{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6IYFBX57YSF7NI4ZSTEJ6TI7ND","short_pith_number":"pith:6IYFBX57","canonical_record":{"source":{"id":"1505.06864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-05-26T09:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"92e7ef5c5fbdae4f0134711efcbe436884fbe3b869c1851a5409b9887e6cc88e","abstract_canon_sha256":"71ae37581f351f496b7e6ea7a5f4910017ee1b5e0506ba661da85b063b7af623"},"schema_version":"1.0"},"canonical_sha256":"f23050dfbfc48bf6a39994c89f4d1f68f0c5c804f3439f9c85285acb00dfb578","source":{"kind":"arxiv","id":"1505.06864","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06864","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06864v1","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06864","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"6IYFBX57YSF7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6IYFBX57YSF7NI4Z","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6IYFBX57","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6IYFBX57YSF7NI4ZSTEJ6TI7ND","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-05-26T09:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"92e7ef5c5fbdae4f0134711efcbe436884fbe3b869c1851a5409b9887e6cc88e","abstract_canon_sha256":"71ae37581f351f496b7e6ea7a5f4910017ee1b5e0506ba661da85b063b7af623"},"schema_version":"1.0"},"canonical_sha256":"f23050dfbfc48bf6a39994c89f4d1f68f0c5c804f3439f9c85285acb00dfb578","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:27.723966Z","signature_b64":"wF69LGwG6yvXeRLJl52vp0T1lyD1CQHEssj9vW8TZqDDFNCDEKLP7gd8i9Fq8/tmz7K3V3cZ6fkvD0DQ5ORzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f23050dfbfc48bf6a39994c89f4d1f68f0c5c804f3439f9c85285acb00dfb578","last_reissued_at":"2026-05-18T02:03:27.723577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:27.723577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06864","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":"2026-05-18T02:03:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lV9iB11EPfz9MZPH+Yzv/dob3ebMDGQG2z20yKRW3AfeWVM9i3qhbHhNHk9/7voDSCPPkjbzDn/+Lu3c+2HxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:45:45.846749Z"},"content_sha256":"b844d92d39f766c7de47140865b1d5b2c66d71e96fc635253bc6a5159570c542","schema_version":"1.0","event_id":"sha256:b844d92d39f766c7de47140865b1d5b2c66d71e96fc635253bc6a5159570c542"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6IYFBX57YSF7NI4ZSTEJ6TI7ND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decomposition method for block-tridiagonal matrix systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"E. R. Nugumanov, P. A. Belov, S. L. Yakovlev","submitted_at":"2015-05-26T09:12:43Z","abstract_excerpt":"The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations for its parallel and serial parts. The computational speedup with respect to the conventional sequential Thomas algorithm is assessed for various types of the application of the method. It is observed that the maximum of the analytical speedup for a given number of blocks on the diagonal is achieved at some finite number of parallel processors. The values of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06864","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":"2026-05-18T02:03:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaZqvV0EQMcvt8xHWB46wr8v6RSoAqbsQ05gYOCXD5DY1mH4LoihhOrbaij+xywwgkKLNjpzh+SReXliRxOkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:45:45.847087Z"},"content_sha256":"da86eea3640cba7368ef0448b25705caf4b88b59ac1b70798f308f5aabf9e286","schema_version":"1.0","event_id":"sha256:da86eea3640cba7368ef0448b25705caf4b88b59ac1b70798f308f5aabf9e286"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND/bundle.json","state_url":"https://pith.science/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND/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":"2026-06-01T07:45:45Z","links":{"resolver":"https://pith.science/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND","bundle":"https://pith.science/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND/bundle.json","state":"https://pith.science/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IYFBX57YSF7NI4ZSTEJ6TI7ND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6IYFBX57YSF7NI4ZSTEJ6TI7ND","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":"71ae37581f351f496b7e6ea7a5f4910017ee1b5e0506ba661da85b063b7af623","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-05-26T09:12:43Z","title_canon_sha256":"92e7ef5c5fbdae4f0134711efcbe436884fbe3b869c1851a5409b9887e6cc88e"},"schema_version":"1.0","source":{"id":"1505.06864","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06864","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06864v1","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06864","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"6IYFBX57YSF7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6IYFBX57YSF7NI4Z","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6IYFBX57","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:da86eea3640cba7368ef0448b25705caf4b88b59ac1b70798f308f5aabf9e286","target":"graph","created_at":"2026-05-18T02:03:27Z","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 decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations for its parallel and serial parts. The computational speedup with respect to the conventional sequential Thomas algorithm is assessed for various types of the application of the method. It is observed that the maximum of the analytical speedup for a given number of blocks on the diagonal is achieved at some finite number of parallel processors. The values of t","authors_text":"E. R. Nugumanov, P. A. Belov, S. L. Yakovlev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-05-26T09:12:43Z","title":"Decomposition method for block-tridiagonal matrix systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06864","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:b844d92d39f766c7de47140865b1d5b2c66d71e96fc635253bc6a5159570c542","target":"record","created_at":"2026-05-18T02:03:27Z","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":"71ae37581f351f496b7e6ea7a5f4910017ee1b5e0506ba661da85b063b7af623","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-05-26T09:12:43Z","title_canon_sha256":"92e7ef5c5fbdae4f0134711efcbe436884fbe3b869c1851a5409b9887e6cc88e"},"schema_version":"1.0","source":{"id":"1505.06864","kind":"arxiv","version":1}},"canonical_sha256":"f23050dfbfc48bf6a39994c89f4d1f68f0c5c804f3439f9c85285acb00dfb578","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f23050dfbfc48bf6a39994c89f4d1f68f0c5c804f3439f9c85285acb00dfb578","first_computed_at":"2026-05-18T02:03:27.723577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:27.723577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wF69LGwG6yvXeRLJl52vp0T1lyD1CQHEssj9vW8TZqDDFNCDEKLP7gd8i9Fq8/tmz7K3V3cZ6fkvD0DQ5ORzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:27.723966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06864","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b844d92d39f766c7de47140865b1d5b2c66d71e96fc635253bc6a5159570c542","sha256:da86eea3640cba7368ef0448b25705caf4b88b59ac1b70798f308f5aabf9e286"],"state_sha256":"5edb4ced87ce99b8fb5e6cb5a9384f87e47a9b55e373da1fb06d9a5efe061c80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4LPIDTkB1S42sNKr8H1jcpkF6jurgflMMtZBNPaRRonYLUq1Kt7U6ihKkp3DXBVyBWpDgF/nsEAfW9ZnB/NAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:45:45.849077Z","bundle_sha256":"c816b798ac3859b3b37522ce51a3a40c7a4fb5ced7b48bc953cce9de99c08655"}}