{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:Y4LO6SKVANBHZOVCNHWZBCXYIT","short_pith_number":"pith:Y4LO6SKV","canonical_record":{"source":{"id":"2104.00280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-01T06:39:26Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bf2a37d28ccb061770df5e7ea3ea0ca98c643d8b9af1561c2a4d0d1cffb71ec2","abstract_canon_sha256":"6923bc83286971ca6fd93929cf9bf06645bfc9963c3206f17e5dcbfa84a0ca6b"},"schema_version":"1.0"},"canonical_sha256":"c716ef495503427cbaa269ed908af844dca6fa063821d2c25fb98f83e84a19dc","source":{"kind":"arxiv","id":"2104.00280","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.00280","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"2104.00280v3","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.00280","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"Y4LO6SKVANBH","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"pith_short_16","alias_value":"Y4LO6SKVANBHZOVC","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"pith_short_8","alias_value":"Y4LO6SKV","created_at":"2026-07-05T10:52:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:Y4LO6SKVANBHZOVCNHWZBCXYIT","target":"record","payload":{"canonical_record":{"source":{"id":"2104.00280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-01T06:39:26Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bf2a37d28ccb061770df5e7ea3ea0ca98c643d8b9af1561c2a4d0d1cffb71ec2","abstract_canon_sha256":"6923bc83286971ca6fd93929cf9bf06645bfc9963c3206f17e5dcbfa84a0ca6b"},"schema_version":"1.0"},"canonical_sha256":"c716ef495503427cbaa269ed908af844dca6fa063821d2c25fb98f83e84a19dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:52:52.756435Z","signature_b64":"kbQ67cpZCUsJYWFH4RiCeCMVqcB3HbpXRbcV5bAkNO4QpMW0NK3/Quvpy5BvuFOgxkFaZSw5jVSK4L5r4aduCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c716ef495503427cbaa269ed908af844dca6fa063821d2c25fb98f83e84a19dc","last_reissued_at":"2026-07-05T10:52:52.756033Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:52:52.756033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.00280","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G6UdRzvJwm39ZQl7LcKIb9D57KtRx4eu1mSh2pauAvw7Gce+hsubKd1VHe1Btypna7pfsR/iGmUs+8DrF2zxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:14:17.866709Z"},"content_sha256":"ef8a5582919321e81fbfeff1c2c0b62684f9c90e637868f5ce40d7c40a9d4a0b","schema_version":"1.0","event_id":"sha256:ef8a5582919321e81fbfeff1c2c0b62684f9c90e637868f5ce40d7c40a9d4a0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:Y4LO6SKVANBHZOVCNHWZBCXYIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"GenEO spectral coarse spaces in SPD domain decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nicole Spillane (CMAP)","submitted_at":"2021-04-01T06:39:26Z","abstract_excerpt":"Two-level domain decomposition methods are preconditioned Krylov solvers. What separates one- and two-level domain decomposition methods is the presence of a coarse space in the latter. The abstract Schwarz framework is a formalism that allows to define and study a large variety of two-level methods. The objective of this article is to define, in the abstract Schwarz framework, a family of coarse spaces called the GenEO coarse spaces (for Generalized Eigenvalues in the Overlaps). In detail, this work is a generalization of several methods, each of which exists for a particular choice of domain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00280","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.00280/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yr461bvbCQ88eWEr+pDctkX/q08W7sTZZxf/lRz4PDgQogrkmxo/+SIIIOwFsf9c0LMQIyMtwZOlwtJpZxUXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:14:17.867651Z"},"content_sha256":"0eda39aac2076d7f10de46fbfff900096606eacc8f61b731fb13749abf3856fd","schema_version":"1.0","event_id":"sha256:0eda39aac2076d7f10de46fbfff900096606eacc8f61b731fb13749abf3856fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT/bundle.json","state_url":"https://pith.science/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT/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":"2026-08-14T19:14:17Z","links":{"resolver":"https://pith.science/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT","bundle":"https://pith.science/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT/bundle.json","state":"https://pith.science/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4LO6SKVANBHZOVCNHWZBCXYIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Y4LO6SKVANBHZOVCNHWZBCXYIT","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":"6923bc83286971ca6fd93929cf9bf06645bfc9963c3206f17e5dcbfa84a0ca6b","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-01T06:39:26Z","title_canon_sha256":"bf2a37d28ccb061770df5e7ea3ea0ca98c643d8b9af1561c2a4d0d1cffb71ec2"},"schema_version":"1.0","source":{"id":"2104.00280","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.00280","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"2104.00280v3","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.00280","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"Y4LO6SKVANBH","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"pith_short_16","alias_value":"Y4LO6SKVANBHZOVC","created_at":"2026-07-05T10:52:52Z"},{"alias_kind":"pith_short_8","alias_value":"Y4LO6SKV","created_at":"2026-07-05T10:52:52Z"}],"graph_snapshots":[{"event_id":"sha256:0eda39aac2076d7f10de46fbfff900096606eacc8f61b731fb13749abf3856fd","target":"graph","created_at":"2026-07-05T10:52:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.00280/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two-level domain decomposition methods are preconditioned Krylov solvers. What separates one- and two-level domain decomposition methods is the presence of a coarse space in the latter. The abstract Schwarz framework is a formalism that allows to define and study a large variety of two-level methods. The objective of this article is to define, in the abstract Schwarz framework, a family of coarse spaces called the GenEO coarse spaces (for Generalized Eigenvalues in the Overlaps). In detail, this work is a generalization of several methods, each of which exists for a particular choice of domain","authors_text":"Nicole Spillane (CMAP)","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-01T06:39:26Z","title":"GenEO spectral coarse spaces in SPD domain decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00280","kind":"arxiv","version":3},"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:ef8a5582919321e81fbfeff1c2c0b62684f9c90e637868f5ce40d7c40a9d4a0b","target":"record","created_at":"2026-07-05T10:52:52Z","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":"6923bc83286971ca6fd93929cf9bf06645bfc9963c3206f17e5dcbfa84a0ca6b","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-01T06:39:26Z","title_canon_sha256":"bf2a37d28ccb061770df5e7ea3ea0ca98c643d8b9af1561c2a4d0d1cffb71ec2"},"schema_version":"1.0","source":{"id":"2104.00280","kind":"arxiv","version":3}},"canonical_sha256":"c716ef495503427cbaa269ed908af844dca6fa063821d2c25fb98f83e84a19dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c716ef495503427cbaa269ed908af844dca6fa063821d2c25fb98f83e84a19dc","first_computed_at":"2026-07-05T10:52:52.756033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:52.756033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kbQ67cpZCUsJYWFH4RiCeCMVqcB3HbpXRbcV5bAkNO4QpMW0NK3/Quvpy5BvuFOgxkFaZSw5jVSK4L5r4aduCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:52.756435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.00280","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef8a5582919321e81fbfeff1c2c0b62684f9c90e637868f5ce40d7c40a9d4a0b","sha256:0eda39aac2076d7f10de46fbfff900096606eacc8f61b731fb13749abf3856fd"],"state_sha256":"b0e4a1ab2ae2d346e7b4259d1e739f2eb990adb6a8b8f478be38b20cc1a2c2ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ys3z6mugp6pI2CEc77wKeCDJ5G8feOmzxzWR3YfvRShSFHbmZWl/bG/06Em0utWYSGAOLvl3ne7QtOII7XpRCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:14:17.876177Z","bundle_sha256":"3809682e674c5dab39734d61a1f2bc558f656930d97ef1ab0e9322cd60092209"}}