{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:W7PWUQZHXAQ2ONADCAK6R64SWQ","short_pith_number":"pith:W7PWUQZH","canonical_record":{"source":{"id":"1209.1910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-09-10T09:04:13Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"de72d750862f07111d1ab08bfb3a10e82adce017acd849e15c3b5000cff29db7","abstract_canon_sha256":"a156a7a713cd1d0c2bd78c64f34453d4e541e67d1ab8ba3d3027dae205f5baea"},"schema_version":"1.0"},"canonical_sha256":"b7df6a4327b821a734031015e8fb92b41303147977fe9c0ea670fe66aa7949aa","source":{"kind":"arxiv","id":"1209.1910","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1910","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1910v1","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1910","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"W7PWUQZHXAQ2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7PWUQZHXAQ2ONAD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7PWUQZH","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:W7PWUQZHXAQ2ONADCAK6R64SWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-09-10T09:04:13Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"de72d750862f07111d1ab08bfb3a10e82adce017acd849e15c3b5000cff29db7","abstract_canon_sha256":"a156a7a713cd1d0c2bd78c64f34453d4e541e67d1ab8ba3d3027dae205f5baea"},"schema_version":"1.0"},"canonical_sha256":"b7df6a4327b821a734031015e8fb92b41303147977fe9c0ea670fe66aa7949aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:54.085797Z","signature_b64":"nb4zsCAhXthrStSLD0qu7MOu0vDPhBCs/HRNBUz+t7NPdVAUhYWg2rIH//1qNc5HdwFkHFWrvh4qZ+VajBgSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7df6a4327b821a734031015e8fb92b41303147977fe9c0ea670fe66aa7949aa","last_reissued_at":"2026-05-18T03:45:54.085331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:54.085331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1910","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":"2026-05-18T03:45:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lqvs4/HxiZmS0Pv5yO/b6UTdOTXmh4+Os7okaRAo7ujNJAq5RjP/n+IuWRPYwJpHLxJy4CSdZmgZXnrHNpdGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:08:47.780603Z"},"content_sha256":"f498ce599b7b0f8a9a3e40b752ebfb4c14f4a004d07c2e557319fe7cecea5a0e","schema_version":"1.0","event_id":"sha256:f498ce599b7b0f8a9a3e40b752ebfb4c14f4a004d07c2e557319fe7cecea5a0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:W7PWUQZHXAQ2ONADCAK6R64SWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Implementation and Evaluation of Inverse Iteration Algorithm with compact WY Orthogonalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura","submitted_at":"2012-09-10T09:04:13Z","abstract_excerpt":"A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse iteration. This algorithm is sequential and causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the orthogonalization process of the inverse iteration with the Householder transformation. This change results in drastically reduced synchronization cost in parallel computing. The new algorithm is evalua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1910","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":"2026-05-18T03:45:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6AqGIZ4wiZpBxDr4px4D5vZsflXXwrMINhAR3jXD69dRtNLRmZ7YDZ4HEhAZspCWtWgFx7urqgwJjpz77PDSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:08:47.780955Z"},"content_sha256":"5cb75a87e25f736ad38f7ae1ee29baefa61cb10e4f72aa260cab29209e60469f","schema_version":"1.0","event_id":"sha256:5cb75a87e25f736ad38f7ae1ee29baefa61cb10e4f72aa260cab29209e60469f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ/bundle.json","state_url":"https://pith.science/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ/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":"2026-06-23T17:08:47Z","links":{"resolver":"https://pith.science/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ","bundle":"https://pith.science/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ/bundle.json","state":"https://pith.science/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7PWUQZHXAQ2ONADCAK6R64SWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W7PWUQZHXAQ2ONADCAK6R64SWQ","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":"a156a7a713cd1d0c2bd78c64f34453d4e541e67d1ab8ba3d3027dae205f5baea","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-09-10T09:04:13Z","title_canon_sha256":"de72d750862f07111d1ab08bfb3a10e82adce017acd849e15c3b5000cff29db7"},"schema_version":"1.0","source":{"id":"1209.1910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1910","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1910v1","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1910","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"W7PWUQZHXAQ2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7PWUQZHXAQ2ONAD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7PWUQZH","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:5cb75a87e25f736ad38f7ae1ee29baefa61cb10e4f72aa260cab29209e60469f","target":"graph","created_at":"2026-05-18T03:45:54Z","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":"A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse iteration. This algorithm is sequential and causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the orthogonalization process of the inverse iteration with the Householder transformation. This change results in drastically reduced synchronization cost in parallel computing. The new algorithm is evalua","authors_text":"Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-09-10T09:04:13Z","title":"On Implementation and Evaluation of Inverse Iteration Algorithm with compact WY Orthogonalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1910","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:f498ce599b7b0f8a9a3e40b752ebfb4c14f4a004d07c2e557319fe7cecea5a0e","target":"record","created_at":"2026-05-18T03:45:54Z","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":"a156a7a713cd1d0c2bd78c64f34453d4e541e67d1ab8ba3d3027dae205f5baea","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-09-10T09:04:13Z","title_canon_sha256":"de72d750862f07111d1ab08bfb3a10e82adce017acd849e15c3b5000cff29db7"},"schema_version":"1.0","source":{"id":"1209.1910","kind":"arxiv","version":1}},"canonical_sha256":"b7df6a4327b821a734031015e8fb92b41303147977fe9c0ea670fe66aa7949aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7df6a4327b821a734031015e8fb92b41303147977fe9c0ea670fe66aa7949aa","first_computed_at":"2026-05-18T03:45:54.085331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:54.085331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nb4zsCAhXthrStSLD0qu7MOu0vDPhBCs/HRNBUz+t7NPdVAUhYWg2rIH//1qNc5HdwFkHFWrvh4qZ+VajBgSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:54.085797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f498ce599b7b0f8a9a3e40b752ebfb4c14f4a004d07c2e557319fe7cecea5a0e","sha256:5cb75a87e25f736ad38f7ae1ee29baefa61cb10e4f72aa260cab29209e60469f"],"state_sha256":"b39b85592d471aa6d7434a31963668511933793285ac498a7b0064b9a8851c92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNavue9QOdk7HWh3Bbo98jfDzK3iYOLo42hpsV5UAjvKRDsbLMSNknOv66QsDc2I2Cfv4IRjrkNsc/qn/o9tCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:08:47.782939Z","bundle_sha256":"d88ef718c324a1fb936824a7e4cabc1e2aac7ac80dbbe7a1e436e872f800d376"}}