{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZIWLSSLHK3XNYYHUHVTKF4MWMO","short_pith_number":"pith:ZIWLSSLH","canonical_record":{"source":{"id":"1305.2449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-10T22:31:33Z","cross_cats_sorted":[],"title_canon_sha256":"8a224e8786f4e1533e79068cc9e888a776e42e3a855e5fb10f42a8f0d853364f","abstract_canon_sha256":"91585225c19591d59de1e57b107e6d4dabe634308e37f49e30417bfc2825eb95"},"schema_version":"1.0"},"canonical_sha256":"ca2cb9496756eedc60f43d66a2f19663b4c70df6fb780eae026f46a2d2a3c9c7","source":{"kind":"arxiv","id":"1305.2449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2449","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2449v1","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2449","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZIWLSSLHK3XN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZIWLSSLHK3XNYYHU","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZIWLSSLH","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZIWLSSLHK3XNYYHUHVTKF4MWMO","target":"record","payload":{"canonical_record":{"source":{"id":"1305.2449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-10T22:31:33Z","cross_cats_sorted":[],"title_canon_sha256":"8a224e8786f4e1533e79068cc9e888a776e42e3a855e5fb10f42a8f0d853364f","abstract_canon_sha256":"91585225c19591d59de1e57b107e6d4dabe634308e37f49e30417bfc2825eb95"},"schema_version":"1.0"},"canonical_sha256":"ca2cb9496756eedc60f43d66a2f19663b4c70df6fb780eae026f46a2d2a3c9c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:57.834441Z","signature_b64":"lWKloajpwnaOUsaQRtHC91qyDnvfwJzZTjNbuV6aCoKsfF5PaF0oCTLaOhyt3SozlrI3dK0tVm1iC80bq2AACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca2cb9496756eedc60f43d66a2f19663b4c70df6fb780eae026f46a2d2a3c9c7","last_reissued_at":"2026-05-18T03:25:57.833839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:57.833839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.2449","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zRMO2delgaVZWeyQ/SxlvFpT2upXZgkXUvhBcBpEz/HYhdd48Z6OfGod7KJF04RorY/ebilG3bWW0IJdkExfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:29:52.322134Z"},"content_sha256":"fcc41aa062a9a5cae43ac745ebba8a4a4521dcf9a66c4997081b7d37dc9d8d8d","schema_version":"1.0","event_id":"sha256:fcc41aa062a9a5cae43ac745ebba8a4a4521dcf9a66c4997081b7d37dc9d8d8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZIWLSSLHK3XNYYHUHVTKF4MWMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cascadic Multilevel Algorithms for Symmetric Saddle Point Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Constantin Bacuta","submitted_at":"2013-05-10T22:31:33Z","abstract_excerpt":"In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of fast and accurate solvers for it symmetric positive definite systems. On each fixed level an efficient solver such as the gradient or the conjugate gradient algorithm for inverting a Schur complement is implemented. The level change criterion follows the cascade principle and requires that the iteration error be close to the expected discretization error. We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2449","kind":"arxiv","version":1},"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":"2026-05-18T03:25:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBz++BmUv/PuMG3fIquWd5AsKJhHSO6wULZ0TJmSDERStKs9MHzek+MhMaVqQ3pcKxoL6e0payXUAiEJ21CRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:29:52.322504Z"},"content_sha256":"52165b26a26055d8b220bc60f6c5624c1146d17295056ef59a214f65891dd574","schema_version":"1.0","event_id":"sha256:52165b26a26055d8b220bc60f6c5624c1146d17295056ef59a214f65891dd574"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO/bundle.json","state_url":"https://pith.science/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO/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":"2026-06-01T13:29:52Z","links":{"resolver":"https://pith.science/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO","bundle":"https://pith.science/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO/bundle.json","state":"https://pith.science/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIWLSSLHK3XNYYHUHVTKF4MWMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZIWLSSLHK3XNYYHUHVTKF4MWMO","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":"91585225c19591d59de1e57b107e6d4dabe634308e37f49e30417bfc2825eb95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-10T22:31:33Z","title_canon_sha256":"8a224e8786f4e1533e79068cc9e888a776e42e3a855e5fb10f42a8f0d853364f"},"schema_version":"1.0","source":{"id":"1305.2449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2449","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2449v1","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2449","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZIWLSSLHK3XN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZIWLSSLHK3XNYYHU","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZIWLSSLH","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:52165b26a26055d8b220bc60f6c5624c1146d17295056ef59a214f65891dd574","target":"graph","created_at":"2026-05-18T03:25:57Z","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":"In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of fast and accurate solvers for it symmetric positive definite systems. On each fixed level an efficient solver such as the gradient or the conjugate gradient algorithm for inverting a Schur complement is implemented. The level change criterion follows the cascade principle and requires that the iteration error be close to the expected discretization error. We p","authors_text":"Constantin Bacuta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-10T22:31:33Z","title":"Cascadic Multilevel Algorithms for Symmetric Saddle Point Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2449","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:fcc41aa062a9a5cae43ac745ebba8a4a4521dcf9a66c4997081b7d37dc9d8d8d","target":"record","created_at":"2026-05-18T03:25:57Z","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":"91585225c19591d59de1e57b107e6d4dabe634308e37f49e30417bfc2825eb95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-10T22:31:33Z","title_canon_sha256":"8a224e8786f4e1533e79068cc9e888a776e42e3a855e5fb10f42a8f0d853364f"},"schema_version":"1.0","source":{"id":"1305.2449","kind":"arxiv","version":1}},"canonical_sha256":"ca2cb9496756eedc60f43d66a2f19663b4c70df6fb780eae026f46a2d2a3c9c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca2cb9496756eedc60f43d66a2f19663b4c70df6fb780eae026f46a2d2a3c9c7","first_computed_at":"2026-05-18T03:25:57.833839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:57.833839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lWKloajpwnaOUsaQRtHC91qyDnvfwJzZTjNbuV6aCoKsfF5PaF0oCTLaOhyt3SozlrI3dK0tVm1iC80bq2AACA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:57.834441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcc41aa062a9a5cae43ac745ebba8a4a4521dcf9a66c4997081b7d37dc9d8d8d","sha256:52165b26a26055d8b220bc60f6c5624c1146d17295056ef59a214f65891dd574"],"state_sha256":"dccee1b514034c03960fdd7099106c4cc94e63691093e758091311ed417d399b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dut4UkAwrun5CjJoGhkghZLvehLDFhclBwoJAo1YpS2vkHs8yBsgLWKR56gazVpGLM3OLB50PT3kULp9HHzqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:29:52.324459Z","bundle_sha256":"b4866fff86636216e0a64f743f210486120a0a4c218cad0ce779fc712f75aff6"}}