{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SAZ7CHWR6QYY7G4KPF22QGP2EI","short_pith_number":"pith:SAZ7CHWR","canonical_record":{"source":{"id":"1811.09025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-22T05:37:20Z","cross_cats_sorted":[],"title_canon_sha256":"8e0ad2e7b4822e8ab51d6f1101c5b9e6611accc97f1be950e7864a0f8dbe155a","abstract_canon_sha256":"783f1fca9e856b3518608cfe46b255e7f821473f1be564445c9eb6a2f2dda4fb"},"schema_version":"1.0"},"canonical_sha256":"9033f11ed1f4318f9b8a7975a819fa22096eae911af8468cbfbf0568307c7b17","source":{"kind":"arxiv","id":"1811.09025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09025","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09025v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09025","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"SAZ7CHWR6QYY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SAZ7CHWR6QYY7G4K","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SAZ7CHWR","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SAZ7CHWR6QYY7G4KPF22QGP2EI","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-22T05:37:20Z","cross_cats_sorted":[],"title_canon_sha256":"8e0ad2e7b4822e8ab51d6f1101c5b9e6611accc97f1be950e7864a0f8dbe155a","abstract_canon_sha256":"783f1fca9e856b3518608cfe46b255e7f821473f1be564445c9eb6a2f2dda4fb"},"schema_version":"1.0"},"canonical_sha256":"9033f11ed1f4318f9b8a7975a819fa22096eae911af8468cbfbf0568307c7b17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:07.258382Z","signature_b64":"e8nlJVpiB9PwvjussKQZbtj6zslSosAAjmlosX1AKZkScACq8nqI6JkIQS1V7FIFz44dae278bAjc5eE2pusBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9033f11ed1f4318f9b8a7975a819fa22096eae911af8468cbfbf0568307c7b17","last_reissued_at":"2026-05-18T00:00:07.257590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:07.257590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09025","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":"2026-05-18T00:00:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ashG0pQI7AVVo6SqCHAH27IXHbXmysRpoXcQOfoRzOs/MCUKVgTnZXrR9TQSWceteOfOxH5VN6NhoQHCzfWdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:33:10.364969Z"},"content_sha256":"1a4b4a0a9fcdd918a9ee6a42306dc29d69b862f579fff41cfbcced956107532f","schema_version":"1.0","event_id":"sha256:1a4b4a0a9fcdd918a9ee6a42306dc29d69b862f579fff41cfbcced956107532f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SAZ7CHWR6QYY7G4KPF22QGP2EI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Introduction to Krylov Subspace Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Shitao Fan","submitted_at":"2018-11-22T05:37:20Z","abstract_excerpt":"Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem. However, it is difficult to understand mathematical principles behind these methods. In the first part of the article, Krylov methods are discussed in detail. Thus, readers equipped with a basic knowledge of linear algebra should be able to understand these methods. In this part, the knowledge of Krylov methods are put into some examples for simple implementa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09025","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":"2026-05-18T00:00:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oEeNchB4VUdbMCs/9rA5h7R6FPCrcHndGFk+uizeawHLP5fFzLPkDM3ZGSk97aTyroYGrbAafTZbgwJ84Z2OAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:33:10.365673Z"},"content_sha256":"0e654faeef3f8c2da33e4a064261b160c025849de9fb2e6d20045234ec9e36d0","schema_version":"1.0","event_id":"sha256:0e654faeef3f8c2da33e4a064261b160c025849de9fb2e6d20045234ec9e36d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI/bundle.json","state_url":"https://pith.science/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI/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":"2026-05-31T01:33:10Z","links":{"resolver":"https://pith.science/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI","bundle":"https://pith.science/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI/bundle.json","state":"https://pith.science/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAZ7CHWR6QYY7G4KPF22QGP2EI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SAZ7CHWR6QYY7G4KPF22QGP2EI","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":"783f1fca9e856b3518608cfe46b255e7f821473f1be564445c9eb6a2f2dda4fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-22T05:37:20Z","title_canon_sha256":"8e0ad2e7b4822e8ab51d6f1101c5b9e6611accc97f1be950e7864a0f8dbe155a"},"schema_version":"1.0","source":{"id":"1811.09025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09025","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09025v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09025","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"SAZ7CHWR6QYY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SAZ7CHWR6QYY7G4K","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SAZ7CHWR","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:0e654faeef3f8c2da33e4a064261b160c025849de9fb2e6d20045234ec9e36d0","target":"graph","created_at":"2026-05-18T00:00:07Z","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":"Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem. However, it is difficult to understand mathematical principles behind these methods. In the first part of the article, Krylov methods are discussed in detail. Thus, readers equipped with a basic knowledge of linear algebra should be able to understand these methods. In this part, the knowledge of Krylov methods are put into some examples for simple implementa","authors_text":"Shitao Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-22T05:37:20Z","title":"An Introduction to Krylov Subspace Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09025","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":"sha256:1a4b4a0a9fcdd918a9ee6a42306dc29d69b862f579fff41cfbcced956107532f","target":"record","created_at":"2026-05-18T00:00:07Z","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":"783f1fca9e856b3518608cfe46b255e7f821473f1be564445c9eb6a2f2dda4fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-22T05:37:20Z","title_canon_sha256":"8e0ad2e7b4822e8ab51d6f1101c5b9e6611accc97f1be950e7864a0f8dbe155a"},"schema_version":"1.0","source":{"id":"1811.09025","kind":"arxiv","version":1}},"canonical_sha256":"9033f11ed1f4318f9b8a7975a819fa22096eae911af8468cbfbf0568307c7b17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9033f11ed1f4318f9b8a7975a819fa22096eae911af8468cbfbf0568307c7b17","first_computed_at":"2026-05-18T00:00:07.257590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:07.257590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e8nlJVpiB9PwvjussKQZbtj6zslSosAAjmlosX1AKZkScACq8nqI6JkIQS1V7FIFz44dae278bAjc5eE2pusBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:07.258382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a4b4a0a9fcdd918a9ee6a42306dc29d69b862f579fff41cfbcced956107532f","sha256:0e654faeef3f8c2da33e4a064261b160c025849de9fb2e6d20045234ec9e36d0"],"state_sha256":"0b7a3c068039d59b263f91018567198fa1706992a02304ed5cb82553f1b54f68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSZrfbXEH4KyPwrYySNfWPpU/B1dcmQwbcGGGTCm/l13oZ97y35BSJzg+GEl90gef+0Fj6Ff6K1JPCzEIcf5Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:33:10.369383Z","bundle_sha256":"3300074ee130b2814d5374545a815c63556c32673498289aefe9490c4ffb05ee"}}