{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:OWKEWYMXTMRUCWSJR6AAG2WL4X","short_pith_number":"pith:OWKEWYMX","schema_version":"1.0","canonical_sha256":"75944b61979b23415a498f80036acbe5d5cb5094ef4a9c1e6044ece7ee51bbaf","source":{"kind":"arxiv","id":"2304.06542","version":1},"attestation_state":"computed","paper":{"title":"The global solution of the minimal surface flow and translating surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Li Ma, Yuxin Pan","submitted_at":"2023-04-13T13:53:14Z","abstract_excerpt":"In this paper, we study evolved surfaces over convex planar domains which are evolving by the minimal surface flow $$u_{t}= div\\left(\\frac{Du}{\\sqrt{1+|Du|^2}}\\right)-H(x,Du).$$ Here, we specify the angle of contact of the evolved surface to the boundary cylinder. The interesting question is to find translating solitons of the form $u(x,t)=\\omega t+w(x)$ where $\\omega\\in \\mathbb R$. Under an angle condition, we can prove the a priori estimate holds true for the translating solitons (i.e., translator), which makes the solitons exist. We can prove for suitable condition on $H(x,p)$ that there is"},"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":"2304.06542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-04-13T13:53:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0bf2f86f2c9fbded0b4eb32020b5e77cb0b603f8656c3833aa3cef26cc42e8af","abstract_canon_sha256":"43d7c1efdb8c4bfc9bdf27330201fab6c094b82e6997b1a3b89e4e5699f6896a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:00:45.072047Z","signature_b64":"IGEcs/fLZMcvKySObIv8vTUo1sRN1rkXZu3Az8almODk4I/3oo7HwKeeOuAtpWP8We52w4Wei7dcNdxFl/EjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75944b61979b23415a498f80036acbe5d5cb5094ef4a9c1e6044ece7ee51bbaf","last_reissued_at":"2026-07-05T06:00:45.071597Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:00:45.071597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The global solution of the minimal surface flow and translating surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Li Ma, Yuxin Pan","submitted_at":"2023-04-13T13:53:14Z","abstract_excerpt":"In this paper, we study evolved surfaces over convex planar domains which are evolving by the minimal surface flow $$u_{t}= div\\left(\\frac{Du}{\\sqrt{1+|Du|^2}}\\right)-H(x,Du).$$ Here, we specify the angle of contact of the evolved surface to the boundary cylinder. The interesting question is to find translating solitons of the form $u(x,t)=\\omega t+w(x)$ where $\\omega\\in \\mathbb R$. Under an angle condition, we can prove the a priori estimate holds true for the translating solitons (i.e., translator), which makes the solitons exist. We can prove for suitable condition on $H(x,p)$ that there is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06542","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/2304.06542/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":"2304.06542","created_at":"2026-07-05T06:00:45.071656+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.06542v1","created_at":"2026-07-05T06:00:45.071656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.06542","created_at":"2026-07-05T06:00:45.071656+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWKEWYMXTMRU","created_at":"2026-07-05T06:00:45.071656+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWKEWYMXTMRUCWSJ","created_at":"2026-07-05T06:00:45.071656+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWKEWYMX","created_at":"2026-07-05T06:00:45.071656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.13972","citing_title":"Governance Challenges in Reinforcement Learning from Human Feedback: Evaluator Rationality and Reinforcement Stability","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X","json":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X.json","graph_json":"https://pith.science/api/pith-number/OWKEWYMXTMRUCWSJR6AAG2WL4X/graph.json","events_json":"https://pith.science/api/pith-number/OWKEWYMXTMRUCWSJR6AAG2WL4X/events.json","paper":"https://pith.science/paper/OWKEWYMX"},"agent_actions":{"view_html":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X","download_json":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X.json","view_paper":"https://pith.science/paper/OWKEWYMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.06542&json=true","fetch_graph":"https://pith.science/api/pith-number/OWKEWYMXTMRUCWSJR6AAG2WL4X/graph.json","fetch_events":"https://pith.science/api/pith-number/OWKEWYMXTMRUCWSJR6AAG2WL4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X/action/storage_attestation","attest_author":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X/action/author_attestation","sign_citation":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X/action/citation_signature","submit_replication":"https://pith.science/pith/OWKEWYMXTMRUCWSJR6AAG2WL4X/action/replication_record"}},"created_at":"2026-07-05T06:00:45.071656+00:00","updated_at":"2026-07-05T06:00:45.071656+00:00"}