{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:REOKEWRPZX5N6VTEIZ3CFSDO62","short_pith_number":"pith:REOKEWRP","canonical_record":{"source":{"id":"1304.1864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-04-06T08:14:25Z","cross_cats_sorted":["cs.MS"],"title_canon_sha256":"83279455676f5b4f5ecad47bcbae416ea7044a45964110ef8a412cb67223b2f8","abstract_canon_sha256":"31b771613ade26253a6be1928cd649bedb0e487858c1ac404ce869290b5069dd"},"schema_version":"1.0"},"canonical_sha256":"891ca25a2fcdfadf5664467622c86ef6ae97417f314c4630ea60ff3ebeccbe00","source":{"kind":"arxiv","id":"1304.1864","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1864","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1864v3","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1864","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"REOKEWRPZX5N","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"REOKEWRPZX5N6VTE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"REOKEWRP","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:REOKEWRPZX5N6VTEIZ3CFSDO62","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-04-06T08:14:25Z","cross_cats_sorted":["cs.MS"],"title_canon_sha256":"83279455676f5b4f5ecad47bcbae416ea7044a45964110ef8a412cb67223b2f8","abstract_canon_sha256":"31b771613ade26253a6be1928cd649bedb0e487858c1ac404ce869290b5069dd"},"schema_version":"1.0"},"canonical_sha256":"891ca25a2fcdfadf5664467622c86ef6ae97417f314c4630ea60ff3ebeccbe00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:09.089540Z","signature_b64":"xMcz+GxlHSK6ZddNwUQMuHoFeLCNG00nBL4JPsay9qjEbKy2ATsEH31LwleAkdU/rKtCszQqscLYlZFj/v6bCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"891ca25a2fcdfadf5664467622c86ef6ae97417f314c4630ea60ff3ebeccbe00","last_reissued_at":"2026-05-18T03:20:09.088995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:09.088995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1864","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7AVN23WKTW4aUIW4+uRKZA6c7bFXELs86Sh98ZpJ0hHdVT7BA6xjXexfC0Eymiung2H8uR8Ec7cxdybnCuOHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:06:37.611920Z"},"content_sha256":"2e43e6eb684d465e0fc4632fdefed7eb49e2b12263e91fb460b123b7de6b258f","schema_version":"1.0","event_id":"sha256:2e43e6eb684d465e0fc4632fdefed7eb49e2b12263e91fb460b123b7de6b258f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:REOKEWRPZX5N6VTEIZ3CFSDO62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Accuracy and Parallelism for MRRR-based Eigensolvers -- A Mixed Precision Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS"],"primary_cat":"cs.NA","authors_text":"((1) AICES, (2) Universidad Jaume I), Enrique Quintana-Orti (2), Matthias Petschow (1), Paolo Bientinesi (1), RWTH Aachen","submitted_at":"2013-04-06T08:14:25Z","abstract_excerpt":"The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to tridiagonal form. For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR) is among the fastest methods. Although fast, the solvers based on MRRR do not deliver the same accuracy as competing methods like Divide & Conquer or the QR algorithm. In this paper, we demonstrate that the use of mixed precisions leads to improved accuracy of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1864","kind":"arxiv","version":3},"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":"2026-05-18T03:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/zIXkCVcKwF4MB6frvPRrtVB3afTmvNQlXyvW2nBi+/v0RjUpTjo7BbxjXcYwRqox6Gb2SIC3LG/inzpt5/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:06:37.612414Z"},"content_sha256":"c45f9df0897ee650a596588f5e78f8bf3682ac45913a486dfa4a073c4ff0a5f4","schema_version":"1.0","event_id":"sha256:c45f9df0897ee650a596588f5e78f8bf3682ac45913a486dfa4a073c4ff0a5f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REOKEWRPZX5N6VTEIZ3CFSDO62/bundle.json","state_url":"https://pith.science/pith/REOKEWRPZX5N6VTEIZ3CFSDO62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REOKEWRPZX5N6VTEIZ3CFSDO62/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":"2026-05-27T08:06:37Z","links":{"resolver":"https://pith.science/pith/REOKEWRPZX5N6VTEIZ3CFSDO62","bundle":"https://pith.science/pith/REOKEWRPZX5N6VTEIZ3CFSDO62/bundle.json","state":"https://pith.science/pith/REOKEWRPZX5N6VTEIZ3CFSDO62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REOKEWRPZX5N6VTEIZ3CFSDO62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:REOKEWRPZX5N6VTEIZ3CFSDO62","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":"31b771613ade26253a6be1928cd649bedb0e487858c1ac404ce869290b5069dd","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-04-06T08:14:25Z","title_canon_sha256":"83279455676f5b4f5ecad47bcbae416ea7044a45964110ef8a412cb67223b2f8"},"schema_version":"1.0","source":{"id":"1304.1864","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1864","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1864v3","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1864","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"REOKEWRPZX5N","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"REOKEWRPZX5N6VTE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"REOKEWRP","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:c45f9df0897ee650a596588f5e78f8bf3682ac45913a486dfa4a073c4ff0a5f4","target":"graph","created_at":"2026-05-18T03:20:09Z","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":"The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to tridiagonal form. For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR) is among the fastest methods. Although fast, the solvers based on MRRR do not deliver the same accuracy as competing methods like Divide & Conquer or the QR algorithm. In this paper, we demonstrate that the use of mixed precisions leads to improved accuracy of","authors_text":"((1) AICES, (2) Universidad Jaume I), Enrique Quintana-Orti (2), Matthias Petschow (1), Paolo Bientinesi (1), RWTH Aachen","cross_cats":["cs.MS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-04-06T08:14:25Z","title":"Improved Accuracy and Parallelism for MRRR-based Eigensolvers -- A Mixed Precision Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1864","kind":"arxiv","version":3},"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":"sha256:2e43e6eb684d465e0fc4632fdefed7eb49e2b12263e91fb460b123b7de6b258f","target":"record","created_at":"2026-05-18T03:20:09Z","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":"31b771613ade26253a6be1928cd649bedb0e487858c1ac404ce869290b5069dd","cross_cats_sorted":["cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-04-06T08:14:25Z","title_canon_sha256":"83279455676f5b4f5ecad47bcbae416ea7044a45964110ef8a412cb67223b2f8"},"schema_version":"1.0","source":{"id":"1304.1864","kind":"arxiv","version":3}},"canonical_sha256":"891ca25a2fcdfadf5664467622c86ef6ae97417f314c4630ea60ff3ebeccbe00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"891ca25a2fcdfadf5664467622c86ef6ae97417f314c4630ea60ff3ebeccbe00","first_computed_at":"2026-05-18T03:20:09.088995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:09.088995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xMcz+GxlHSK6ZddNwUQMuHoFeLCNG00nBL4JPsay9qjEbKy2ATsEH31LwleAkdU/rKtCszQqscLYlZFj/v6bCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:09.089540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1864","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e43e6eb684d465e0fc4632fdefed7eb49e2b12263e91fb460b123b7de6b258f","sha256:c45f9df0897ee650a596588f5e78f8bf3682ac45913a486dfa4a073c4ff0a5f4"],"state_sha256":"4cd7f8e6b67d4fe5dbf8707534704a20d0fbc7c80cd6728363a4271b17ce0560"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZRApfO5s9Yc07Z8L4BPqX0VDcgY706y0L/T9epa6hmuJQMzJfaO/XyDOjBJ/vhp1pBdaSMXGidYfO3eFhKsDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:06:37.615877Z","bundle_sha256":"fe4614c5d5717d08c97c189e5f799293269ffa65f6a181139e3b8a5cb4e667ce"}}