{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TTMWSOYC66O33XZCHYR2AAIELK","short_pith_number":"pith:TTMWSOYC","canonical_record":{"source":{"id":"1109.0580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-03T00:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"7843a9d3377244e7336ea4904b3d97622eefb736a0f31e32e256d88938401a40","abstract_canon_sha256":"74cad3e1b3d0409b4c50831d1756cfa2eef1f8d1127eebd4799a9a464d953592"},"schema_version":"1.0"},"canonical_sha256":"9cd9693b02f79dbddf223e23a001045a9de5fa3baea73b7a3ea1c9dd0f87d5ff","source":{"kind":"arxiv","id":"1109.0580","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0580","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0580v2","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0580","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"TTMWSOYC66O3","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TTMWSOYC66O33XZC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TTMWSOYC","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TTMWSOYC66O33XZCHYR2AAIELK","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-03T00:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"7843a9d3377244e7336ea4904b3d97622eefb736a0f31e32e256d88938401a40","abstract_canon_sha256":"74cad3e1b3d0409b4c50831d1756cfa2eef1f8d1127eebd4799a9a464d953592"},"schema_version":"1.0"},"canonical_sha256":"9cd9693b02f79dbddf223e23a001045a9de5fa3baea73b7a3ea1c9dd0f87d5ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.810121Z","signature_b64":"TJis677A8SuCEcOKupxeDUzOby0nOc8ttUK0mzqpdiuLFXN0etMUKLkm8U5UPuxG8ZMjCXHjqKJ5x5eGHGvqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cd9693b02f79dbddf223e23a001045a9de5fa3baea73b7a3ea1c9dd0f87d5ff","last_reissued_at":"2026-05-18T02:47:31.809438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.809438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0580","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":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6cPMWAax5Fx/Oo7Lu6TONk6Ofi2ttTmNblPFUQ0a4ItLfe5NlQky0/cLi2d+8naj7e0hTcSFYCc7EW1BaOr7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:52:40.772976Z"},"content_sha256":"9d5759349999b3c29caeb1df0dfa9437329acd07ba7d563f88c4764ee40fe550","schema_version":"1.0","event_id":"sha256:9d5759349999b3c29caeb1df0dfa9437329acd07ba7d563f88c4764ee40fe550"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TTMWSOYC66O33XZCHYR2AAIELK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nested BDDC for a saddle-point problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bed\\v{r}ich Soused\\'ik","submitted_at":"2011-09-03T00:51:32Z","abstract_excerpt":"We propose a Nested BDDC for a class of saddle-point problems. The method solves for both flux and pressure variables. The fluxes are resolved in three-steps: the coarse solve is followed by subdomain solves, and last we look for a divergence-free flux correction and pressure variables using conjugate gradients with a Multilevel BDDC preconditioner. Because the coarse solve in the first step has the same structure as the original problem, we can use this procedure recursively and solve (a hierarchy of) coarse problems only approximately, utilizing the coarse problems known from the BDDC. The r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0580","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":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OYOc+I5ygkbybQcveL8NUy7UPuh2Y5NZYw0Ic0joPcRrgmwFUzi7DYXhDdks1/q/44LrlMVOR+mZN9rBabLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:52:40.773433Z"},"content_sha256":"1ccd6f54f48e34764494a6fca18b2a27781ae0472eaf1bd7917dcb585de9eeb7","schema_version":"1.0","event_id":"sha256:1ccd6f54f48e34764494a6fca18b2a27781ae0472eaf1bd7917dcb585de9eeb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTMWSOYC66O33XZCHYR2AAIELK/bundle.json","state_url":"https://pith.science/pith/TTMWSOYC66O33XZCHYR2AAIELK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTMWSOYC66O33XZCHYR2AAIELK/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":"2026-05-27T13:52:40Z","links":{"resolver":"https://pith.science/pith/TTMWSOYC66O33XZCHYR2AAIELK","bundle":"https://pith.science/pith/TTMWSOYC66O33XZCHYR2AAIELK/bundle.json","state":"https://pith.science/pith/TTMWSOYC66O33XZCHYR2AAIELK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTMWSOYC66O33XZCHYR2AAIELK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TTMWSOYC66O33XZCHYR2AAIELK","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":"74cad3e1b3d0409b4c50831d1756cfa2eef1f8d1127eebd4799a9a464d953592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-03T00:51:32Z","title_canon_sha256":"7843a9d3377244e7336ea4904b3d97622eefb736a0f31e32e256d88938401a40"},"schema_version":"1.0","source":{"id":"1109.0580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0580","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0580v2","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0580","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"TTMWSOYC66O3","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TTMWSOYC66O33XZC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TTMWSOYC","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:1ccd6f54f48e34764494a6fca18b2a27781ae0472eaf1bd7917dcb585de9eeb7","target":"graph","created_at":"2026-05-18T02:47:31Z","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 propose a Nested BDDC for a class of saddle-point problems. The method solves for both flux and pressure variables. The fluxes are resolved in three-steps: the coarse solve is followed by subdomain solves, and last we look for a divergence-free flux correction and pressure variables using conjugate gradients with a Multilevel BDDC preconditioner. Because the coarse solve in the first step has the same structure as the original problem, we can use this procedure recursively and solve (a hierarchy of) coarse problems only approximately, utilizing the coarse problems known from the BDDC. The r","authors_text":"Bed\\v{r}ich Soused\\'ik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-03T00:51:32Z","title":"Nested BDDC for a saddle-point problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0580","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":"sha256:9d5759349999b3c29caeb1df0dfa9437329acd07ba7d563f88c4764ee40fe550","target":"record","created_at":"2026-05-18T02:47:31Z","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":"74cad3e1b3d0409b4c50831d1756cfa2eef1f8d1127eebd4799a9a464d953592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-03T00:51:32Z","title_canon_sha256":"7843a9d3377244e7336ea4904b3d97622eefb736a0f31e32e256d88938401a40"},"schema_version":"1.0","source":{"id":"1109.0580","kind":"arxiv","version":2}},"canonical_sha256":"9cd9693b02f79dbddf223e23a001045a9de5fa3baea73b7a3ea1c9dd0f87d5ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cd9693b02f79dbddf223e23a001045a9de5fa3baea73b7a3ea1c9dd0f87d5ff","first_computed_at":"2026-05-18T02:47:31.809438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:31.809438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TJis677A8SuCEcOKupxeDUzOby0nOc8ttUK0mzqpdiuLFXN0etMUKLkm8U5UPuxG8ZMjCXHjqKJ5x5eGHGvqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:31.810121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d5759349999b3c29caeb1df0dfa9437329acd07ba7d563f88c4764ee40fe550","sha256:1ccd6f54f48e34764494a6fca18b2a27781ae0472eaf1bd7917dcb585de9eeb7"],"state_sha256":"ea1309aa7d3eb3e132a05c7033fba41a64e38f77ee9c25c222993535f5e4aaa5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HsyyaGt5Gj/NIx6fEIzhvwGyFtPzWy8xtoVFXMS2lYkx9oBRPx4wEriF2jFaysGUdf9ubBD/+SwZ/vkYROaZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:52:40.777480Z","bundle_sha256":"da588dac3e659cd6216d02dac4ad285f756edbdb66a6ea03c64e0976d4e19a1c"}}