{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AR5QHP7HFV74USZSAQ4EL35KZ6","short_pith_number":"pith:AR5QHP7H","canonical_record":{"source":{"id":"1506.03296","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-10T13:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"472e6d88d8b0a51659c7e20bf5314bed26fbcdd9d9c8a5462a6b4cade8fa7186","abstract_canon_sha256":"306aada2040fcdac05f8ee731b23b5270b92d511bb61e664a3c374916a06657c"},"schema_version":"1.0"},"canonical_sha256":"047b03bfe72d7fca4b32043845efaacfa32051712279329636077552d7b7cd3c","source":{"kind":"arxiv","id":"1506.03296","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03296","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03296v5","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03296","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"AR5QHP7HFV74","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AR5QHP7HFV74USZS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AR5QHP7H","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AR5QHP7HFV74USZSAQ4EL35KZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03296","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-10T13:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"472e6d88d8b0a51659c7e20bf5314bed26fbcdd9d9c8a5462a6b4cade8fa7186","abstract_canon_sha256":"306aada2040fcdac05f8ee731b23b5270b92d511bb61e664a3c374916a06657c"},"schema_version":"1.0"},"canonical_sha256":"047b03bfe72d7fca4b32043845efaacfa32051712279329636077552d7b7cd3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.775625Z","signature_b64":"i3BA0RJgs05tvbEwNZ8Zmc70Ud063meclXeN7/vgvMauf3eLy+8XQu4VXVojdeA05V88mPavJAkvREx0LDiDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"047b03bfe72d7fca4b32043845efaacfa32051712279329636077552d7b7cd3c","last_reissued_at":"2026-05-18T01:23:18.775030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.775030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03296","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"skrbX/qDi4A2w9uJtgqpvI1ZCaifV+hyPjkPOQjy5B+sgyDVOAweBVmR8U3Nj/kMbbjcsMYfljWJdYa3/Z3DAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:30:51.526423Z"},"content_sha256":"bf945917e29ca18d46a1bd7a311da60d793c624ebe2482072296a8157742f246","schema_version":"1.0","event_id":"sha256:bf945917e29ca18d46a1bd7a311da60d793c624ebe2482072296a8157742f246"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AR5QHP7HFV74USZSAQ4EL35KZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized Iterative Methods for Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Peter Richt\\'arik, Robert M. Gower","submitted_at":"2015-06-10T13:37:27Z","abstract_excerpt":"We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random intersect, random linear solve, random update and random fixed point. By varying its two parameters$-$a positive definite matrix (defining geometry), and a random matrix (sampled in an independently and identically distributed fashion in each iteration)$-$we recover a comprehensive array of well-known algorithms as special cases, including the randomized Kaczm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03296","kind":"arxiv","version":5},"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":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jJeLhPOoL3LHQzSrDPkIgz/3mcGnb5nBaqZZds9PEka+f2+La43xv6vSnncEVxTrkvbpWyw7ejBpaXJhg73Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:30:51.527110Z"},"content_sha256":"ebd7612fd0b8880b16151b0b0a1562d10e25b7932b656fb1bdbb2eb5b08eb072","schema_version":"1.0","event_id":"sha256:ebd7612fd0b8880b16151b0b0a1562d10e25b7932b656fb1bdbb2eb5b08eb072"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AR5QHP7HFV74USZSAQ4EL35KZ6/bundle.json","state_url":"https://pith.science/pith/AR5QHP7HFV74USZSAQ4EL35KZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AR5QHP7HFV74USZSAQ4EL35KZ6/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":"2026-05-24T20:30:51Z","links":{"resolver":"https://pith.science/pith/AR5QHP7HFV74USZSAQ4EL35KZ6","bundle":"https://pith.science/pith/AR5QHP7HFV74USZSAQ4EL35KZ6/bundle.json","state":"https://pith.science/pith/AR5QHP7HFV74USZSAQ4EL35KZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AR5QHP7HFV74USZSAQ4EL35KZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AR5QHP7HFV74USZSAQ4EL35KZ6","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":"306aada2040fcdac05f8ee731b23b5270b92d511bb61e664a3c374916a06657c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-10T13:37:27Z","title_canon_sha256":"472e6d88d8b0a51659c7e20bf5314bed26fbcdd9d9c8a5462a6b4cade8fa7186"},"schema_version":"1.0","source":{"id":"1506.03296","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03296","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03296v5","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03296","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"AR5QHP7HFV74","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AR5QHP7HFV74USZS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AR5QHP7H","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:ebd7612fd0b8880b16151b0b0a1562d10e25b7932b656fb1bdbb2eb5b08eb072","target":"graph","created_at":"2026-05-18T01:23:18Z","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":"We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random intersect, random linear solve, random update and random fixed point. By varying its two parameters$-$a positive definite matrix (defining geometry), and a random matrix (sampled in an independently and identically distributed fashion in each iteration)$-$we recover a comprehensive array of well-known algorithms as special cases, including the randomized Kaczm","authors_text":"Peter Richt\\'arik, Robert M. Gower","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-10T13:37:27Z","title":"Randomized Iterative Methods for Linear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03296","kind":"arxiv","version":5},"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:bf945917e29ca18d46a1bd7a311da60d793c624ebe2482072296a8157742f246","target":"record","created_at":"2026-05-18T01:23:18Z","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":"306aada2040fcdac05f8ee731b23b5270b92d511bb61e664a3c374916a06657c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-10T13:37:27Z","title_canon_sha256":"472e6d88d8b0a51659c7e20bf5314bed26fbcdd9d9c8a5462a6b4cade8fa7186"},"schema_version":"1.0","source":{"id":"1506.03296","kind":"arxiv","version":5}},"canonical_sha256":"047b03bfe72d7fca4b32043845efaacfa32051712279329636077552d7b7cd3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"047b03bfe72d7fca4b32043845efaacfa32051712279329636077552d7b7cd3c","first_computed_at":"2026-05-18T01:23:18.775030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:18.775030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i3BA0RJgs05tvbEwNZ8Zmc70Ud063meclXeN7/vgvMauf3eLy+8XQu4VXVojdeA05V88mPavJAkvREx0LDiDAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:18.775625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03296","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf945917e29ca18d46a1bd7a311da60d793c624ebe2482072296a8157742f246","sha256:ebd7612fd0b8880b16151b0b0a1562d10e25b7932b656fb1bdbb2eb5b08eb072"],"state_sha256":"9ea14f5c753b1e2151622b01b8326ef48cef7af45723cf57a5823134b4f5a189"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+kSdsDfqPer+2kCdfkOOnLZo0CeZUuRrWiuAGoIVXoCWq1e79aPYhP3KWxM2tZ7M8Re8Eh6HCXPzN5Myy/+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T20:30:51.530532Z","bundle_sha256":"f396bd0a2ab6b97ac4afd24759e61817b3be42cfe4bca921ffcf966d96704ce6"}}