{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MSS5LLQPJAL3WYJVAWEHXVCWTR","short_pith_number":"pith:MSS5LLQP","canonical_record":{"source":{"id":"1706.05736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-06-18T22:13:45Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"f17c09c09f6943d6869fa43a0c8348c316d61ab601d7b14a621c0e7ca02429f0","abstract_canon_sha256":"0608d0044cca69ad55de4357a8650c018aceb15a116b03ab16c5c99c99476c11"},"schema_version":"1.0"},"canonical_sha256":"64a5d5ae0f4817bb613505887bd4569c6e292c113771be2fa3587bd0bed59cdd","source":{"kind":"arxiv","id":"1706.05736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05736","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05736v1","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05736","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"MSS5LLQPJAL3","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MSS5LLQPJAL3WYJV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MSS5LLQP","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MSS5LLQPJAL3WYJVAWEHXVCWTR","target":"record","payload":{"canonical_record":{"source":{"id":"1706.05736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-06-18T22:13:45Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"f17c09c09f6943d6869fa43a0c8348c316d61ab601d7b14a621c0e7ca02429f0","abstract_canon_sha256":"0608d0044cca69ad55de4357a8650c018aceb15a116b03ab16c5c99c99476c11"},"schema_version":"1.0"},"canonical_sha256":"64a5d5ae0f4817bb613505887bd4569c6e292c113771be2fa3587bd0bed59cdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:09.045844Z","signature_b64":"XfCWFi1TWEuRNOG1JkriuOM5eaZCnRHwutWY0iov5b8dQRMEqhbG7QDw2GnqiKZUbAAPqETXA3S3fcLvnGD7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64a5d5ae0f4817bb613505887bd4569c6e292c113771be2fa3587bd0bed59cdd","last_reissued_at":"2026-05-18T00:42:09.045349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:09.045349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.05736","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":"2026-05-18T00:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IZa+e1nL2JoCf5+Wm/QTMsPA/oQdesHgsxucMCkBjHDmGOJQ8Pc2UMVR+UBvzsyLIdc8ppf95ctwu4i7sMpkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:54:24.252551Z"},"content_sha256":"bc743cab4d44ed4a4cc4ab57d957f9da0bfeb6ac688f7897162e9d021bf7b7af","schema_version":"1.0","event_id":"sha256:bc743cab4d44ed4a4cc4ab57d957f9da0bfeb6ac688f7897162e9d021bf7b7af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MSS5LLQPJAL3WYJVAWEHXVCWTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.NA","authors_text":"Alp Yurtsever, Joel A. Tropp, Madeleine Udell, Volkan Cevher","submitted_at":"2017-06-18T22:13:45Z","abstract_excerpt":"Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nystrom approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05736","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":"2026-05-18T00:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/PM0X2rk6i25/QQdxr1zlugBNjO7A9JKwqMzczE+FdpfhODEBIZxsUIcg80lwY3rt5qpOMK9dkolESb1W7aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:54:24.253302Z"},"content_sha256":"ba8d3245a92de7433dd49bbcf5a23c3cf6e1e96db8f896a494928a9607ad4720","schema_version":"1.0","event_id":"sha256:ba8d3245a92de7433dd49bbcf5a23c3cf6e1e96db8f896a494928a9607ad4720"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR/bundle.json","state_url":"https://pith.science/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR/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":"2026-06-09T01:54:24Z","links":{"resolver":"https://pith.science/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR","bundle":"https://pith.science/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR/bundle.json","state":"https://pith.science/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSS5LLQPJAL3WYJVAWEHXVCWTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MSS5LLQPJAL3WYJVAWEHXVCWTR","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":"0608d0044cca69ad55de4357a8650c018aceb15a116b03ab16c5c99c99476c11","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-06-18T22:13:45Z","title_canon_sha256":"f17c09c09f6943d6869fa43a0c8348c316d61ab601d7b14a621c0e7ca02429f0"},"schema_version":"1.0","source":{"id":"1706.05736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05736","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05736v1","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05736","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"MSS5LLQPJAL3","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MSS5LLQPJAL3WYJV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MSS5LLQP","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:ba8d3245a92de7433dd49bbcf5a23c3cf6e1e96db8f896a494928a9607ad4720","target":"graph","created_at":"2026-05-18T00:42:09Z","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":"Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nystrom approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exp","authors_text":"Alp Yurtsever, Joel A. Tropp, Madeleine Udell, Volkan Cevher","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-06-18T22:13:45Z","title":"Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05736","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:bc743cab4d44ed4a4cc4ab57d957f9da0bfeb6ac688f7897162e9d021bf7b7af","target":"record","created_at":"2026-05-18T00:42:09Z","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":"0608d0044cca69ad55de4357a8650c018aceb15a116b03ab16c5c99c99476c11","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-06-18T22:13:45Z","title_canon_sha256":"f17c09c09f6943d6869fa43a0c8348c316d61ab601d7b14a621c0e7ca02429f0"},"schema_version":"1.0","source":{"id":"1706.05736","kind":"arxiv","version":1}},"canonical_sha256":"64a5d5ae0f4817bb613505887bd4569c6e292c113771be2fa3587bd0bed59cdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64a5d5ae0f4817bb613505887bd4569c6e292c113771be2fa3587bd0bed59cdd","first_computed_at":"2026-05-18T00:42:09.045349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:09.045349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XfCWFi1TWEuRNOG1JkriuOM5eaZCnRHwutWY0iov5b8dQRMEqhbG7QDw2GnqiKZUbAAPqETXA3S3fcLvnGD7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:09.045844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc743cab4d44ed4a4cc4ab57d957f9da0bfeb6ac688f7897162e9d021bf7b7af","sha256:ba8d3245a92de7433dd49bbcf5a23c3cf6e1e96db8f896a494928a9607ad4720"],"state_sha256":"b20bb22ad99f980d9217b0ea8033d95bb47b0e5129e9c35760f203b4156ea3fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k3h2AnMChPD3Pn7ojAidE5QxO+igLXhNldyvT5busOSJAnQDOiK+QsvhclgPN+Y+zTiYU+2n0+wswC79NOEQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:54:24.257420Z","bundle_sha256":"d7aba93d6fb0588f73e5c8445324b555c98698a713f07bb4cf02687693972473"}}