{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JETLATKFZDCPTJGLHFK2TEG2RN","short_pith_number":"pith:JETLATKF","canonical_record":{"source":{"id":"1907.10550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-24T16:42:34Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"3541cf2e412101740d1a5dc4e7358bbaff1e71f6e7e38c141f0c2eb158d360b4","abstract_canon_sha256":"0347c18d599a4bc9992cea944d42a82f91594f2a33b94f39841f2834a87282b4"},"schema_version":"1.0"},"canonical_sha256":"4926b04d45c8c4f9a4cb3955a990da8b48638b6db7c2832ce90c44c109b8e760","source":{"kind":"arxiv","id":"1907.10550","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10550","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10550v2","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10550","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"JETLATKFZDCP","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"pith_short_16","alias_value":"JETLATKFZDCPTJGL","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"pith_short_8","alias_value":"JETLATKF","created_at":"2026-07-05T00:42:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JETLATKFZDCPTJGLHFK2TEG2RN","target":"record","payload":{"canonical_record":{"source":{"id":"1907.10550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-24T16:42:34Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"3541cf2e412101740d1a5dc4e7358bbaff1e71f6e7e38c141f0c2eb158d360b4","abstract_canon_sha256":"0347c18d599a4bc9992cea944d42a82f91594f2a33b94f39841f2834a87282b4"},"schema_version":"1.0"},"canonical_sha256":"4926b04d45c8c4f9a4cb3955a990da8b48638b6db7c2832ce90c44c109b8e760","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:42:19.871939Z","signature_b64":"7Jvxu+AnRI/6QexRgKAdGek+1Yudczk80eqQ9PPKirThHLepMIRt6heDzg0R4/g7GEELsShP3Ju3HaL0KbynCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4926b04d45c8c4f9a4cb3955a990da8b48638b6db7c2832ce90c44c109b8e760","last_reissued_at":"2026-07-05T00:42:19.871505Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:42:19.871505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.10550","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":"2026-07-05T00:42:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXCO5wkiEZkSny8gFOnBBt6uvQSDIX1EJ5D8ZYNKHTLq6KI3Sr15ECIkGiCLkHbm6dAQridOZk40nJRXd6FYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T17:47:55.600367Z"},"content_sha256":"f32e6818b144881098e0caf7d6045b46c44b7619b59c45f2947056fbeb7d702b","schema_version":"1.0","event_id":"sha256:f32e6818b144881098e0caf7d6045b46c44b7619b59c45f2947056fbeb7d702b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JETLATKFZDCPTJGLHFK2TEG2RN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploiting variable precision in GMRES","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"David Titley-Peloquin, Ehouarn Simon, Philippe Toint, Serge Gratton","submitted_at":"2019-07-24T16:42:34Z","abstract_excerpt":"We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting the convergence rate or final accuracy achieved by the iterates. Our analysis explicitly takes into account the resulting loss of orthogonality in the Arnoldi vectors. We also show how inexact matrix-vector products can be incorporated into this setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10550","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.10550/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:42:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CbyHBjcVUA5Ix+2Hle23ecfgdNbIqQbO1yyj6wPVi3wea5861NEXQQAC7+M0kpQ7L5zyeqj1bPMObh28T+KlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T17:47:55.600756Z"},"content_sha256":"0e9b579d89a51bc0e6380c2ed3bdb836e29a8d6aef36cdade774844d96f7c45f","schema_version":"1.0","event_id":"sha256:0e9b579d89a51bc0e6380c2ed3bdb836e29a8d6aef36cdade774844d96f7c45f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JETLATKFZDCPTJGLHFK2TEG2RN/bundle.json","state_url":"https://pith.science/pith/JETLATKFZDCPTJGLHFK2TEG2RN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JETLATKFZDCPTJGLHFK2TEG2RN/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":"2026-07-06T17:47:55Z","links":{"resolver":"https://pith.science/pith/JETLATKFZDCPTJGLHFK2TEG2RN","bundle":"https://pith.science/pith/JETLATKFZDCPTJGLHFK2TEG2RN/bundle.json","state":"https://pith.science/pith/JETLATKFZDCPTJGLHFK2TEG2RN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JETLATKFZDCPTJGLHFK2TEG2RN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JETLATKFZDCPTJGLHFK2TEG2RN","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":"0347c18d599a4bc9992cea944d42a82f91594f2a33b94f39841f2834a87282b4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-24T16:42:34Z","title_canon_sha256":"3541cf2e412101740d1a5dc4e7358bbaff1e71f6e7e38c141f0c2eb158d360b4"},"schema_version":"1.0","source":{"id":"1907.10550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10550","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10550v2","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10550","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"JETLATKFZDCP","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"pith_short_16","alias_value":"JETLATKFZDCPTJGL","created_at":"2026-07-05T00:42:19Z"},{"alias_kind":"pith_short_8","alias_value":"JETLATKF","created_at":"2026-07-05T00:42:19Z"}],"graph_snapshots":[{"event_id":"sha256:0e9b579d89a51bc0e6380c2ed3bdb836e29a8d6aef36cdade774844d96f7c45f","target":"graph","created_at":"2026-07-05T00:42:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.10550/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting the convergence rate or final accuracy achieved by the iterates. Our analysis explicitly takes into account the resulting loss of orthogonality in the Arnoldi vectors. We also show how inexact matrix-vector products can be incorporated into this setting.","authors_text":"David Titley-Peloquin, Ehouarn Simon, Philippe Toint, Serge Gratton","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-24T16:42:34Z","title":"Exploiting variable precision in GMRES"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10550","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:f32e6818b144881098e0caf7d6045b46c44b7619b59c45f2947056fbeb7d702b","target":"record","created_at":"2026-07-05T00:42:19Z","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":"0347c18d599a4bc9992cea944d42a82f91594f2a33b94f39841f2834a87282b4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-07-24T16:42:34Z","title_canon_sha256":"3541cf2e412101740d1a5dc4e7358bbaff1e71f6e7e38c141f0c2eb158d360b4"},"schema_version":"1.0","source":{"id":"1907.10550","kind":"arxiv","version":2}},"canonical_sha256":"4926b04d45c8c4f9a4cb3955a990da8b48638b6db7c2832ce90c44c109b8e760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4926b04d45c8c4f9a4cb3955a990da8b48638b6db7c2832ce90c44c109b8e760","first_computed_at":"2026-07-05T00:42:19.871505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:42:19.871505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Jvxu+AnRI/6QexRgKAdGek+1Yudczk80eqQ9PPKirThHLepMIRt6heDzg0R4/g7GEELsShP3Ju3HaL0KbynCw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:42:19.871939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.10550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f32e6818b144881098e0caf7d6045b46c44b7619b59c45f2947056fbeb7d702b","sha256:0e9b579d89a51bc0e6380c2ed3bdb836e29a8d6aef36cdade774844d96f7c45f"],"state_sha256":"a4f318f567900e2cc0e551a12f54ec953ea0d40937aae855993df91f3f9ad206"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PYv/CX6SZnig28jjeH8hYaIu2k+8rvRN17gTglIBtccGqNfHHRfwo8xc6qXzAMTt1w1uHXxJnu3ynB8KATKYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T17:47:55.602820Z","bundle_sha256":"588661690e73daa8cd01c2f40fcb4113ae32cefcad4ad17f8b6ad62bcb0bbed4"}}