3dacb95bd4d3de209e5d399133478d8ad8dd0ca88808e211386334e01d9f755e"],"state_sha256":"9d5b8d99568503dacdc357938146b4134035715a34b6d31529f0bf623d398f6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ATPaygoVEYgYpHzw5MrxAb+k+LZrBbVByX6w9czYCk96oSzGveoZPyRku09O8jiC4brNd+/DtaYXuZYBSBfwDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:59:14.446339Z","bundle_sha256":"6a3369623a8a4f39deafee1febf2c703497e39b721cac1b07631871dbb2d19b8"}}