{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5D5X2R344FIMHBWTKFCJIH6NJ4","short_pith_number":"pith:5D5X2R34","canonical_record":{"source":{"id":"2207.01361","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-07-04T12:34:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ebe98fd24fd71954dac121b4fa9695fe9e316feb9c73d4372bdd35cff331ba4f","abstract_canon_sha256":"9ab85fa992f05e2b676dda7b5bd6c782522bc0898eab2442948741887a0cee01"},"schema_version":"1.0"},"canonical_sha256":"e8fb7d477ce150c386d35144941fcd4f18175cd6b887fa570fbf6223351d549a","source":{"kind":"arxiv","id":"2207.01361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.01361","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"2207.01361v1","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.01361","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"5D5X2R344FIM","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"pith_short_16","alias_value":"5D5X2R344FIMHBWT","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"pith_short_8","alias_value":"5D5X2R34","created_at":"2026-07-05T04:37:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5D5X2R344FIMHBWTKFCJIH6NJ4","target":"record","payload":{"canonical_record":{"source":{"id":"2207.01361","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-07-04T12:34:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ebe98fd24fd71954dac121b4fa9695fe9e316feb9c73d4372bdd35cff331ba4f","abstract_canon_sha256":"9ab85fa992f05e2b676dda7b5bd6c782522bc0898eab2442948741887a0cee01"},"schema_version":"1.0"},"canonical_sha256":"e8fb7d477ce150c386d35144941fcd4f18175cd6b887fa570fbf6223351d549a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:37:11.099121Z","signature_b64":"jz2Uky32BKJlB+B4heaBzXKDP6rUCow7uhCX5w2JQGHcYajxJGB3WrpS/RicseVFKC6jn8efkMPuXYWjYLsmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8fb7d477ce150c386d35144941fcd4f18175cd6b887fa570fbf6223351d549a","last_reissued_at":"2026-07-05T04:37:11.098670Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:37:11.098670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.01361","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":"2026-07-05T04:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TEzyZVpyeE2OsYO2O8hDlxfP3UjCQuEQAAvuIbmfAYAU4YtaJznvOgM0Av6Ou08tQ6D55Zd6ZCqp/ND8t8MWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:09:04.687178Z"},"content_sha256":"5ee83bbb8b2f5cbbbe1950ebda2faa04cad25b4b333c4098a471fdd43537416a","schema_version":"1.0","event_id":"sha256:5ee83bbb8b2f5cbbbe1950ebda2faa04cad25b4b333c4098a471fdd43537416a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5D5X2R344FIMHBWTKFCJIH6NJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BDDC preconditioners for divergence free virtual element discretizations of the Stokes equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Simone Scacchi, Tommaso Bevilacqua","submitted_at":"2022-07-04T12:34:48Z","abstract_excerpt":"The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the balancing domain decomposition by constraints (BDDC) preconditioner to the solution of the saddle-point linear system arising from a VEM discretization of the two-dimensional Stokes equations. Under suitable hypotesis on the choice of the primal unknowns, the preconditioned linear system results symmetric and positive definite, thus the preconditioned conjuga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.01361","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.01361/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":"2026-07-05T04:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxASO+rlvl/kV7roFZ3tQd2PYXtHg3AlK27CuYGNEjvGQlVZwSqsMNFAhJTYtYq03wLTtjXZtLogQA8rtrJZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:09:04.687754Z"},"content_sha256":"b0bc5af5e03cc2ec62a5f4bc696a8165c9a54a7b2e5ffedfd64f8680b2ba8b61","schema_version":"1.0","event_id":"sha256:b0bc5af5e03cc2ec62a5f4bc696a8165c9a54a7b2e5ffedfd64f8680b2ba8b61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5D5X2R344FIMHBWTKFCJIH6NJ4/bundle.json","state_url":"https://pith.science/pith/5D5X2R344FIMHBWTKFCJIH6NJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5D5X2R344FIMHBWTKFCJIH6NJ4/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":"2026-08-23T19:09:04Z","links":{"resolver":"https://pith.science/pith/5D5X2R344FIMHBWTKFCJIH6NJ4","bundle":"https://pith.science/pith/5D5X2R344FIMHBWTKFCJIH6NJ4/bundle.json","state":"https://pith.science/pith/5D5X2R344FIMHBWTKFCJIH6NJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5D5X2R344FIMHBWTKFCJIH6NJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5D5X2R344FIMHBWTKFCJIH6NJ4","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":"9ab85fa992f05e2b676dda7b5bd6c782522bc0898eab2442948741887a0cee01","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-07-04T12:34:48Z","title_canon_sha256":"ebe98fd24fd71954dac121b4fa9695fe9e316feb9c73d4372bdd35cff331ba4f"},"schema_version":"1.0","source":{"id":"2207.01361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.01361","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"2207.01361v1","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.01361","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"5D5X2R344FIM","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"pith_short_16","alias_value":"5D5X2R344FIMHBWT","created_at":"2026-07-05T04:37:11Z"},{"alias_kind":"pith_short_8","alias_value":"5D5X2R34","created_at":"2026-07-05T04:37:11Z"}],"graph_snapshots":[{"event_id":"sha256:b0bc5af5e03cc2ec62a5f4bc696a8165c9a54a7b2e5ffedfd64f8680b2ba8b61","target":"graph","created_at":"2026-07-05T04:37:11Z","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/2207.01361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the balancing domain decomposition by constraints (BDDC) preconditioner to the solution of the saddle-point linear system arising from a VEM discretization of the two-dimensional Stokes equations. Under suitable hypotesis on the choice of the primal unknowns, the preconditioned linear system results symmetric and positive definite, thus the preconditioned conjuga","authors_text":"Simone Scacchi, Tommaso Bevilacqua","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-07-04T12:34:48Z","title":"BDDC preconditioners for divergence free virtual element discretizations of the Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.01361","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":"sha256:5ee83bbb8b2f5cbbbe1950ebda2faa04cad25b4b333c4098a471fdd43537416a","target":"record","created_at":"2026-07-05T04:37:11Z","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":"9ab85fa992f05e2b676dda7b5bd6c782522bc0898eab2442948741887a0cee01","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-07-04T12:34:48Z","title_canon_sha256":"ebe98fd24fd71954dac121b4fa9695fe9e316feb9c73d4372bdd35cff331ba4f"},"schema_version":"1.0","source":{"id":"2207.01361","kind":"arxiv","version":1}},"canonical_sha256":"e8fb7d477ce150c386d35144941fcd4f18175cd6b887fa570fbf6223351d549a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8fb7d477ce150c386d35144941fcd4f18175cd6b887fa570fbf6223351d549a","first_computed_at":"2026-07-05T04:37:11.098670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:37:11.098670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jz2Uky32BKJlB+B4heaBzXKDP6rUCow7uhCX5w2JQGHcYajxJGB3WrpS/RicseVFKC6jn8efkMPuXYWjYLsmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:37:11.099121Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.01361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ee83bbb8b2f5cbbbe1950ebda2faa04cad25b4b333c4098a471fdd43537416a","sha256:b0bc5af5e03cc2ec62a5f4bc696a8165c9a54a7b2e5ffedfd64f8680b2ba8b61"],"state_sha256":"6b51bdfd9535c83f7fa339ec9152da25391271624d25f36bbde57741fb61724b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/dnHC781eIB4kkcwYpn7QDaV5EcbMakC4i8ELKAYw5dNpKlDJxa4XNtrMlw/CjtMvaoHHlMwWvcdkxUwJhaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T19:09:04.692723Z","bundle_sha256":"4a14ed97a024d924199a8b201e62193d0a0c9c8da0bf577c328ee85c0e41eeaf"}}