{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CRBGHE4JYGIARGWTJKOZAZD2WZ","short_pith_number":"pith:CRBGHE4J","schema_version":"1.0","canonical_sha256":"1442639389c190089ad34a9d90647ab648e8810fe19606c3f5dd56dc36aa1bfb","source":{"kind":"arxiv","id":"1411.5235","version":2},"attestation_state":"computed","paper":{"title":"Three-field block-preconditioners for models of coupled magma/mantle dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","cs.NA","physics.geo-ph"],"primary_cat":"math.NA","authors_text":"Andrew J. Wathen, Garth N. Wells, Richard F. Katz, Sander Rhebergen","submitted_at":"2014-11-19T14:28:02Z","abstract_excerpt":"For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure as unknowns. Previous work has shown that while optimal preconditioners for the two-field formulation can be obtained, the construction of preconditioners that are uniform with respect to model parameters is difficult. This limits the applicability of two-field preconditioners in certain regimes of practical interest. We address this issue by reformulating the governing equations as a three-field problem, which removes a term that was problematic in"},"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":"1411.5235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-19T14:28:02Z","cross_cats_sorted":["cs.CE","cs.NA","physics.geo-ph"],"title_canon_sha256":"5a5e83c81ff57e95501f9e3e514426f7eaf2fcd24482868a01aa79bf531b5892","abstract_canon_sha256":"7b0dfa8e955619724cf1947807dd2bae54e6d1c33420c61bcabcdbaadc97bae2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:22.645869Z","signature_b64":"pp4WfAkT8uxFM5RFBQUeodEElvY9fEIDEx8Josuizwd5CMVP8PxO/9c3EoEYC+a4058FVlQIzATqFVimxtiTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1442639389c190089ad34a9d90647ab648e8810fe19606c3f5dd56dc36aa1bfb","last_reissued_at":"2026-05-18T01:11:22.645328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:22.645328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-field block-preconditioners for models of coupled magma/mantle dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","cs.NA","physics.geo-ph"],"primary_cat":"math.NA","authors_text":"Andrew J. Wathen, Garth N. Wells, Richard F. Katz, Sander Rhebergen","submitted_at":"2014-11-19T14:28:02Z","abstract_excerpt":"For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure as unknowns. Previous work has shown that while optimal preconditioners for the two-field formulation can be obtained, the construction of preconditioners that are uniform with respect to model parameters is difficult. This limits the applicability of two-field preconditioners in certain regimes of practical interest. We address this issue by reformulating the governing equations as a three-field problem, which removes a term that was problematic in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5235","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.5235","created_at":"2026-05-18T01:11:22.645433+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.5235v2","created_at":"2026-05-18T01:11:22.645433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5235","created_at":"2026-05-18T01:11:22.645433+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRBGHE4JYGIA","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRBGHE4JYGIARGWT","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRBGHE4J","created_at":"2026-05-18T12:28:22.404517+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/CRBGHE4JYGIARGWTJKOZAZD2WZ","json":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ.json","graph_json":"https://pith.science/api/pith-number/CRBGHE4JYGIARGWTJKOZAZD2WZ/graph.json","events_json":"https://pith.science/api/pith-number/CRBGHE4JYGIARGWTJKOZAZD2WZ/events.json","paper":"https://pith.science/paper/CRBGHE4J"},"agent_actions":{"view_html":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ","download_json":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ.json","view_paper":"https://pith.science/paper/CRBGHE4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.5235&json=true","fetch_graph":"https://pith.science/api/pith-number/CRBGHE4JYGIARGWTJKOZAZD2WZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CRBGHE4JYGIARGWTJKOZAZD2WZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ/action/storage_attestation","attest_author":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ/action/author_attestation","sign_citation":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ/action/citation_signature","submit_replication":"https://pith.science/pith/CRBGHE4JYGIARGWTJKOZAZD2WZ/action/replication_record"}},"created_at":"2026-05-18T01:11:22.645433+00:00","updated_at":"2026-05-18T01:11:22.645433+00:00"}