{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7WAZFQ4AK3DYYEVPMGWYZJNTUR","short_pith_number":"pith:7WAZFQ4A","canonical_record":{"source":{"id":"1603.08970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-29T21:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"bb60a22eb0de8baed2bebc7d0475c0ccb6560eff2106593513ffe2a82caad73d","abstract_canon_sha256":"ce9820b93ad46f7efd149a6f52c69ff2681e657354c7ec385520fdf997953240"},"schema_version":"1.0"},"canonical_sha256":"fd8192c38056c78c12af61ad8ca5b3a45fa8e03fcab1737c02e0f72e7d8757ac","source":{"kind":"arxiv","id":"1603.08970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08970","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08970v1","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08970","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"7WAZFQ4AK3DY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7WAZFQ4AK3DYYEVP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7WAZFQ4A","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7WAZFQ4AK3DYYEVPMGWYZJNTUR","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-29T21:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"bb60a22eb0de8baed2bebc7d0475c0ccb6560eff2106593513ffe2a82caad73d","abstract_canon_sha256":"ce9820b93ad46f7efd149a6f52c69ff2681e657354c7ec385520fdf997953240"},"schema_version":"1.0"},"canonical_sha256":"fd8192c38056c78c12af61ad8ca5b3a45fa8e03fcab1737c02e0f72e7d8757ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:04.134900Z","signature_b64":"dpMfNYmY0gj4/SHimctZFqRvA0m2peIJyOjn89164yOffG6C8J3zNT9XbYoe5TZHJ8y1onAdEai6wEnPTtt9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd8192c38056c78c12af61ad8ca5b3a45fa8e03fcab1737c02e0f72e7d8757ac","last_reissued_at":"2026-05-18T01:18:04.134225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:04.134225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08970","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":"2026-05-18T01:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHu8Q0qEHntTdhcqQF0NVwUEPzA3jpGljxCO4zIbuDg9lo6sxITV2RvSr9YuV9pHtD7gCCZxjpdM7apMi1mvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:03:20.367486Z"},"content_sha256":"6dd1acaa30f4813e83e5f3979f4b965caf63e79033532148e03d7cce06c6a6b8","schema_version":"1.0","event_id":"sha256:6dd1acaa30f4813e83e5f3979f4b965caf63e79033532148e03d7cce06c6a6b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7WAZFQ4AK3DYYEVPMGWYZJNTUR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multipreconditioned GMRES for Shifted Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Arvind K. Saibaba, Daniel Szyld, Peter Kitanidis, Scott Ladenheim, Tania Bakhos","submitted_at":"2016-03-29T21:10:15Z","abstract_excerpt":"An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08970","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":"2026-05-18T01:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLfaLManO8vb4Pr+6FPmbu1tLwqU8qzLnyCbqerPDcZwnwFDf+kC5gWP/cZIZXj57QHHoVx4emDx87k+QmWHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:03:20.367821Z"},"content_sha256":"cbb329a3aabf2736077000c59f136e3d2867b1b302ddfa8720be81a59a232546","schema_version":"1.0","event_id":"sha256:cbb329a3aabf2736077000c59f136e3d2867b1b302ddfa8720be81a59a232546"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR/bundle.json","state_url":"https://pith.science/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR/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":"2026-06-27T17:03:20Z","links":{"resolver":"https://pith.science/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR","bundle":"https://pith.science/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR/bundle.json","state":"https://pith.science/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7WAZFQ4AK3DYYEVPMGWYZJNTUR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7WAZFQ4AK3DYYEVPMGWYZJNTUR","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":"ce9820b93ad46f7efd149a6f52c69ff2681e657354c7ec385520fdf997953240","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-29T21:10:15Z","title_canon_sha256":"bb60a22eb0de8baed2bebc7d0475c0ccb6560eff2106593513ffe2a82caad73d"},"schema_version":"1.0","source":{"id":"1603.08970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08970","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08970v1","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08970","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"7WAZFQ4AK3DY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7WAZFQ4AK3DYYEVP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7WAZFQ4A","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:cbb329a3aabf2736077000c59f136e3d2867b1b302ddfa8720be81a59a232546","target":"graph","created_at":"2026-05-18T01:18:04Z","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":"An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different m","authors_text":"Arvind K. Saibaba, Daniel Szyld, Peter Kitanidis, Scott Ladenheim, Tania Bakhos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-29T21:10:15Z","title":"Multipreconditioned GMRES for Shifted Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08970","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":"sha256:6dd1acaa30f4813e83e5f3979f4b965caf63e79033532148e03d7cce06c6a6b8","target":"record","created_at":"2026-05-18T01:18:04Z","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":"ce9820b93ad46f7efd149a6f52c69ff2681e657354c7ec385520fdf997953240","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-03-29T21:10:15Z","title_canon_sha256":"bb60a22eb0de8baed2bebc7d0475c0ccb6560eff2106593513ffe2a82caad73d"},"schema_version":"1.0","source":{"id":"1603.08970","kind":"arxiv","version":1}},"canonical_sha256":"fd8192c38056c78c12af61ad8ca5b3a45fa8e03fcab1737c02e0f72e7d8757ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd8192c38056c78c12af61ad8ca5b3a45fa8e03fcab1737c02e0f72e7d8757ac","first_computed_at":"2026-05-18T01:18:04.134225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:04.134225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dpMfNYmY0gj4/SHimctZFqRvA0m2peIJyOjn89164yOffG6C8J3zNT9XbYoe5TZHJ8y1onAdEai6wEnPTtt9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:04.134900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dd1acaa30f4813e83e5f3979f4b965caf63e79033532148e03d7cce06c6a6b8","sha256:cbb329a3aabf2736077000c59f136e3d2867b1b302ddfa8720be81a59a232546"],"state_sha256":"6eb207e882c947cf18d98b92eda189ce091a68da9d9cd945034138608c1252b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P398K8sHV2uaoyhrM+VgCqEtjTdu8Gq5gq2k/Ob13kCr7eRlN52oXtKtaZN45U+ukN7MSIgCi7bhOK8NQA/0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T17:03:20.369771Z","bundle_sha256":"6c65297569a0dbde820636f2c1b300c12fa5d65063f5a3ad672395f923ecc3a1"}}