{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IDVWJTCJ6DDJORHN7B2HKN6ACX","short_pith_number":"pith:IDVWJTCJ","canonical_record":{"source":{"id":"1811.01285","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-03T21:09:38Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"462aac7550aa939715c614fd791b3771c1be4227a844d756e3946dcf87d14a61","abstract_canon_sha256":"237285028b7bd3d2e55676774d8675cd1bc40fd5b7bde50020dd457106a75285"},"schema_version":"1.0"},"canonical_sha256":"40eb64cc49f0c69744edf8747537c015cfea6d4c27e8c2b61781454f22412b2e","source":{"kind":"arxiv","id":"1811.01285","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01285","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01285v2","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01285","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"IDVWJTCJ6DDJ","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"IDVWJTCJ6DDJORHN","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"IDVWJTCJ","created_at":"2026-07-05T06:41:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IDVWJTCJ6DDJORHN7B2HKN6ACX","target":"record","payload":{"canonical_record":{"source":{"id":"1811.01285","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-03T21:09:38Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"462aac7550aa939715c614fd791b3771c1be4227a844d756e3946dcf87d14a61","abstract_canon_sha256":"237285028b7bd3d2e55676774d8675cd1bc40fd5b7bde50020dd457106a75285"},"schema_version":"1.0"},"canonical_sha256":"40eb64cc49f0c69744edf8747537c015cfea6d4c27e8c2b61781454f22412b2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:41:42.395592Z","signature_b64":"k4nWbH4GOe6GQm1ZHtq0bVEVySbsw31vHKV8vtKkG0CkXkn/mVkwdrngarhwoYRaHtN2aTAsSIhAcpf6CvOZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40eb64cc49f0c69744edf8747537c015cfea6d4c27e8c2b61781454f22412b2e","last_reissued_at":"2026-07-05T06:41:42.395123Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:41:42.395123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.01285","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":"2026-07-05T06:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rh02kBSchaLf/+DkceJ8+KXnWIb1OQyoD7QMU3Z5gLidWAu3r17r0YDPxkaFBzyWAwMTCMpNYjFxwHIZdKEFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:30:13.078093Z"},"content_sha256":"3d8aca3d10ec68b9b79705365ac2e1b25e41be4c038d84a394e4e8f4fe5e8cfd","schema_version":"1.0","event_id":"sha256:3d8aca3d10ec68b9b79705365ac2e1b25e41be4c038d84a394e4e8f4fe5e8cfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IDVWJTCJ6DDJORHN7B2HKN6ACX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DIRK Schemes with High Weak Stage Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Benjamin Seibold, David Ketcheson, David Shirokoff, Dong Zhou","submitted_at":"2018-11-03T21:09:38Z","abstract_excerpt":"Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01285","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.01285/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpYS+lgmYANvQSRPVpBGR+6O4ZojkBPiZRnN/aT1b7PXkJMiRgq2ziC1A5Po47JyNVk9PasRg6JV/ZOo+ToRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:30:13.079512Z"},"content_sha256":"63a6961ab1358a7fb1f8e020e801cb657d06748bb5583a09b3781106de6fa08b","schema_version":"1.0","event_id":"sha256:63a6961ab1358a7fb1f8e020e801cb657d06748bb5583a09b3781106de6fa08b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX/bundle.json","state_url":"https://pith.science/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX/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":"2026-08-06T11:30:13Z","links":{"resolver":"https://pith.science/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX","bundle":"https://pith.science/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX/bundle.json","state":"https://pith.science/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDVWJTCJ6DDJORHN7B2HKN6ACX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IDVWJTCJ6DDJORHN7B2HKN6ACX","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":"237285028b7bd3d2e55676774d8675cd1bc40fd5b7bde50020dd457106a75285","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-03T21:09:38Z","title_canon_sha256":"462aac7550aa939715c614fd791b3771c1be4227a844d756e3946dcf87d14a61"},"schema_version":"1.0","source":{"id":"1811.01285","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01285","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01285v2","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01285","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"IDVWJTCJ6DDJ","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"IDVWJTCJ6DDJORHN","created_at":"2026-07-05T06:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"IDVWJTCJ","created_at":"2026-07-05T06:41:42Z"}],"graph_snapshots":[{"event_id":"sha256:63a6961ab1358a7fb1f8e020e801cb657d06748bb5583a09b3781106de6fa08b","target":"graph","created_at":"2026-07-05T06:41:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.01285/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate","authors_text":"Benjamin Seibold, David Ketcheson, David Shirokoff, Dong Zhou","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-03T21:09:38Z","title":"DIRK Schemes with High Weak Stage Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01285","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":"sha256:3d8aca3d10ec68b9b79705365ac2e1b25e41be4c038d84a394e4e8f4fe5e8cfd","target":"record","created_at":"2026-07-05T06:41:42Z","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":"237285028b7bd3d2e55676774d8675cd1bc40fd5b7bde50020dd457106a75285","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-03T21:09:38Z","title_canon_sha256":"462aac7550aa939715c614fd791b3771c1be4227a844d756e3946dcf87d14a61"},"schema_version":"1.0","source":{"id":"1811.01285","kind":"arxiv","version":2}},"canonical_sha256":"40eb64cc49f0c69744edf8747537c015cfea6d4c27e8c2b61781454f22412b2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40eb64cc49f0c69744edf8747537c015cfea6d4c27e8c2b61781454f22412b2e","first_computed_at":"2026-07-05T06:41:42.395123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:41:42.395123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k4nWbH4GOe6GQm1ZHtq0bVEVySbsw31vHKV8vtKkG0CkXkn/mVkwdrngarhwoYRaHtN2aTAsSIhAcpf6CvOZAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:41:42.395592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01285","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d8aca3d10ec68b9b79705365ac2e1b25e41be4c038d84a394e4e8f4fe5e8cfd","sha256:63a6961ab1358a7fb1f8e020e801cb657d06748bb5583a09b3781106de6fa08b"],"state_sha256":"af1cec1f4684c44e79819ce9376b3605cf2420ce89088429116dcceee2596c30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NvS7fNbFL4d0qPC5m/0npPxMB/FD7hoc5sBkm7MByg69/QmkYFmS2IbiNJgfoK87gleUYAKnAqP8DYkA51LDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T11:30:13.084669Z","bundle_sha256":"870aa08014254b4f1a280ea13e59fe9f994075c9f65c3b72da89b653ed6208af"}}