{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C4H4GTVHKML5OZEQ7XWCVE4KNB","short_pith_number":"pith:C4H4GTVH","canonical_record":{"source":{"id":"1612.06013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-19T00:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"1a44224eec93b347e24e76befd6dc054a4c3a9f89a40304c3fbce8604d145b16","abstract_canon_sha256":"ba7f55a3356f42614b18c56f6d60df8b5c779542180bac188300859fd612a1e7"},"schema_version":"1.0"},"canonical_sha256":"170fc34ea75317d76490fdec2a938a6846377b0c6cc5e251ed7dfaf7a407e4e5","source":{"kind":"arxiv","id":"1612.06013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06013","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06013v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06013","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"C4H4GTVHKML5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C4H4GTVHKML5OZEQ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C4H4GTVH","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C4H4GTVHKML5OZEQ7XWCVE4KNB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-19T00:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"1a44224eec93b347e24e76befd6dc054a4c3a9f89a40304c3fbce8604d145b16","abstract_canon_sha256":"ba7f55a3356f42614b18c56f6d60df8b5c779542180bac188300859fd612a1e7"},"schema_version":"1.0"},"canonical_sha256":"170fc34ea75317d76490fdec2a938a6846377b0c6cc5e251ed7dfaf7a407e4e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:46.115980Z","signature_b64":"hfLIkLQqu/PkP68MTW3vPe1RFlhDasQpjdIW7A43U1xJFwbVfTZ0wDDuzN4ifNpmNFgQrJObRQ/aeu7RvPQ3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"170fc34ea75317d76490fdec2a938a6846377b0c6cc5e251ed7dfaf7a407e4e5","last_reissued_at":"2026-05-18T00:54:46.115258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:46.115258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06013","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":"2026-05-18T00:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q8Yaj/Ed5t5H0xX4UvjFQrXLr41RqEcz/k4s5NlC0yF/BMi8K4uLQomcwe9oVg85oFUy2LD4iHxjgsjaiZ/2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:34:52.364323Z"},"content_sha256":"f9ae8fd023992835a614d0ff9c99e02279c83eae48cc1b2f4c8b8a5c73282174","schema_version":"1.0","event_id":"sha256:f9ae8fd023992835a614d0ff9c99e02279c83eae48cc1b2f4c8b8a5c73282174"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C4H4GTVHKML5OZEQ7XWCVE4KNB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sketch and Project: Randomized Iterative Methods for Linear Systems and Inverting Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Robert M. Gower","submitted_at":"2016-12-19T00:33:29Z","abstract_excerpt":"Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these ideas influence these fields is via the development and analysis of randomized algorithms for solving standard and new problems of these fields. Such methods are typically easier to analyze, and often lead to faster and/or more scalable and versatile methods in practice.\n  This thesis explores the design and analysis of new randomized iterative methods for so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06013","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":"2026-05-18T00:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"asCZlF+xEWqWoksouDldivML6I/22XoymDrMOP8W23GZdCVmZj7byRhmTEZCj276F83N+1lP3pS9boet76HqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:34:52.364785Z"},"content_sha256":"24000840d11d5d15bee47898069ab41a7df93da3c05711472252b72260fcfe6e","schema_version":"1.0","event_id":"sha256:24000840d11d5d15bee47898069ab41a7df93da3c05711472252b72260fcfe6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB/bundle.json","state_url":"https://pith.science/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB/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":"2026-08-10T14:34:52Z","links":{"resolver":"https://pith.science/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB","bundle":"https://pith.science/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB/bundle.json","state":"https://pith.science/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4H4GTVHKML5OZEQ7XWCVE4KNB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C4H4GTVHKML5OZEQ7XWCVE4KNB","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":"ba7f55a3356f42614b18c56f6d60df8b5c779542180bac188300859fd612a1e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-19T00:33:29Z","title_canon_sha256":"1a44224eec93b347e24e76befd6dc054a4c3a9f89a40304c3fbce8604d145b16"},"schema_version":"1.0","source":{"id":"1612.06013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06013","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06013v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06013","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"C4H4GTVHKML5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C4H4GTVHKML5OZEQ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C4H4GTVH","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:24000840d11d5d15bee47898069ab41a7df93da3c05711472252b72260fcfe6e","target":"graph","created_at":"2026-05-18T00:54:46Z","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":"Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these ideas influence these fields is via the development and analysis of randomized algorithms for solving standard and new problems of these fields. Such methods are typically easier to analyze, and often lead to faster and/or more scalable and versatile methods in practice.\n  This thesis explores the design and analysis of new randomized iterative methods for so","authors_text":"Robert M. Gower","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-19T00:33:29Z","title":"Sketch and Project: Randomized Iterative Methods for Linear Systems and Inverting Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06013","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:f9ae8fd023992835a614d0ff9c99e02279c83eae48cc1b2f4c8b8a5c73282174","target":"record","created_at":"2026-05-18T00:54:46Z","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":"ba7f55a3356f42614b18c56f6d60df8b5c779542180bac188300859fd612a1e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-19T00:33:29Z","title_canon_sha256":"1a44224eec93b347e24e76befd6dc054a4c3a9f89a40304c3fbce8604d145b16"},"schema_version":"1.0","source":{"id":"1612.06013","kind":"arxiv","version":1}},"canonical_sha256":"170fc34ea75317d76490fdec2a938a6846377b0c6cc5e251ed7dfaf7a407e4e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"170fc34ea75317d76490fdec2a938a6846377b0c6cc5e251ed7dfaf7a407e4e5","first_computed_at":"2026-05-18T00:54:46.115258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:46.115258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hfLIkLQqu/PkP68MTW3vPe1RFlhDasQpjdIW7A43U1xJFwbVfTZ0wDDuzN4ifNpmNFgQrJObRQ/aeu7RvPQ3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:46.115980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9ae8fd023992835a614d0ff9c99e02279c83eae48cc1b2f4c8b8a5c73282174","sha256:24000840d11d5d15bee47898069ab41a7df93da3c05711472252b72260fcfe6e"],"state_sha256":"21515d3aba97ad0cb12262b87171bd2c124ee30b76513e19cf6809430a2070d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MFKx7lAsb9mX3swhQc0JtQXMjZoFQX+H7PnjTd/Zf+8AvPgStAXyINwSUopDxwpY3WIKTNT6H36X/lLhve0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T14:34:52.368684Z","bundle_sha256":"3cdae7015853dfeee605179f3f34ed172717180db79237351b1e7ba1f94bb3b9"}}