{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZVCFW3CPVJKMLJ4EDN66AGXWOI","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":"0d6afd4b5a7200101c9ac82bc1fcd8be928f40262aee7c463b986566ff3b19a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-12T08:12:20Z","title_canon_sha256":"a69f84fee2e87c14eccd59903899d6509e6b7924246f29b4223745bde624f061"},"schema_version":"1.0","source":{"id":"1205.2750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2750","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2750v1","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2750","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZVCFW3CPVJKM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZVCFW3CPVJKMLJ4E","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZVCFW3CP","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:0dc95648cc4f57d4ae93f1e867ab1ac0425c7e94055f80cf3ef22266bfb7e65d","target":"graph","created_at":"2026-05-18T03:55:46Z","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 present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has its own time-step sequence. This paper contains a description of the methods, an analysis of their basic properties, and a posteriori error analysis. In the accompanying paper [A. Logg, SIAM J. Sci. Comput., 27 (2003), pp. 741-758], we present adaptive algorithms for time-stepping and global error control based on the results of the current pape","authors_text":"Anders Logg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-12T08:12:20Z","title":"Multi-Adaptive Galerkin Methods for ODEs I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2750","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:eb1092db61aa1a60d92e3b1059506670789ad1d3bc918de8b6d2febd2b6d2112","target":"record","created_at":"2026-05-18T03:55:46Z","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":"0d6afd4b5a7200101c9ac82bc1fcd8be928f40262aee7c463b986566ff3b19a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-12T08:12:20Z","title_canon_sha256":"a69f84fee2e87c14eccd59903899d6509e6b7924246f29b4223745bde624f061"},"schema_version":"1.0","source":{"id":"1205.2750","kind":"arxiv","version":1}},"canonical_sha256":"cd445b6c4faa54c5a7841b7de01af6723496f00810792a2dfbb1bd7ff473565f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd445b6c4faa54c5a7841b7de01af6723496f00810792a2dfbb1bd7ff473565f","first_computed_at":"2026-05-18T03:55:46.091583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:46.091583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d4vpMloc8UQrMML5VZCotBD1iroK5vOdwYGzryUxUUC8O9SrRqc86DaxmtnmyuE16jpQ38CyC309gk9qtXxdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:46.092056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb1092db61aa1a60d92e3b1059506670789ad1d3bc918de8b6d2febd2b6d2112","sha256:0dc95648cc4f57d4ae93f1e867ab1ac0425c7e94055f80cf3ef22266bfb7e65d"],"state_sha256":"f1b0e7e79b011aa3f6388ea071ad140e2c1ef4a51280a7aa62e6503014ea6026"}