{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A4WRIHOVSXKD6GE2W7FNI4B7SI","short_pith_number":"pith:A4WRIHOV","canonical_record":{"source":{"id":"1805.08990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-23T07:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"2b3062b07643019359ce72d2d28a043a81f285e28ede4d136ef7d329ae14b434","abstract_canon_sha256":"342a3c6709a04fea206b6f5baf62d798ee166153cc894c34fe0ee1886afe25e6"},"schema_version":"1.0"},"canonical_sha256":"072d141dd595d43f189ab7cad4703f92084a36f34a383e1e26eb3696a82f3a7a","source":{"kind":"arxiv","id":"1805.08990","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08990","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08990v2","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08990","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"A4WRIHOVSXKD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A4WRIHOVSXKD6GE2","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A4WRIHOV","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A4WRIHOVSXKD6GE2W7FNI4B7SI","target":"record","payload":{"canonical_record":{"source":{"id":"1805.08990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-23T07:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"2b3062b07643019359ce72d2d28a043a81f285e28ede4d136ef7d329ae14b434","abstract_canon_sha256":"342a3c6709a04fea206b6f5baf62d798ee166153cc894c34fe0ee1886afe25e6"},"schema_version":"1.0"},"canonical_sha256":"072d141dd595d43f189ab7cad4703f92084a36f34a383e1e26eb3696a82f3a7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:44.815621Z","signature_b64":"HuY98AwsdrAyTE3nGFOhbc+4YppCZF0ZAden47iHb/hnDDw+RAFjQNX52sMAsHp7Oe5ZMAL+0lhzd0t7OnnvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"072d141dd595d43f189ab7cad4703f92084a36f34a383e1e26eb3696a82f3a7a","last_reissued_at":"2026-05-18T00:02:44.815190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:44.815190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.08990","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":"2026-05-18T00:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhW5ur+k/v5PQ0v6e4C7m948s220YRy/f+jwJFhSIm2P6HjGw27ryZCrqndKoxX28FmssCvFI/jPWK9HjLp0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:53:24.428876Z"},"content_sha256":"1a2b0314b2f3c232efff3afef04ec518189bf6e3b5e927a658364980b05c864b","schema_version":"1.0","event_id":"sha256:1a2b0314b2f3c232efff3afef04ec518189bf6e3b5e927a658364980b05c864b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A4WRIHOVSXKD6GE2W7FNI4B7SI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"GPU acceleration of splitting schemes applied to differential matrix equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hermann Mena, Lena-Maria Pfurtscheller, Tony Stillfjord","submitted_at":"2018-05-23T07:37:13Z","abstract_excerpt":"We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08990","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":"2026-05-18T00:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7yi5VcKipj00s/+F+f591oY9gjQjNdaKYPX9wk/A6GLeRkeqEzz1oMa3H0rCIhHpvCUuSthYJwTvm3dilRLjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:53:24.429676Z"},"content_sha256":"4fcb7bf137eed20453db077f03fc37f10e5ca8a71fab1b659780c560a73706dd","schema_version":"1.0","event_id":"sha256:4fcb7bf137eed20453db077f03fc37f10e5ca8a71fab1b659780c560a73706dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI/bundle.json","state_url":"https://pith.science/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI/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":"2026-06-11T18:53:24Z","links":{"resolver":"https://pith.science/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI","bundle":"https://pith.science/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI/bundle.json","state":"https://pith.science/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4WRIHOVSXKD6GE2W7FNI4B7SI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A4WRIHOVSXKD6GE2W7FNI4B7SI","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":"342a3c6709a04fea206b6f5baf62d798ee166153cc894c34fe0ee1886afe25e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-23T07:37:13Z","title_canon_sha256":"2b3062b07643019359ce72d2d28a043a81f285e28ede4d136ef7d329ae14b434"},"schema_version":"1.0","source":{"id":"1805.08990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08990","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08990v2","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08990","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"A4WRIHOVSXKD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A4WRIHOVSXKD6GE2","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A4WRIHOV","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:4fcb7bf137eed20453db077f03fc37f10e5ca8a71fab1b659780c560a73706dd","target":"graph","created_at":"2026-05-18T00:02:44Z","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 consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for s","authors_text":"Hermann Mena, Lena-Maria Pfurtscheller, Tony Stillfjord","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-23T07:37:13Z","title":"GPU acceleration of splitting schemes applied to differential matrix equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08990","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":"sha256:1a2b0314b2f3c232efff3afef04ec518189bf6e3b5e927a658364980b05c864b","target":"record","created_at":"2026-05-18T00:02:44Z","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":"342a3c6709a04fea206b6f5baf62d798ee166153cc894c34fe0ee1886afe25e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-23T07:37:13Z","title_canon_sha256":"2b3062b07643019359ce72d2d28a043a81f285e28ede4d136ef7d329ae14b434"},"schema_version":"1.0","source":{"id":"1805.08990","kind":"arxiv","version":2}},"canonical_sha256":"072d141dd595d43f189ab7cad4703f92084a36f34a383e1e26eb3696a82f3a7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"072d141dd595d43f189ab7cad4703f92084a36f34a383e1e26eb3696a82f3a7a","first_computed_at":"2026-05-18T00:02:44.815190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:44.815190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HuY98AwsdrAyTE3nGFOhbc+4YppCZF0ZAden47iHb/hnDDw+RAFjQNX52sMAsHp7Oe5ZMAL+0lhzd0t7OnnvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:44.815621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a2b0314b2f3c232efff3afef04ec518189bf6e3b5e927a658364980b05c864b","sha256:4fcb7bf137eed20453db077f03fc37f10e5ca8a71fab1b659780c560a73706dd"],"state_sha256":"f7c70aaa635e6c1eeaa79a3a0f3e3ad0ec165dc9f8c5c219c50c20160a410438"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXfD/ALziJ3p7koDhbH/dVOzbRxTL/7AHhF5V6u9xD7VleAJQnh8L+quYGJyx3fbJpSoJMK+7YOATaDHzIRdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T18:53:24.434081Z","bundle_sha256":"4965a9518b144e936b2ef72e008ee6d3277c95d22d4d82564a2d6525fa4359e1"}}