{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MXZIUDM7PUBRCYIQFALF6PPT7F","short_pith_number":"pith:MXZIUDM7","canonical_record":{"source":{"id":"1307.1312","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-04T12:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"ae3cc6ac045851df9000b93b6ad4e7072b3a94c7aac94c6fd237271cc5f0957f","abstract_canon_sha256":"24e6ea78a624240de99d914cb5823bb081fd9816f0427426658f481738987122"},"schema_version":"1.0"},"canonical_sha256":"65f28a0d9f7d0311611028165f3df3f9489eee8b52c8efda31fe02c05147af1e","source":{"kind":"arxiv","id":"1307.1312","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1312","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1312v4","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1312","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"MXZIUDM7PUBR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MXZIUDM7PUBRCYIQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MXZIUDM7","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MXZIUDM7PUBRCYIQFALF6PPT7F","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1312","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-04T12:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"ae3cc6ac045851df9000b93b6ad4e7072b3a94c7aac94c6fd237271cc5f0957f","abstract_canon_sha256":"24e6ea78a624240de99d914cb5823bb081fd9816f0427426658f481738987122"},"schema_version":"1.0"},"canonical_sha256":"65f28a0d9f7d0311611028165f3df3f9489eee8b52c8efda31fe02c05147af1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:49.466730Z","signature_b64":"5xLIETopnVr+5uaUu4OI1Ld6XULcA1mheLf95mlzPKy4/zDN/IA652MBbAPpXqmuhYs3Sn4DfdzMD3GSlbHVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65f28a0d9f7d0311611028165f3df3f9489eee8b52c8efda31fe02c05147af1e","last_reissued_at":"2026-05-18T01:30:49.466167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:49.466167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1312","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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43jtomtqf/OmD3dNyNhE4xudQisId0g8Q8EUNXH4hh4NvxnL6ti/VJlbYNoOaBkEMSFK/Ss2tOi8DCxku3YfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T21:46:22.412291Z"},"content_sha256":"54cd2f303149a651adf4acebf2ef809370fd3f64fd3e263b2eef3798c8ccf338","schema_version":"1.0","event_id":"sha256:54cd2f303149a651adf4acebf2ef809370fd3f64fd3e263b2eef3798c8ccf338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MXZIUDM7PUBRCYIQFALF6PPT7F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A multi-level spectral deferred correction method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Daniel Ruprecht, Matthew Emmett, Matthias Bolten, Michael Minion, Robert Speck, Rolf Krause","submitted_at":"2013-07-04T12:50:26Z","abstract_excerpt":"The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser leve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1312","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":""},"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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQOZ4ua3I5KnOSDoGbarzBuERKzuGfpWcE1+N1H9LAA1naUnslm3KGwa14390kz0rD4I29izFeevXgVWy0iJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T21:46:22.412840Z"},"content_sha256":"99fd69d7bf3baf96789ba841dc5b97859b3487b70f7d4411377a123e167a9dbb","schema_version":"1.0","event_id":"sha256:99fd69d7bf3baf96789ba841dc5b97859b3487b70f7d4411377a123e167a9dbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXZIUDM7PUBRCYIQFALF6PPT7F/bundle.json","state_url":"https://pith.science/pith/MXZIUDM7PUBRCYIQFALF6PPT7F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXZIUDM7PUBRCYIQFALF6PPT7F/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":"2026-05-23T21:46:22Z","links":{"resolver":"https://pith.science/pith/MXZIUDM7PUBRCYIQFALF6PPT7F","bundle":"https://pith.science/pith/MXZIUDM7PUBRCYIQFALF6PPT7F/bundle.json","state":"https://pith.science/pith/MXZIUDM7PUBRCYIQFALF6PPT7F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXZIUDM7PUBRCYIQFALF6PPT7F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MXZIUDM7PUBRCYIQFALF6PPT7F","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":"24e6ea78a624240de99d914cb5823bb081fd9816f0427426658f481738987122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-04T12:50:26Z","title_canon_sha256":"ae3cc6ac045851df9000b93b6ad4e7072b3a94c7aac94c6fd237271cc5f0957f"},"schema_version":"1.0","source":{"id":"1307.1312","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1312","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1312v4","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1312","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"MXZIUDM7PUBR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MXZIUDM7PUBRCYIQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MXZIUDM7","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:99fd69d7bf3baf96789ba841dc5b97859b3487b70f7d4411377a123e167a9dbb","target":"graph","created_at":"2026-05-18T01:30:49Z","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"},"paper":{"abstract_excerpt":"The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser leve","authors_text":"Daniel Ruprecht, Matthew Emmett, Matthias Bolten, Michael Minion, Robert Speck, Rolf Krause","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-04T12:50:26Z","title":"A multi-level spectral deferred correction method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1312","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":"sha256:54cd2f303149a651adf4acebf2ef809370fd3f64fd3e263b2eef3798c8ccf338","target":"record","created_at":"2026-05-18T01:30:49Z","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":"24e6ea78a624240de99d914cb5823bb081fd9816f0427426658f481738987122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-04T12:50:26Z","title_canon_sha256":"ae3cc6ac045851df9000b93b6ad4e7072b3a94c7aac94c6fd237271cc5f0957f"},"schema_version":"1.0","source":{"id":"1307.1312","kind":"arxiv","version":4}},"canonical_sha256":"65f28a0d9f7d0311611028165f3df3f9489eee8b52c8efda31fe02c05147af1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65f28a0d9f7d0311611028165f3df3f9489eee8b52c8efda31fe02c05147af1e","first_computed_at":"2026-05-18T01:30:49.466167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:49.466167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xLIETopnVr+5uaUu4OI1Ld6XULcA1mheLf95mlzPKy4/zDN/IA652MBbAPpXqmuhYs3Sn4DfdzMD3GSlbHVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:49.466730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1312","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54cd2f303149a651adf4acebf2ef809370fd3f64fd3e263b2eef3798c8ccf338","sha256:99fd69d7bf3baf96789ba841dc5b97859b3487b70f7d4411377a123e167a9dbb"],"state_sha256":"cf169ce659bca0393fbaf76e5548f3243a3329d9eaf9e82839ab311c204848f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KUSkhjBCbWTX0J7HIn5jC1fjGAbyTOHdZgBS3SvPcF+EEDFH41oJrvm7vkXjyYPST/2Xw0fMgknPv5/SIqFIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T21:46:22.416213Z","bundle_sha256":"207f57c858f91ae68959fdf503daee403f4cb04078053e8de1d6e309e1674548"}}