{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:H2IA7IBBVDL46G26WJYNNFUH2R","short_pith_number":"pith:H2IA7IBB","schema_version":"1.0","canonical_sha256":"3e900fa021a8d7cf1b5eb270d69687d476907c9e4955764daa6203a164ad4602","source":{"kind":"arxiv","id":"1409.3644","version":2},"attestation_state":"computed","paper":{"title":"Stable soliton resolution for exterior wave maps in all equivariance classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andrew Lawrie, Baoping Liu, Carlos Kenig, Wilhelm Schlag","submitted_at":"2014-09-12T03:32:46Z","abstract_excerpt":"In this paper we consider finite energy, \\ell-equivariant wave maps from 1+3-dimensional Minkowski space exterior to the unit ball at the origin into the 3-sphere. We impose a Dirichlet boundary condition at r=1, which in this context means that the boundary of the unit ball in the domain gets mapped to the north pole. Each such \\ell-equivariant wave map has a fixed integer-valued topological degree, and in each degree class there is a unique harmonic map, which minimizes the energy for maps of the same degree. We prove that an arbitrary \\ell-equivariant exterior wave map with finite energy sc"},"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":"1409.3644","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-12T03:32:46Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1bb29a586ad0e8fa12236bdbb19c7003d0d8cba91912c2548b41167a948ab9b7","abstract_canon_sha256":"08f3de612e498f004238c7556a59fa7f83140f4f63f00a53b60145b16e266c63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:12.067066Z","signature_b64":"QIFUPNqty+OI/LrWPB2g+n6jBLMrAbihmO6YghVHbCzQkRqL/qEoGk0bA1UIRm+OtpbPp0BMsH/ELkcD4JdnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e900fa021a8d7cf1b5eb270d69687d476907c9e4955764daa6203a164ad4602","last_reissued_at":"2026-05-18T01:35:12.066407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:12.066407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable soliton resolution for exterior wave maps in all equivariance classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andrew Lawrie, Baoping Liu, Carlos Kenig, Wilhelm Schlag","submitted_at":"2014-09-12T03:32:46Z","abstract_excerpt":"In this paper we consider finite energy, \\ell-equivariant wave maps from 1+3-dimensional Minkowski space exterior to the unit ball at the origin into the 3-sphere. We impose a Dirichlet boundary condition at r=1, which in this context means that the boundary of the unit ball in the domain gets mapped to the north pole. Each such \\ell-equivariant wave map has a fixed integer-valued topological degree, and in each degree class there is a unique harmonic map, which minimizes the energy for maps of the same degree. We prove that an arbitrary \\ell-equivariant exterior wave map with finite energy sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3644","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":""},"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":"1409.3644","created_at":"2026-05-18T01:35:12.066527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3644v2","created_at":"2026-05-18T01:35:12.066527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3644","created_at":"2026-05-18T01:35:12.066527+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2IA7IBBVDL4","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2IA7IBBVDL46G26","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2IA7IBB","created_at":"2026-05-18T12:28:30.664211+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/H2IA7IBBVDL46G26WJYNNFUH2R","json":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R.json","graph_json":"https://pith.science/api/pith-number/H2IA7IBBVDL46G26WJYNNFUH2R/graph.json","events_json":"https://pith.science/api/pith-number/H2IA7IBBVDL46G26WJYNNFUH2R/events.json","paper":"https://pith.science/paper/H2IA7IBB"},"agent_actions":{"view_html":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R","download_json":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R.json","view_paper":"https://pith.science/paper/H2IA7IBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3644&json=true","fetch_graph":"https://pith.science/api/pith-number/H2IA7IBBVDL46G26WJYNNFUH2R/graph.json","fetch_events":"https://pith.science/api/pith-number/H2IA7IBBVDL46G26WJYNNFUH2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R/action/storage_attestation","attest_author":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R/action/author_attestation","sign_citation":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R/action/citation_signature","submit_replication":"https://pith.science/pith/H2IA7IBBVDL46G26WJYNNFUH2R/action/replication_record"}},"created_at":"2026-05-18T01:35:12.066527+00:00","updated_at":"2026-05-18T01:35:12.066527+00:00"}