{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BYKPF4DD2V6ORZ4XHSH4EMLP3N","short_pith_number":"pith:BYKPF4DD","schema_version":"1.0","canonical_sha256":"0e14f2f063d57ce8e7973c8fc2316fdb521fc0dbe1cda338570bdfe2d42ad673","source":{"kind":"arxiv","id":"2606.22514","version":1},"attestation_state":"computed","paper":{"title":"PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jizu Huang, Tao Zhou, Yue Qian","submitted_at":"2026-06-21T14:06:53Z","abstract_excerpt":"Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent years, operator learning has emerged as a powerful and efficient paradigm for solving evolution PDEs by learning mappings between infinite-dimensional function spaces, enabling solution prediction without explicit time-step integration. In this work, we propose PI-DOSnet, a physics-informed operator learning framework built upon DOSnet and operator splitting. Unlike purely data-driven operator learning methods, PI-DOSn"},"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":"2606.22514","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-21T14:06:53Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8b16aba677e5def7fa7d11513b6185446e39759a2f39b51a6024a9b55f1b471f","abstract_canon_sha256":"45c6a6abe105b925a4f43cb538a63446833fb483b19ed54fe6fbdd99a347b5d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:40.512944Z","signature_b64":"acAvie5aiv6Hc4C3xYZfv28L+GPbpIysKLFyj4jFDxdAPVcKPeBgt+24VZc0KvSVvcHes4I1sKPMlcCl1QciCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e14f2f063d57ce8e7973c8fc2316fdb521fc0dbe1cda338570bdfe2d42ad673","last_reissued_at":"2026-06-23T02:13:40.512538Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:40.512538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jizu Huang, Tao Zhou, Yue Qian","submitted_at":"2026-06-21T14:06:53Z","abstract_excerpt":"Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent years, operator learning has emerged as a powerful and efficient paradigm for solving evolution PDEs by learning mappings between infinite-dimensional function spaces, enabling solution prediction without explicit time-step integration. In this work, we propose PI-DOSnet, a physics-informed operator learning framework built upon DOSnet and operator splitting. Unlike purely data-driven operator learning methods, PI-DOSn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22514","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/2606.22514/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":"2606.22514","created_at":"2026-06-23T02:13:40.512607+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22514v1","created_at":"2026-06-23T02:13:40.512607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22514","created_at":"2026-06-23T02:13:40.512607+00:00"},{"alias_kind":"pith_short_12","alias_value":"BYKPF4DD2V6O","created_at":"2026-06-23T02:13:40.512607+00:00"},{"alias_kind":"pith_short_16","alias_value":"BYKPF4DD2V6ORZ4X","created_at":"2026-06-23T02:13:40.512607+00:00"},{"alias_kind":"pith_short_8","alias_value":"BYKPF4DD","created_at":"2026-06-23T02:13:40.512607+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/BYKPF4DD2V6ORZ4XHSH4EMLP3N","json":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N.json","graph_json":"https://pith.science/api/pith-number/BYKPF4DD2V6ORZ4XHSH4EMLP3N/graph.json","events_json":"https://pith.science/api/pith-number/BYKPF4DD2V6ORZ4XHSH4EMLP3N/events.json","paper":"https://pith.science/paper/BYKPF4DD"},"agent_actions":{"view_html":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N","download_json":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N.json","view_paper":"https://pith.science/paper/BYKPF4DD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22514&json=true","fetch_graph":"https://pith.science/api/pith-number/BYKPF4DD2V6ORZ4XHSH4EMLP3N/graph.json","fetch_events":"https://pith.science/api/pith-number/BYKPF4DD2V6ORZ4XHSH4EMLP3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N/action/storage_attestation","attest_author":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N/action/author_attestation","sign_citation":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N/action/citation_signature","submit_replication":"https://pith.science/pith/BYKPF4DD2V6ORZ4XHSH4EMLP3N/action/replication_record"}},"created_at":"2026-06-23T02:13:40.512607+00:00","updated_at":"2026-06-23T02:13:40.512607+00:00"}