{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OAPAY3MAIQW7RB6TTXS4FYBUQR","short_pith_number":"pith:OAPAY3MA","canonical_record":{"source":{"id":"1503.02094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-06T21:32:47Z","cross_cats_sorted":[],"title_canon_sha256":"c96dbf3de4e8b0fd51085afa40d94edad474b8f6a5e3c3c9f739a0f9d31d4290","abstract_canon_sha256":"1f9a46673be6ae20f89cc59863a5af57666cfb8a111775bec880bda7e7290cb8"},"schema_version":"1.0"},"canonical_sha256":"701e0c6d80442df887d39de5c2e034844a936cef578bd0581f07123bf5bfe097","source":{"kind":"arxiv","id":"1503.02094","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02094","created_at":"2026-05-18T01:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02094v2","created_at":"2026-05-18T01:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02094","created_at":"2026-05-18T01:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"OAPAY3MAIQW7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OAPAY3MAIQW7RB6T","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OAPAY3MA","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OAPAY3MAIQW7RB6TTXS4FYBUQR","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-06T21:32:47Z","cross_cats_sorted":[],"title_canon_sha256":"c96dbf3de4e8b0fd51085afa40d94edad474b8f6a5e3c3c9f739a0f9d31d4290","abstract_canon_sha256":"1f9a46673be6ae20f89cc59863a5af57666cfb8a111775bec880bda7e7290cb8"},"schema_version":"1.0"},"canonical_sha256":"701e0c6d80442df887d39de5c2e034844a936cef578bd0581f07123bf5bfe097","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:34.338495Z","signature_b64":"4BRs8Iu9CceiTpOc9ZIODjm0lkuG5DiAYY5nHBhnsVZ1qnkWysa9hawc/S6EiOIIt4VVathWFQGJIjr03elzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"701e0c6d80442df887d39de5c2e034844a936cef578bd0581f07123bf5bfe097","last_reissued_at":"2026-05-18T01:26:34.337734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:34.337734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02094","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":"2026-05-18T01:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w52nobF6X7uiMTmcOopHwVEXu+BIhskYnD5ay8R3jBYVOHy7QA49sVNvxFJOr+HNBWxUQdSDntSnn2dGbGLvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:15:24.728793Z"},"content_sha256":"73d6ace746ec8c9f247f1fd49c0bef67f5fed4177fa50cd3d4b7dcdcb6e76ca2","schema_version":"1.0","event_id":"sha256:73d6ace746ec8c9f247f1fd49c0bef67f5fed4177fa50cd3d4b7dcdcb6e76ca2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OAPAY3MAIQW7RB6TTXS4FYBUQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parareal methods for highly oscillatory dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gil Ariel, Richard Tsai, Seong Jun Kim","submitted_at":"2015-03-06T21:32:47Z","abstract_excerpt":"We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an appropriate multiscale integrator, which is refined using parallel fine scale integrations. Convergence is obtained using an alignment algorithm for fast phase-like variables. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02094","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":"2026-05-18T01:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tk0YuCXlJnlr4FdeyWUkLq2Knu/g0vKnk9/BwS8U7mz2k+sJwcp5kGBCj9uI0ipfUTzF5cXefxEbu+qNvDp1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:15:24.729356Z"},"content_sha256":"ae618e5f9779eb9581470b094ff6de6b0b55a074df776f8c314768393e6fb009","schema_version":"1.0","event_id":"sha256:ae618e5f9779eb9581470b094ff6de6b0b55a074df776f8c314768393e6fb009"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR/bundle.json","state_url":"https://pith.science/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR/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":"2026-05-31T07:15:24Z","links":{"resolver":"https://pith.science/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR","bundle":"https://pith.science/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR/bundle.json","state":"https://pith.science/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OAPAY3MAIQW7RB6TTXS4FYBUQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OAPAY3MAIQW7RB6TTXS4FYBUQR","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":"1f9a46673be6ae20f89cc59863a5af57666cfb8a111775bec880bda7e7290cb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-06T21:32:47Z","title_canon_sha256":"c96dbf3de4e8b0fd51085afa40d94edad474b8f6a5e3c3c9f739a0f9d31d4290"},"schema_version":"1.0","source":{"id":"1503.02094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02094","created_at":"2026-05-18T01:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02094v2","created_at":"2026-05-18T01:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02094","created_at":"2026-05-18T01:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"OAPAY3MAIQW7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OAPAY3MAIQW7RB6T","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OAPAY3MA","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:ae618e5f9779eb9581470b094ff6de6b0b55a074df776f8c314768393e6fb009","target":"graph","created_at":"2026-05-18T01:26:34Z","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 introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an appropriate multiscale integrator, which is refined using parallel fine scale integrations. Convergence is obtained using an alignment algorithm for fast phase-like variables. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the sta","authors_text":"Gil Ariel, Richard Tsai, Seong Jun Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-06T21:32:47Z","title":"Parareal methods for highly oscillatory dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02094","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":"sha256:73d6ace746ec8c9f247f1fd49c0bef67f5fed4177fa50cd3d4b7dcdcb6e76ca2","target":"record","created_at":"2026-05-18T01:26:34Z","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":"1f9a46673be6ae20f89cc59863a5af57666cfb8a111775bec880bda7e7290cb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-06T21:32:47Z","title_canon_sha256":"c96dbf3de4e8b0fd51085afa40d94edad474b8f6a5e3c3c9f739a0f9d31d4290"},"schema_version":"1.0","source":{"id":"1503.02094","kind":"arxiv","version":2}},"canonical_sha256":"701e0c6d80442df887d39de5c2e034844a936cef578bd0581f07123bf5bfe097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"701e0c6d80442df887d39de5c2e034844a936cef578bd0581f07123bf5bfe097","first_computed_at":"2026-05-18T01:26:34.337734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:34.337734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4BRs8Iu9CceiTpOc9ZIODjm0lkuG5DiAYY5nHBhnsVZ1qnkWysa9hawc/S6EiOIIt4VVathWFQGJIjr03elzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:34.338495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73d6ace746ec8c9f247f1fd49c0bef67f5fed4177fa50cd3d4b7dcdcb6e76ca2","sha256:ae618e5f9779eb9581470b094ff6de6b0b55a074df776f8c314768393e6fb009"],"state_sha256":"b3f290f8df88b3f69ef33e9dae60c25f4de2ca110f1e757155d0955511f9a4cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"767Q3q4LC1yYQ3S/jbZFa49CyGb43aNvuCgfTVaMbTyPOSoBVuIbnrWDlPtidmUQ1LWyEmYQdJtVS9Ix2seGDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:15:24.732148Z","bundle_sha256":"9b588a43264871f0ed28fa6ae4baacee5ebd61ba160a9a10e421854d50050b3b"}}