{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DPCYUN6U25OF6D74ENTG4WXONB","short_pith_number":"pith:DPCYUN6U","schema_version":"1.0","canonical_sha256":"1bc58a37d4d75c5f0ffc23666e5aee6864527fdfa23e286c44ac4f3b97667432","source":{"kind":"arxiv","id":"2506.07128","version":1},"attestation_state":"computed","paper":{"title":"New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Dawei Chen, Minghui Li, Qinzhen Ren","submitted_at":"2025-06-08T13:15:01Z","abstract_excerpt":"In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-step algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system."},"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":"2506.07128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-08T13:15:01Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"5c0648d2db0fb31d12adb4ef7f523430f7c8785f43bf8f0d5a2b00e59184ad2d","abstract_canon_sha256":"c0ce2a1cc205a4e25268ecfc12a3e9e562b4446dbd4636091be856cb80a367d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:02.119415Z","signature_b64":"FgwvNEmg0eJwAluvZ3QQQvK/STWx07S9S5cy3nXgqPstG+Ca9OTLo8xarItP5uvsMykT58cIjimL1WYlDUYUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bc58a37d4d75c5f0ffc23666e5aee6864527fdfa23e286c44ac4f3b97667432","last_reissued_at":"2026-07-05T11:18:02.118876Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:02.118876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Dawei Chen, Minghui Li, Qinzhen Ren","submitted_at":"2025-06-08T13:15:01Z","abstract_excerpt":"In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-step algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07128","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/2506.07128/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":"2506.07128","created_at":"2026-07-05T11:18:02.118943+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.07128v1","created_at":"2026-07-05T11:18:02.118943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07128","created_at":"2026-07-05T11:18:02.118943+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPCYUN6U25OF","created_at":"2026-07-05T11:18:02.118943+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPCYUN6U25OF6D74","created_at":"2026-07-05T11:18:02.118943+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPCYUN6U","created_at":"2026-07-05T11:18:02.118943+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/DPCYUN6U25OF6D74ENTG4WXONB","json":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB.json","graph_json":"https://pith.science/api/pith-number/DPCYUN6U25OF6D74ENTG4WXONB/graph.json","events_json":"https://pith.science/api/pith-number/DPCYUN6U25OF6D74ENTG4WXONB/events.json","paper":"https://pith.science/paper/DPCYUN6U"},"agent_actions":{"view_html":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB","download_json":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB.json","view_paper":"https://pith.science/paper/DPCYUN6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.07128&json=true","fetch_graph":"https://pith.science/api/pith-number/DPCYUN6U25OF6D74ENTG4WXONB/graph.json","fetch_events":"https://pith.science/api/pith-number/DPCYUN6U25OF6D74ENTG4WXONB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB/action/storage_attestation","attest_author":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB/action/author_attestation","sign_citation":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB/action/citation_signature","submit_replication":"https://pith.science/pith/DPCYUN6U25OF6D74ENTG4WXONB/action/replication_record"}},"created_at":"2026-07-05T11:18:02.118943+00:00","updated_at":"2026-07-05T11:18:02.118943+00:00"}