{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:M7CWVYCHEWI5CNBD3E4BX4YS34","short_pith_number":"pith:M7CWVYCH","canonical_record":{"source":{"id":"1005.3097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-18T04:24:36Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"920bc892e4043115d585cb4cd23023d07acc5b1d77dc56695ad3ec97d0b60cf7","abstract_canon_sha256":"63dead5be14de8014b5e3bb5ca7f72a03b4dcd5cedb8c490e8e1767b342843d1"},"schema_version":"1.0"},"canonical_sha256":"67c56ae0472591d13423d9381bf312df29dcb6e30a07564a8158df757fcc99b3","source":{"kind":"arxiv","id":"1005.3097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3097","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3097v1","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3097","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_12","alias_value":"M7CWVYCHEWI5","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_16","alias_value":"M7CWVYCHEWI5CNBD","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_8","alias_value":"M7CWVYCH","created_at":"2026-06-03T23:06:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:M7CWVYCHEWI5CNBD3E4BX4YS34","target":"record","payload":{"canonical_record":{"source":{"id":"1005.3097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-18T04:24:36Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"920bc892e4043115d585cb4cd23023d07acc5b1d77dc56695ad3ec97d0b60cf7","abstract_canon_sha256":"63dead5be14de8014b5e3bb5ca7f72a03b4dcd5cedb8c490e8e1767b342843d1"},"schema_version":"1.0"},"canonical_sha256":"67c56ae0472591d13423d9381bf312df29dcb6e30a07564a8158df757fcc99b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:37.404028Z","signature_b64":"w7pFO5Vyu7nGoq4dJ//hz4+rODeZN/wC7AUY/A7jT7IOO4qJjvaJYr/lc/+A58IPHGKnpX0NvtJZNytDDuWBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67c56ae0472591d13423d9381bf312df29dcb6e30a07564a8158df757fcc99b3","last_reissued_at":"2026-06-03T23:06:37.403617Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:37.403617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.3097","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":"2026-06-03T23:06:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9y/lU9zmt8tnC/2fDphmpka7imcobIp4ko1PF8xasEGYDPRd9/rEGSb82QS1BTJQW/K5fKvsryR2hDxgN8XRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:53:59.899992Z"},"content_sha256":"a383f470c27d29a91991bb2f31e96c2624d4f28ef1471bdbabfd04946d0191b2","schema_version":"1.0","event_id":"sha256:a383f470c27d29a91991bb2f31e96c2624d4f28ef1471bdbabfd04946d0191b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:M7CWVYCHEWI5CNBD3E4BX4YS34","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective Resistances, Statistical Leverage, and Applications to Linear Equation Solving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"cs.NA","authors_text":"Michael W. Mahoney, Petros Drineas","submitted_at":"2010-05-18T04:24:36Z","abstract_excerpt":"Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead to practical algorithms. In an effort to bridge this gap, we describe in this paper two related results. Our first and main result is a simple algorithm to approximate the solution to a set of linear equations defined by a Laplacian (for a graph $G$ with $n$ nodes and $m \\le n^2$ edges) constraint matrix. The algorithm is a non-recursive algorithm; even thoug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3097","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1005.3097/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":"2026-06-03T23:06:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swNCmY/SAypH3OGXRrtESJ/0JZnxeDLchO3SSXriZZXUPGE6tmGtAkfxFgP4RJidJ7NNh12gFGCy/oCZ8qaxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:53:59.900392Z"},"content_sha256":"6924e39a5946d3e62e4d2e78165d7306431bbedfe8f35a00f97f17525d72fcd8","schema_version":"1.0","event_id":"sha256:6924e39a5946d3e62e4d2e78165d7306431bbedfe8f35a00f97f17525d72fcd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7CWVYCHEWI5CNBD3E4BX4YS34/bundle.json","state_url":"https://pith.science/pith/M7CWVYCHEWI5CNBD3E4BX4YS34/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7CWVYCHEWI5CNBD3E4BX4YS34/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":"2026-06-05T09:53:59Z","links":{"resolver":"https://pith.science/pith/M7CWVYCHEWI5CNBD3E4BX4YS34","bundle":"https://pith.science/pith/M7CWVYCHEWI5CNBD3E4BX4YS34/bundle.json","state":"https://pith.science/pith/M7CWVYCHEWI5CNBD3E4BX4YS34/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7CWVYCHEWI5CNBD3E4BX4YS34/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:M7CWVYCHEWI5CNBD3E4BX4YS34","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":"63dead5be14de8014b5e3bb5ca7f72a03b4dcd5cedb8c490e8e1767b342843d1","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-18T04:24:36Z","title_canon_sha256":"920bc892e4043115d585cb4cd23023d07acc5b1d77dc56695ad3ec97d0b60cf7"},"schema_version":"1.0","source":{"id":"1005.3097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3097","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3097v1","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3097","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_12","alias_value":"M7CWVYCHEWI5","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_16","alias_value":"M7CWVYCHEWI5CNBD","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_8","alias_value":"M7CWVYCH","created_at":"2026-06-03T23:06:37Z"}],"graph_snapshots":[{"event_id":"sha256:6924e39a5946d3e62e4d2e78165d7306431bbedfe8f35a00f97f17525d72fcd8","target":"graph","created_at":"2026-06-03T23:06:37Z","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/1005.3097/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead to practical algorithms. In an effort to bridge this gap, we describe in this paper two related results. Our first and main result is a simple algorithm to approximate the solution to a set of linear equations defined by a Laplacian (for a graph $G$ with $n$ nodes and $m \\le n^2$ edges) constraint matrix. The algorithm is a non-recursive algorithm; even thoug","authors_text":"Michael W. Mahoney, Petros Drineas","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-18T04:24:36Z","title":"Effective Resistances, Statistical Leverage, and Applications to Linear Equation Solving"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3097","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:a383f470c27d29a91991bb2f31e96c2624d4f28ef1471bdbabfd04946d0191b2","target":"record","created_at":"2026-06-03T23:06:37Z","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":"63dead5be14de8014b5e3bb5ca7f72a03b4dcd5cedb8c490e8e1767b342843d1","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-18T04:24:36Z","title_canon_sha256":"920bc892e4043115d585cb4cd23023d07acc5b1d77dc56695ad3ec97d0b60cf7"},"schema_version":"1.0","source":{"id":"1005.3097","kind":"arxiv","version":1}},"canonical_sha256":"67c56ae0472591d13423d9381bf312df29dcb6e30a07564a8158df757fcc99b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67c56ae0472591d13423d9381bf312df29dcb6e30a07564a8158df757fcc99b3","first_computed_at":"2026-06-03T23:06:37.403617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:37.403617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w7pFO5Vyu7nGoq4dJ//hz4+rODeZN/wC7AUY/A7jT7IOO4qJjvaJYr/lc/+A58IPHGKnpX0NvtJZNytDDuWBCA==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:37.404028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a383f470c27d29a91991bb2f31e96c2624d4f28ef1471bdbabfd04946d0191b2","sha256:6924e39a5946d3e62e4d2e78165d7306431bbedfe8f35a00f97f17525d72fcd8"],"state_sha256":"f77cd9cdec606e046b591921b1fe812f17e7ff3b26e7593e8870a32ba48fb820"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9GqiYZG33U40agmRuM7YLbvcB7LJkx11q9tZ8UaLwFzKdbceOAZ+eKv2EKfzwz1h1O8znS0b63NwkD8TAOEAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:53:59.902542Z","bundle_sha256":"bbe4b0b29bc2afa3648f949fb208de5e77e67af4fc1a848c752888a831da38bc"}}