{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:A4Q4AV7OZNZSQVL7QWJGKY7U4K","short_pith_number":"pith:A4Q4AV7O","canonical_record":{"source":{"id":"1205.2107","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2012-05-09T21:20:55Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"31ca2d22c0499f5c9813d69a52041ee3c269cc98597b5d3f2970594362895bd8","abstract_canon_sha256":"3a88a8ddab36bf908caf6293100bec00336d7fcfcd96db48d82b0f5bf374eb08"},"schema_version":"1.0"},"canonical_sha256":"0721c057eecb7328557f85926563f4e29a98331fd64cd6e203e2a164eee7a780","source":{"kind":"arxiv","id":"1205.2107","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2107","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2107v2","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2107","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"A4Q4AV7OZNZS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A4Q4AV7OZNZSQVL7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A4Q4AV7O","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:A4Q4AV7OZNZSQVL7QWJGKY7U4K","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2107","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2012-05-09T21:20:55Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"31ca2d22c0499f5c9813d69a52041ee3c269cc98597b5d3f2970594362895bd8","abstract_canon_sha256":"3a88a8ddab36bf908caf6293100bec00336d7fcfcd96db48d82b0f5bf374eb08"},"schema_version":"1.0"},"canonical_sha256":"0721c057eecb7328557f85926563f4e29a98331fd64cd6e203e2a164eee7a780","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:47.083144Z","signature_b64":"KSu9sQviVwoeOzubMEDxNk3Yd/DJlT4QZ9RJQtnuz8xstl8qFYXoScPXCaRvmgfNzbqxCIxsBG6XsytMRFTrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0721c057eecb7328557f85926563f4e29a98331fd64cd6e203e2a164eee7a780","last_reissued_at":"2026-05-18T03:44:47.082382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:47.082382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2107","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":"2026-05-18T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xJjhO1p/NI7vseRpUjgdy85gexn62t+1xG97aA12rhOJIeTFU8DLPsCUCWJKnU8tQyzJ9sPx3TWnpRqRD2cgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:16:23.396402Z"},"content_sha256":"a144e9db3c3bb673a755d2b6f966213d07f5675ba9bc7423072787c0c347d7ae","schema_version":"1.0","event_id":"sha256:a144e9db3c3bb673a755d2b6f966213d07f5675ba9bc7423072787c0c347d7ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:A4Q4AV7OZNZSQVL7QWJGKY7U4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High-Performance Solvers for Dense Hermitian Eigenproblems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"cs.MS","authors_text":"Elmar Peise (1), Matthias Petschow (1), Paolo Bientinesi (1) ((1) AICES, RWTH Aachen)","submitted_at":"2012-05-09T21:20:55Z","abstract_excerpt":"We introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the Algorithm of Multiple Relatively Robust Representations - referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is desi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2107","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":"2026-05-18T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xiaS4A/uXLhawofrNDCWcQV9dS5RDxuRu20/PLfgAXmGdt3zGHDbrNFN/GaF29Qs/3xO/5Nb9ZgtCjq2d8/yAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:16:23.397026Z"},"content_sha256":"9ca740a4e3c11f4396b3a3aadfc1e2a98fd58cff34ccb068e3c7b9abf5fd2acc","schema_version":"1.0","event_id":"sha256:9ca740a4e3c11f4396b3a3aadfc1e2a98fd58cff34ccb068e3c7b9abf5fd2acc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K/bundle.json","state_url":"https://pith.science/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K/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":"2026-06-09T01:16:23Z","links":{"resolver":"https://pith.science/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K","bundle":"https://pith.science/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K/bundle.json","state":"https://pith.science/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4Q4AV7OZNZSQVL7QWJGKY7U4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A4Q4AV7OZNZSQVL7QWJGKY7U4K","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":"3a88a8ddab36bf908caf6293100bec00336d7fcfcd96db48d82b0f5bf374eb08","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2012-05-09T21:20:55Z","title_canon_sha256":"31ca2d22c0499f5c9813d69a52041ee3c269cc98597b5d3f2970594362895bd8"},"schema_version":"1.0","source":{"id":"1205.2107","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2107","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2107v2","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2107","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"A4Q4AV7OZNZS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A4Q4AV7OZNZSQVL7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A4Q4AV7O","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:9ca740a4e3c11f4396b3a3aadfc1e2a98fd58cff34ccb068e3c7b9abf5fd2acc","target":"graph","created_at":"2026-05-18T03:44:47Z","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 introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the Algorithm of Multiple Relatively Robust Representations - referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is desi","authors_text":"Elmar Peise (1), Matthias Petschow (1), Paolo Bientinesi (1) ((1) AICES, RWTH Aachen)","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2012-05-09T21:20:55Z","title":"High-Performance Solvers for Dense Hermitian Eigenproblems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2107","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:a144e9db3c3bb673a755d2b6f966213d07f5675ba9bc7423072787c0c347d7ae","target":"record","created_at":"2026-05-18T03:44:47Z","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":"3a88a8ddab36bf908caf6293100bec00336d7fcfcd96db48d82b0f5bf374eb08","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2012-05-09T21:20:55Z","title_canon_sha256":"31ca2d22c0499f5c9813d69a52041ee3c269cc98597b5d3f2970594362895bd8"},"schema_version":"1.0","source":{"id":"1205.2107","kind":"arxiv","version":2}},"canonical_sha256":"0721c057eecb7328557f85926563f4e29a98331fd64cd6e203e2a164eee7a780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0721c057eecb7328557f85926563f4e29a98331fd64cd6e203e2a164eee7a780","first_computed_at":"2026-05-18T03:44:47.082382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:47.082382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KSu9sQviVwoeOzubMEDxNk3Yd/DJlT4QZ9RJQtnuz8xstl8qFYXoScPXCaRvmgfNzbqxCIxsBG6XsytMRFTrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:47.083144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2107","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a144e9db3c3bb673a755d2b6f966213d07f5675ba9bc7423072787c0c347d7ae","sha256:9ca740a4e3c11f4396b3a3aadfc1e2a98fd58cff34ccb068e3c7b9abf5fd2acc"],"state_sha256":"9f412204cb0b96196b63ffea5fb0adc5bdebacf202cd2e7665490e356942efea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cI+nzApS1/R3eq3nT1Nur67gmVTHN3/m7R4nTSv1fKwyJ7krcrdReAcQmf6SIa4jxo8je9ATL2U3DiVDlDMyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:16:23.401236Z","bundle_sha256":"e25d4d1a711c7ec851cbf242061894d45e51b0a0a6c9da2bced84e2d8a958459"}}