{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:J7D2YQ45EDIRA2XGHXGVG5G4XV","short_pith_number":"pith:J7D2YQ45","canonical_record":{"source":{"id":"1206.1506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-07T14:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"f3bc1f5648cb3472ba34f37bbb96426110e32999b05a2d251da0f81baaebada8","abstract_canon_sha256":"e43bfe7f790ceae6109758fbed7f8331f1b080934124a94499ce8247db7e91b1"},"schema_version":"1.0"},"canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","source":{"kind":"arxiv","id":"1206.1506","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1506","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1506v2","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1506","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"J7D2YQ45EDIR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"J7D2YQ45EDIRA2XG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"J7D2YQ45","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:J7D2YQ45EDIRA2XGHXGVG5G4XV","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-07T14:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"f3bc1f5648cb3472ba34f37bbb96426110e32999b05a2d251da0f81baaebada8","abstract_canon_sha256":"e43bfe7f790ceae6109758fbed7f8331f1b080934124a94499ce8247db7e91b1"},"schema_version":"1.0"},"canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:59.948496Z","signature_b64":"lrNUJUsORkcVfIKkPHWCQCAkNQsa+FC7/g8fnCIIqNe/CIX4K6+AH+39ps8aUsNODCs4le8st8F/qY6Ygt08BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","last_reissued_at":"2026-05-18T01:29:59.947998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:59.947998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1506","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sS+2qGOVztLiTZxRWmnf3FyW0F0PUAlD0SfYPIovOWMkb+1eYKAo3ezBd3akn/NBHMRjwipGRvuCrDoTKGyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:20:40.996629Z"},"content_sha256":"27b85d406fcac3699f08b554fb71719cc2a68a01e30fb830c89125c7c175ea9d","schema_version":"1.0","event_id":"sha256:27b85d406fcac3699f08b554fb71719cc2a68a01e30fb830c89125c7c175ea9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:J7D2YQ45EDIRA2XGHXGVG5G4XV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A framework for deflated and augmented Krylov subspace methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andr\\'e Gaul, J\\\"org Liesen, Martin H. Gutknecht, Reinhard Nabben","submitted_at":"2012-06-07T14:30:03Z","abstract_excerpt":"We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually different from preconditioning. Deflation (in the sense the term is used here) \"removes\" certain parts from the operator making it singular, while augmentation adds a subspace to the Krylov subspace (often the one that is generated by the singular operator); in contrast, preconditioning changes the spectrum of the operator without making it singular. Deflation a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1506","kind":"arxiv","version":2},"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":"2026-05-18T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XhBg1uSqi+Acx2A6tgbdj+Rnx3iRbvklQ1X/jdOSefLqAUPnN1GQwsHAu8PiVLOnppj8aEPUm5lH4qGunUF2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:20:40.997363Z"},"content_sha256":"5701c129ca6fdf3b6690ef05787d2f52ad4b67ab23d57700fc79c3fa562b502d","schema_version":"1.0","event_id":"sha256:5701c129ca6fdf3b6690ef05787d2f52ad4b67ab23d57700fc79c3fa562b502d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/bundle.json","state_url":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/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":"2026-06-09T17:20:40Z","links":{"resolver":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV","bundle":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/bundle.json","state":"https://pith.science/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7D2YQ45EDIRA2XGHXGVG5G4XV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J7D2YQ45EDIRA2XGHXGVG5G4XV","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":"e43bfe7f790ceae6109758fbed7f8331f1b080934124a94499ce8247db7e91b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-07T14:30:03Z","title_canon_sha256":"f3bc1f5648cb3472ba34f37bbb96426110e32999b05a2d251da0f81baaebada8"},"schema_version":"1.0","source":{"id":"1206.1506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1506","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1506v2","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1506","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"J7D2YQ45EDIR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"J7D2YQ45EDIRA2XG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"J7D2YQ45","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:5701c129ca6fdf3b6690ef05787d2f52ad4b67ab23d57700fc79c3fa562b502d","target":"graph","created_at":"2026-05-18T01:29:59Z","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 consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually different from preconditioning. Deflation (in the sense the term is used here) \"removes\" certain parts from the operator making it singular, while augmentation adds a subspace to the Krylov subspace (often the one that is generated by the singular operator); in contrast, preconditioning changes the spectrum of the operator without making it singular. Deflation a","authors_text":"Andr\\'e Gaul, J\\\"org Liesen, Martin H. Gutknecht, Reinhard Nabben","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-07T14:30:03Z","title":"A framework for deflated and augmented Krylov subspace methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1506","kind":"arxiv","version":2},"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":"sha256:27b85d406fcac3699f08b554fb71719cc2a68a01e30fb830c89125c7c175ea9d","target":"record","created_at":"2026-05-18T01:29:59Z","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":"e43bfe7f790ceae6109758fbed7f8331f1b080934124a94499ce8247db7e91b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-07T14:30:03Z","title_canon_sha256":"f3bc1f5648cb3472ba34f37bbb96426110e32999b05a2d251da0f81baaebada8"},"schema_version":"1.0","source":{"id":"1206.1506","kind":"arxiv","version":2}},"canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fc7ac439d20d1106ae63dcd5374dcbd51fc5bd1f7b8c199ff3fb485413497af","first_computed_at":"2026-05-18T01:29:59.947998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:59.947998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lrNUJUsORkcVfIKkPHWCQCAkNQsa+FC7/g8fnCIIqNe/CIX4K6+AH+39ps8aUsNODCs4le8st8F/qY6Ygt08BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:59.948496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27b85d406fcac3699f08b554fb71719cc2a68a01e30fb830c89125c7c175ea9d","sha256:5701c129ca6fdf3b6690ef05787d2f52ad4b67ab23d57700fc79c3fa562b502d"],"state_sha256":"d0d7b1a3b90dbcac7907b10f3da7996c3a5e272e8882c580de0d1d336ad5b143"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqNiuTrT9hmIx+V3EJapIvByrG30W1zfT6BjP62qEhg5R3d3CuLQIzo6M5HQ0YaVVJW0gIoG2AcZAb1J0FlFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:20:41.001824Z","bundle_sha256":"d438fbad4dca2a73a1f6337c4cf78e1d930c0750aa060ed71f851d693d73b783"}}