{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GMUPVI3PCYKR2GPJA44VQK645U","short_pith_number":"pith:GMUPVI3P","canonical_record":{"source":{"id":"1102.0642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-02-03T10:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"e5c4f4edcb8ae83f3906dd9b66abd658bea0954eaf757058d73774c7e38d38bc","abstract_canon_sha256":"fe4e2a548f10e629eaa4404b10139f359e41f440986867bd0fa4e339d4bd0bbd"},"schema_version":"1.0"},"canonical_sha256":"3328faa36f16151d19e90739582bdced06726722a3eac4e1e9e1c16d1f89c666","source":{"kind":"arxiv","id":"1102.0642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0642","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0642v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0642","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"GMUPVI3PCYKR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GMUPVI3PCYKR2GPJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GMUPVI3P","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GMUPVI3PCYKR2GPJA44VQK645U","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-02-03T10:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"e5c4f4edcb8ae83f3906dd9b66abd658bea0954eaf757058d73774c7e38d38bc","abstract_canon_sha256":"fe4e2a548f10e629eaa4404b10139f359e41f440986867bd0fa4e339d4bd0bbd"},"schema_version":"1.0"},"canonical_sha256":"3328faa36f16151d19e90739582bdced06726722a3eac4e1e9e1c16d1f89c666","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:04.311950Z","signature_b64":"C7pma73akvlxnpeSoZXMO/ZZ8Oydp8Dn4iBL2BmLeo/2+ObB0q9yC8Jip9VpDP9gXrhPEuAMQQ6tyrflgY1pCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3328faa36f16151d19e90739582bdced06726722a3eac4e1e9e1c16d1f89c666","last_reissued_at":"2026-05-18T04:30:04.311254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:04.311254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0642","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":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tipdl1ZGTfiQaIx8zAuD0wG7lCOtfShYFHuTzT4tqUKoCVh1VIGtB4nRDSKHTcaVtEEN1XyrbJgwkiij0i5hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:04:50.020585Z"},"content_sha256":"c5e103156de0de611f07fb7f4b521c39cb08e9a229f427cb10f8cb0b986520a1","schema_version":"1.0","event_id":"sha256:c5e103156de0de611f07fb7f4b521c39cb08e9a229f427cb10f8cb0b986520a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GMUPVI3PCYKR2GPJA44VQK645U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Domain decomposition schemes for the Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Petr N. Vabishchevich","submitted_at":"2011-02-03T10:51:42Z","abstract_excerpt":"Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value problems for the Stokes system of equations in the primitive variables pressure-velocity. Unconditionally stable schemes of domain decomposition are based on the partition of unit for a computational domain and the corresponding Hilbert spaces of grid functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0642","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":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7qU9NUL+jS+J5APz0fR7otuogCT0t3KCVneMku14qQPFXzxgG0xTeLCBmP3rrQoH6DECcUf3RJ5FNql2VdsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:04:50.021295Z"},"content_sha256":"e42262d585e98e8264caf8763377e793728f8930f9d9c1c9be3d0d6fb1456cd4","schema_version":"1.0","event_id":"sha256:e42262d585e98e8264caf8763377e793728f8930f9d9c1c9be3d0d6fb1456cd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMUPVI3PCYKR2GPJA44VQK645U/bundle.json","state_url":"https://pith.science/pith/GMUPVI3PCYKR2GPJA44VQK645U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMUPVI3PCYKR2GPJA44VQK645U/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":"2026-06-09T23:04:50Z","links":{"resolver":"https://pith.science/pith/GMUPVI3PCYKR2GPJA44VQK645U","bundle":"https://pith.science/pith/GMUPVI3PCYKR2GPJA44VQK645U/bundle.json","state":"https://pith.science/pith/GMUPVI3PCYKR2GPJA44VQK645U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMUPVI3PCYKR2GPJA44VQK645U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GMUPVI3PCYKR2GPJA44VQK645U","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":"fe4e2a548f10e629eaa4404b10139f359e41f440986867bd0fa4e339d4bd0bbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-02-03T10:51:42Z","title_canon_sha256":"e5c4f4edcb8ae83f3906dd9b66abd658bea0954eaf757058d73774c7e38d38bc"},"schema_version":"1.0","source":{"id":"1102.0642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0642","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0642v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0642","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"GMUPVI3PCYKR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GMUPVI3PCYKR2GPJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GMUPVI3P","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e42262d585e98e8264caf8763377e793728f8930f9d9c1c9be3d0d6fb1456cd4","target":"graph","created_at":"2026-05-18T04:30:04Z","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":"Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value problems for the Stokes system of equations in the primitive variables pressure-velocity. Unconditionally stable schemes of domain decomposition are based on the partition of unit for a computational domain and the corresponding Hilbert spaces of grid functions.","authors_text":"Petr N. Vabishchevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-02-03T10:51:42Z","title":"Domain decomposition schemes for the Stokes equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0642","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:c5e103156de0de611f07fb7f4b521c39cb08e9a229f427cb10f8cb0b986520a1","target":"record","created_at":"2026-05-18T04:30:04Z","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":"fe4e2a548f10e629eaa4404b10139f359e41f440986867bd0fa4e339d4bd0bbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-02-03T10:51:42Z","title_canon_sha256":"e5c4f4edcb8ae83f3906dd9b66abd658bea0954eaf757058d73774c7e38d38bc"},"schema_version":"1.0","source":{"id":"1102.0642","kind":"arxiv","version":1}},"canonical_sha256":"3328faa36f16151d19e90739582bdced06726722a3eac4e1e9e1c16d1f89c666","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3328faa36f16151d19e90739582bdced06726722a3eac4e1e9e1c16d1f89c666","first_computed_at":"2026-05-18T04:30:04.311254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:04.311254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C7pma73akvlxnpeSoZXMO/ZZ8Oydp8Dn4iBL2BmLeo/2+ObB0q9yC8Jip9VpDP9gXrhPEuAMQQ6tyrflgY1pCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:04.311950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5e103156de0de611f07fb7f4b521c39cb08e9a229f427cb10f8cb0b986520a1","sha256:e42262d585e98e8264caf8763377e793728f8930f9d9c1c9be3d0d6fb1456cd4"],"state_sha256":"f173abcc4938651fe9cb67b4d2412b7dfb3eda29afeb26386a0b5c089765b874"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/IjS1+10EozkEB6lGbGtxAtJPbgBn8SZPWA21klXIW83YyZ2hCzJ7e18Bwg//VqAltU7R1KntXyG280h073LBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T23:04:50.025608Z","bundle_sha256":"8388ecd3ec5d290443ca597e127c1774c37b8d4a9fe62308e92dd144cb57ece4"}}