{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HRYHY24JI25DBY5FKXJYRMHJ7R","short_pith_number":"pith:HRYHY24J","canonical_record":{"source":{"id":"1605.00445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-02T11:54:12Z","cross_cats_sorted":[],"title_canon_sha256":"1f6e9629f1e7af52b080c9d6290cd28d3fdc028d7fc22c4b574a7fc01824e477","abstract_canon_sha256":"0a5c02f74c09df7e33a350df29444b8c5e1769dfc407d7a54bd747d602960975"},"schema_version":"1.0"},"canonical_sha256":"3c707c6b8946ba30e3a555d388b0e9fc5428f2bbacecd474f141aa3bb6ae3dd1","source":{"kind":"arxiv","id":"1605.00445","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00445","created_at":"2026-05-18T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00445v1","created_at":"2026-05-18T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00445","created_at":"2026-05-18T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"HRYHY24JI25D","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HRYHY24JI25DBY5F","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HRYHY24J","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HRYHY24JI25DBY5FKXJYRMHJ7R","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-02T11:54:12Z","cross_cats_sorted":[],"title_canon_sha256":"1f6e9629f1e7af52b080c9d6290cd28d3fdc028d7fc22c4b574a7fc01824e477","abstract_canon_sha256":"0a5c02f74c09df7e33a350df29444b8c5e1769dfc407d7a54bd747d602960975"},"schema_version":"1.0"},"canonical_sha256":"3c707c6b8946ba30e3a555d388b0e9fc5428f2bbacecd474f141aa3bb6ae3dd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:55.779899Z","signature_b64":"CKbHDa0uXspa/mZbrKe0xnrtKBbOeh5qcDZzSR/fn02aFB18IYG2mLpPCFSACV3c2F7KW3LiSxFY0h9EhG0uDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c707c6b8946ba30e3a555d388b0e9fc5428f2bbacecd474f141aa3bb6ae3dd1","last_reissued_at":"2026-05-18T01:15:55.779193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:55.779193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00445","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":"2026-05-18T01:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8CkpszULRNKywYCls6YJlqi4eUVdR7cGO+X6UEOdmVW1dTKITgo0xqsK4N/7NLlQXTqnypRN3xDkLfLqoIvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T17:01:01.494989Z"},"content_sha256":"04f183cf0c155bafcf52ee068ab272ab8afb0e2933060ba85d5bb265bb5f4c80","schema_version":"1.0","event_id":"sha256:04f183cf0c155bafcf52ee068ab272ab8afb0e2933060ba85d5bb265bb5f4c80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HRYHY24JI25DBY5FKXJYRMHJ7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Setup of Order Conditions for Splitting Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Harald Hofst\\\"atter, Othmar Koch, Winfried Auzinger, Wolfgang Herfort","submitted_at":"2016-05-02T11:54:12Z","abstract_excerpt":"This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting methods. Along with a brief review of these materials and some theoretical background, we discuss the implementation of the ideas from these papers in computer algebra, in particular using Maple 18. A parallel version of such a code is described."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00445","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":"2026-05-18T01:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i1CW9by0V9epgsQ/mDgne1ph5hHiQIyaYFDZNs2J/1x+xtQGwGK2LfmjC1SIqtNPmOqDVVybzyoB00PaVGN3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T17:01:01.495763Z"},"content_sha256":"e0312118844310653982b0dae2f13af19a6af78c98b54f7dd8fd247d2a1588a2","schema_version":"1.0","event_id":"sha256:e0312118844310653982b0dae2f13af19a6af78c98b54f7dd8fd247d2a1588a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRYHY24JI25DBY5FKXJYRMHJ7R/bundle.json","state_url":"https://pith.science/pith/HRYHY24JI25DBY5FKXJYRMHJ7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRYHY24JI25DBY5FKXJYRMHJ7R/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":"2026-06-10T17:01:01Z","links":{"resolver":"https://pith.science/pith/HRYHY24JI25DBY5FKXJYRMHJ7R","bundle":"https://pith.science/pith/HRYHY24JI25DBY5FKXJYRMHJ7R/bundle.json","state":"https://pith.science/pith/HRYHY24JI25DBY5FKXJYRMHJ7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRYHY24JI25DBY5FKXJYRMHJ7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HRYHY24JI25DBY5FKXJYRMHJ7R","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":"0a5c02f74c09df7e33a350df29444b8c5e1769dfc407d7a54bd747d602960975","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-02T11:54:12Z","title_canon_sha256":"1f6e9629f1e7af52b080c9d6290cd28d3fdc028d7fc22c4b574a7fc01824e477"},"schema_version":"1.0","source":{"id":"1605.00445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00445","created_at":"2026-05-18T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00445v1","created_at":"2026-05-18T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00445","created_at":"2026-05-18T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"HRYHY24JI25D","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HRYHY24JI25DBY5F","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HRYHY24J","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:e0312118844310653982b0dae2f13af19a6af78c98b54f7dd8fd247d2a1588a2","target":"graph","created_at":"2026-05-18T01:15:55Z","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":"This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting methods. Along with a brief review of these materials and some theoretical background, we discuss the implementation of the ideas from these papers in computer algebra, in particular using Maple 18. A parallel version of such a code is described.","authors_text":"Harald Hofst\\\"atter, Othmar Koch, Winfried Auzinger, Wolfgang Herfort","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-02T11:54:12Z","title":"Setup of Order Conditions for Splitting Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00445","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":"sha256:04f183cf0c155bafcf52ee068ab272ab8afb0e2933060ba85d5bb265bb5f4c80","target":"record","created_at":"2026-05-18T01:15:55Z","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":"0a5c02f74c09df7e33a350df29444b8c5e1769dfc407d7a54bd747d602960975","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-05-02T11:54:12Z","title_canon_sha256":"1f6e9629f1e7af52b080c9d6290cd28d3fdc028d7fc22c4b574a7fc01824e477"},"schema_version":"1.0","source":{"id":"1605.00445","kind":"arxiv","version":1}},"canonical_sha256":"3c707c6b8946ba30e3a555d388b0e9fc5428f2bbacecd474f141aa3bb6ae3dd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c707c6b8946ba30e3a555d388b0e9fc5428f2bbacecd474f141aa3bb6ae3dd1","first_computed_at":"2026-05-18T01:15:55.779193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:55.779193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CKbHDa0uXspa/mZbrKe0xnrtKBbOeh5qcDZzSR/fn02aFB18IYG2mLpPCFSACV3c2F7KW3LiSxFY0h9EhG0uDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:55.779899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04f183cf0c155bafcf52ee068ab272ab8afb0e2933060ba85d5bb265bb5f4c80","sha256:e0312118844310653982b0dae2f13af19a6af78c98b54f7dd8fd247d2a1588a2"],"state_sha256":"d83b6d5a8aba165a2041367f745050e4c0aa467b08e4761a607a28e79e5603fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9D3nj3bC8S1GhaM89+d4kxhbFyTzIRWL4yr14Pk0icDtiEkNpXiMl4hwhjC7/El1EKvkbfEpIhyfd0DSMvX1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T17:01:01.500619Z","bundle_sha256":"3cab23cb170ad15031fd113f2460f81b6b4a9c04faf2761e806cd16e5e4e968a"}}