{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OHUVOQ3DKHPNMW7ZPKY4SDIC5K","short_pith_number":"pith:OHUVOQ3D","schema_version":"1.0","canonical_sha256":"71e957436351ded65bf97ab1c90d02ea91c9fdee4602890ae49b5f9933a4a407","source":{"kind":"arxiv","id":"2504.17729","version":1},"attestation_state":"computed","paper":{"title":"Fully-Mixed Virtual Element Method for the Biot Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Anna Scotti, Daniele Prada, Michele Botti, Michele Visinoni","submitted_at":"2025-04-24T16:42:50Z","abstract_excerpt":"Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and stress field, as well as satisfying local mass and momentum conservation. In this work, we focus on a novel four-fields Virtual Element discretization of Biot's equations. The stress symmetry is strongly imposed in the definition of the discrete space, thus avoiding the use of an additional Lagrange multiplier. A complete a priori analysis is performed, showing"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.17729","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-04-24T16:42:50Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"87d0b262d1b69be0aaf1ae5335908075e95cc1116a3af9ce9bf1dec009f48afd","abstract_canon_sha256":"c55fd70e54673ce3a338c729b90deae7c90a44bed5b9d87bad7a88f485ca2a3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:53:40.185728Z","signature_b64":"XUQn5deW2hAA4CKuuKDw4h5ExGbKoB3u69MuSKYYeWMZY+gJg9qgwEiO3TYGk8R16BgcgXwo6/LhONs3eNuPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71e957436351ded65bf97ab1c90d02ea91c9fdee4602890ae49b5f9933a4a407","last_reissued_at":"2026-07-05T10:53:40.185289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:53:40.185289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fully-Mixed Virtual Element Method for the Biot Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Anna Scotti, Daniele Prada, Michele Botti, Michele Visinoni","submitted_at":"2025-04-24T16:42:50Z","abstract_excerpt":"Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and stress field, as well as satisfying local mass and momentum conservation. In this work, we focus on a novel four-fields Virtual Element discretization of Biot's equations. The stress symmetry is strongly imposed in the definition of the discrete space, thus avoiding the use of an additional Lagrange multiplier. A complete a priori analysis is performed, showing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17729","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/2504.17729/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.17729","created_at":"2026-07-05T10:53:40.185360+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.17729v1","created_at":"2026-07-05T10:53:40.185360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.17729","created_at":"2026-07-05T10:53:40.185360+00:00"},{"alias_kind":"pith_short_12","alias_value":"OHUVOQ3DKHPN","created_at":"2026-07-05T10:53:40.185360+00:00"},{"alias_kind":"pith_short_16","alias_value":"OHUVOQ3DKHPNMW7Z","created_at":"2026-07-05T10:53:40.185360+00:00"},{"alias_kind":"pith_short_8","alias_value":"OHUVOQ3D","created_at":"2026-07-05T10:53:40.185360+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K","json":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K.json","graph_json":"https://pith.science/api/pith-number/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/graph.json","events_json":"https://pith.science/api/pith-number/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/events.json","paper":"https://pith.science/paper/OHUVOQ3D"},"agent_actions":{"view_html":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K","download_json":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K.json","view_paper":"https://pith.science/paper/OHUVOQ3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.17729&json=true","fetch_graph":"https://pith.science/api/pith-number/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/graph.json","fetch_events":"https://pith.science/api/pith-number/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/action/storage_attestation","attest_author":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/action/author_attestation","sign_citation":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/action/citation_signature","submit_replication":"https://pith.science/pith/OHUVOQ3DKHPNMW7ZPKY4SDIC5K/action/replication_record"}},"created_at":"2026-07-05T10:53:40.185360+00:00","updated_at":"2026-07-05T10:53:40.185360+00:00"}