{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:B54VWAM6Z4CJR3WA442FQ33FLY","short_pith_number":"pith:B54VWAM6","schema_version":"1.0","canonical_sha256":"0f795b019ecf0498eec0e734586f655e0eb7a80932174552d2a6a1d90bb95da0","source":{"kind":"arxiv","id":"2601.04120","version":2},"attestation_state":"computed","paper":{"title":"A Single-Loop Bilevel Deep Learning Method for Optimal Control of Obstacle Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Jin Zhang, Lvgang Zhang, Shangzhi Zeng, Yongcun Song","submitted_at":"2026-01-07T17:30:42Z","abstract_excerpt":"Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure. Classical numerical approaches rely on mesh-based discretization and typically require solving a sequence of costly subproblems. In this work, we propose a single-loop bilevel deep learning method, which is mesh-free, scalable to high-dimensional and complex domains, and avoids repeated solution of discretized subproblems. The method employs constraint-embedding neural networks to approximate the state and control and pres"},"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":"2601.04120","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-01-07T17:30:42Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"cc73f97e4e8d1f7849dcbe431b5fcd2de115f881b7bf075012323a34fb81c20a","abstract_canon_sha256":"1f3330102e25ef17b9e6b6a61e5d390117d8f328dfae3863b0d494a1dd594c9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:47.460002Z","signature_b64":"E7eW3I5HTsRugfjy/uBouzn1VSXdDjK1iWhajRUEA0KkSFcwbaKtyEPQdGVEqCnzsVGs4wGWmzZaK+0+dw5aAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f795b019ecf0498eec0e734586f655e0eb7a80932174552d2a6a1d90bb95da0","last_reissued_at":"2026-06-03T01:05:47.459505Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:47.459505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Single-Loop Bilevel Deep Learning Method for Optimal Control of Obstacle Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Jin Zhang, Lvgang Zhang, Shangzhi Zeng, Yongcun Song","submitted_at":"2026-01-07T17:30:42Z","abstract_excerpt":"Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure. Classical numerical approaches rely on mesh-based discretization and typically require solving a sequence of costly subproblems. In this work, we propose a single-loop bilevel deep learning method, which is mesh-free, scalable to high-dimensional and complex domains, and avoids repeated solution of discretized subproblems. The method employs constraint-embedding neural networks to approximate the state and control and pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04120","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.04120/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":"2601.04120","created_at":"2026-06-03T01:05:47.459568+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.04120v2","created_at":"2026-06-03T01:05:47.459568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.04120","created_at":"2026-06-03T01:05:47.459568+00:00"},{"alias_kind":"pith_short_12","alias_value":"B54VWAM6Z4CJ","created_at":"2026-06-03T01:05:47.459568+00:00"},{"alias_kind":"pith_short_16","alias_value":"B54VWAM6Z4CJR3WA","created_at":"2026-06-03T01:05:47.459568+00:00"},{"alias_kind":"pith_short_8","alias_value":"B54VWAM6","created_at":"2026-06-03T01:05:47.459568+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/B54VWAM6Z4CJR3WA442FQ33FLY","json":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY.json","graph_json":"https://pith.science/api/pith-number/B54VWAM6Z4CJR3WA442FQ33FLY/graph.json","events_json":"https://pith.science/api/pith-number/B54VWAM6Z4CJR3WA442FQ33FLY/events.json","paper":"https://pith.science/paper/B54VWAM6"},"agent_actions":{"view_html":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY","download_json":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY.json","view_paper":"https://pith.science/paper/B54VWAM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.04120&json=true","fetch_graph":"https://pith.science/api/pith-number/B54VWAM6Z4CJR3WA442FQ33FLY/graph.json","fetch_events":"https://pith.science/api/pith-number/B54VWAM6Z4CJR3WA442FQ33FLY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY/action/storage_attestation","attest_author":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY/action/author_attestation","sign_citation":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY/action/citation_signature","submit_replication":"https://pith.science/pith/B54VWAM6Z4CJR3WA442FQ33FLY/action/replication_record"}},"created_at":"2026-06-03T01:05:47.459568+00:00","updated_at":"2026-06-03T01:05:47.459568+00:00"}