{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EJH3KM7ZKIIZMHGPWRNCTVUNKL","short_pith_number":"pith:EJH3KM7Z","schema_version":"1.0","canonical_sha256":"224fb533f95211961ccfb45a29d68d52e8f9b895c4c5ae3b922a354290552ae6","source":{"kind":"arxiv","id":"1809.01447","version":2},"attestation_state":"computed","paper":{"title":"Control of harmonic map heat flow with an external field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuning Liu","submitted_at":"2018-09-05T11:54:13Z","abstract_excerpt":"We investigate the control problem of harmonic map heat flow by means of an external magnetic field. In contrast to the situation of a parabolic system with internal or boundary control, the magnetic field acts as the coefficients of the lower order terms of the equation. We show that for initial data whose image stays in a hemisphere, with one control acting on a subset of the domain plus a spatial-independent control acting on the whole domain, the state of the system can be steered to any ground state, i.e. any given unit vector, within any short time. To achieve this, in the first step a s"},"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":"1809.01447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T11:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"84c43e67e4458bfb251d5f2bbced53c8caf46e6100f806f355a4fe160cb41a45","abstract_canon_sha256":"35a79a460364cf8eb84cc46546b1c5e5e47c8a00a796efe7195b8648cffbe246"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:25:01.108376Z","signature_b64":"DkYtJFB5eaRNdWycHHcoWEy8tcn4hL/XfJBiOKDvBocBob3SXbK5x6RjcGG1WgTvptoB4++PpawcGDx/vR3VBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"224fb533f95211961ccfb45a29d68d52e8f9b895c4c5ae3b922a354290552ae6","last_reissued_at":"2026-07-05T01:25:01.107867Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:25:01.107867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Control of harmonic map heat flow with an external field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuning Liu","submitted_at":"2018-09-05T11:54:13Z","abstract_excerpt":"We investigate the control problem of harmonic map heat flow by means of an external magnetic field. In contrast to the situation of a parabolic system with internal or boundary control, the magnetic field acts as the coefficients of the lower order terms of the equation. We show that for initial data whose image stays in a hemisphere, with one control acting on a subset of the domain plus a spatial-independent control acting on the whole domain, the state of the system can be steered to any ground state, i.e. any given unit vector, within any short time. To achieve this, in the first step a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01447","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/1809.01447/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":"1809.01447","created_at":"2026-07-05T01:25:01.107927+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01447v2","created_at":"2026-07-05T01:25:01.107927+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01447","created_at":"2026-07-05T01:25:01.107927+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJH3KM7ZKIIZ","created_at":"2026-07-05T01:25:01.107927+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJH3KM7ZKIIZMHGP","created_at":"2026-07-05T01:25:01.107927+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJH3KM7Z","created_at":"2026-07-05T01:25:01.107927+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.18980","citing_title":"Local Exact Controllability of Landau-Lifshitz-Gilbert Equation","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL","json":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL.json","graph_json":"https://pith.science/api/pith-number/EJH3KM7ZKIIZMHGPWRNCTVUNKL/graph.json","events_json":"https://pith.science/api/pith-number/EJH3KM7ZKIIZMHGPWRNCTVUNKL/events.json","paper":"https://pith.science/paper/EJH3KM7Z"},"agent_actions":{"view_html":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL","download_json":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL.json","view_paper":"https://pith.science/paper/EJH3KM7Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01447&json=true","fetch_graph":"https://pith.science/api/pith-number/EJH3KM7ZKIIZMHGPWRNCTVUNKL/graph.json","fetch_events":"https://pith.science/api/pith-number/EJH3KM7ZKIIZMHGPWRNCTVUNKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL/action/storage_attestation","attest_author":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL/action/author_attestation","sign_citation":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL/action/citation_signature","submit_replication":"https://pith.science/pith/EJH3KM7ZKIIZMHGPWRNCTVUNKL/action/replication_record"}},"created_at":"2026-07-05T01:25:01.107927+00:00","updated_at":"2026-07-05T01:25:01.107927+00:00"}