{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RWMVEUIDFECX5PQBCNNN7YJAPA","short_pith_number":"pith:RWMVEUID","canonical_record":{"source":{"id":"1804.07716","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T16:45:36Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"678836d4d7455761fa12a8905ec6de842320b28cf61dc29f8467b39709ab790e","abstract_canon_sha256":"217609161a3b781c21138c72cf95d15802980ee5ad319d49ac3e7027ce1d7580"},"schema_version":"1.0"},"canonical_sha256":"8d9952510329057ebe01135adfe1207805bf31964e6ae86cecefa83b14b5ad02","source":{"kind":"arxiv","id":"1804.07716","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07716","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07716v4","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07716","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"pith_short_12","alias_value":"RWMVEUIDFECX","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"pith_short_16","alias_value":"RWMVEUIDFECX5PQB","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"pith_short_8","alias_value":"RWMVEUID","created_at":"2026-06-04T19:11:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RWMVEUIDFECX5PQBCNNN7YJAPA","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07716","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T16:45:36Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"678836d4d7455761fa12a8905ec6de842320b28cf61dc29f8467b39709ab790e","abstract_canon_sha256":"217609161a3b781c21138c72cf95d15802980ee5ad319d49ac3e7027ce1d7580"},"schema_version":"1.0"},"canonical_sha256":"8d9952510329057ebe01135adfe1207805bf31964e6ae86cecefa83b14b5ad02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:49.024006Z","signature_b64":"cnqf74dxpkFHgIHtTfy1Y95a82ZrCjw5iEmhN2V65qoB2CBuaJOUpOmfQR4qgSA/w0owjKJeJQk5K5HHTDl9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d9952510329057ebe01135adfe1207805bf31964e6ae86cecefa83b14b5ad02","last_reissued_at":"2026-06-04T19:11:49.023450Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:49.023450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07716","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:11:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZEi1Z2LcxXB2MxRbxDll+Cdh9l9l2sXvgqi9cJp6tul0oTm9quQPUe7leY3P1nvhEqkByZ9tpGtagSnxD3O3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:04:40.101920Z"},"content_sha256":"323d2c714bde83ed3bd34e02fd67e3f5d3adec2082e88f6649c9d2ce5b124c59","schema_version":"1.0","event_id":"sha256:323d2c714bde83ed3bd34e02fd67e3f5d3adec2082e88f6649c9d2ce5b124c59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RWMVEUIDFECX5PQBCNNN7YJAPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Design of High-Order Decoupled Multirate GARK Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Adrian Sandu, Arash Sarshar, Steven Roberts","submitted_at":"2018-04-20T16:45:36Z","abstract_excerpt":"Multirate time integration methods apply different step sizes to resolve different components of the system based on the local activity levels. This local selection of step sizes allows increased computational efficiency while achieving the desired solution accuracy. While the multirate idea is elegant and has been around for decades, multirate methods are not yet widely used in applications. This is due, in part, to the difficulties raised by the construction of high order multirate schemes.\n  Seeking to overcome these challenges, this work focuses on the design of practical high-order multir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07716","kind":"arxiv","version":4},"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/1804.07716/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":"2026-06-04T19:11:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzAUU9XAL7JxZ4md/AUfrpft6qxGa/LRsTn8TFeiZsuU3hCJIaxNE+4vfUsmnkIA0fS6EEBrb1SPIowmuoAKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:04:40.102409Z"},"content_sha256":"bf2101b646a9f887a0146b1f52c49c118dbec1d2adf26005d41d11e985d3543b","schema_version":"1.0","event_id":"sha256:bf2101b646a9f887a0146b1f52c49c118dbec1d2adf26005d41d11e985d3543b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWMVEUIDFECX5PQBCNNN7YJAPA/bundle.json","state_url":"https://pith.science/pith/RWMVEUIDFECX5PQBCNNN7YJAPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWMVEUIDFECX5PQBCNNN7YJAPA/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":"2026-06-25T06:04:40Z","links":{"resolver":"https://pith.science/pith/RWMVEUIDFECX5PQBCNNN7YJAPA","bundle":"https://pith.science/pith/RWMVEUIDFECX5PQBCNNN7YJAPA/bundle.json","state":"https://pith.science/pith/RWMVEUIDFECX5PQBCNNN7YJAPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWMVEUIDFECX5PQBCNNN7YJAPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RWMVEUIDFECX5PQBCNNN7YJAPA","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":"217609161a3b781c21138c72cf95d15802980ee5ad319d49ac3e7027ce1d7580","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T16:45:36Z","title_canon_sha256":"678836d4d7455761fa12a8905ec6de842320b28cf61dc29f8467b39709ab790e"},"schema_version":"1.0","source":{"id":"1804.07716","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07716","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07716v4","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07716","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"pith_short_12","alias_value":"RWMVEUIDFECX","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"pith_short_16","alias_value":"RWMVEUIDFECX5PQB","created_at":"2026-06-04T19:11:49Z"},{"alias_kind":"pith_short_8","alias_value":"RWMVEUID","created_at":"2026-06-04T19:11:49Z"}],"graph_snapshots":[{"event_id":"sha256:bf2101b646a9f887a0146b1f52c49c118dbec1d2adf26005d41d11e985d3543b","target":"graph","created_at":"2026-06-04T19:11:49Z","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/1804.07716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multirate time integration methods apply different step sizes to resolve different components of the system based on the local activity levels. This local selection of step sizes allows increased computational efficiency while achieving the desired solution accuracy. While the multirate idea is elegant and has been around for decades, multirate methods are not yet widely used in applications. This is due, in part, to the difficulties raised by the construction of high order multirate schemes.\n  Seeking to overcome these challenges, this work focuses on the design of practical high-order multir","authors_text":"Adrian Sandu, Arash Sarshar, Steven Roberts","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T16:45:36Z","title":"Design of High-Order Decoupled Multirate GARK Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07716","kind":"arxiv","version":4},"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":"sha256:323d2c714bde83ed3bd34e02fd67e3f5d3adec2082e88f6649c9d2ce5b124c59","target":"record","created_at":"2026-06-04T19:11:49Z","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":"217609161a3b781c21138c72cf95d15802980ee5ad319d49ac3e7027ce1d7580","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-20T16:45:36Z","title_canon_sha256":"678836d4d7455761fa12a8905ec6de842320b28cf61dc29f8467b39709ab790e"},"schema_version":"1.0","source":{"id":"1804.07716","kind":"arxiv","version":4}},"canonical_sha256":"8d9952510329057ebe01135adfe1207805bf31964e6ae86cecefa83b14b5ad02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d9952510329057ebe01135adfe1207805bf31964e6ae86cecefa83b14b5ad02","first_computed_at":"2026-06-04T19:11:49.023450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:49.023450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cnqf74dxpkFHgIHtTfy1Y95a82ZrCjw5iEmhN2V65qoB2CBuaJOUpOmfQR4qgSA/w0owjKJeJQk5K5HHTDl9AQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:49.024006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07716","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:323d2c714bde83ed3bd34e02fd67e3f5d3adec2082e88f6649c9d2ce5b124c59","sha256:bf2101b646a9f887a0146b1f52c49c118dbec1d2adf26005d41d11e985d3543b"],"state_sha256":"907201e2cc1c7b94e45bdb7f1219f72ad5c65bbb3c930a7fe657c9aeb72596b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZlX6qXOHtjByb/mlbrJjgBuo8ApRvVZFPFzq81LiHalCjcEe3WQXgwuFNkH101eqEQf8gFi6B/xg+S/XcuSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:04:40.104443Z","bundle_sha256":"59ae86f1ea36158db8f5a5df884e2aea526d8286192fb8da55824b7af874400e"}}