{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NZGFXBPFYAAB772OFGAZUDZKZN","short_pith_number":"pith:NZGFXBPF","schema_version":"1.0","canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","source":{"kind":"arxiv","id":"1401.0271","version":1},"attestation_state":"computed","paper":{"title":"Solutions without any symmetry for semilinear elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Pacard, Juncheng Wei, Monica Musso, Weiwei Ao","submitted_at":"2014-01-01T10:46:00Z","abstract_excerpt":"We prove the existence of infinitely many solitary waves for the nonlinear Klein-Gordon or Schr\\\"odinger equation $$ \\Delta u-u+ u^3 =0 , $$ in ${\\bf R}^2$, which have finite energy and whose maximal group of symmetry reduces to the identity."},"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":"1401.0271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T10:46:00Z","cross_cats_sorted":[],"title_canon_sha256":"22fc33352ec827685ed9b6338af7a95db1a5eb183dc7cdf4ee94c1aff5db1004","abstract_canon_sha256":"b023634a5a3708baa0d3459afde4c7d8475632d1d7006ff9f8394deaad36ecf2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:23.607975Z","signature_b64":"3GZhhb/z6qiWWH5+QWc9laN7qAqlXsDiUZ1Yi5+aIAGPk0nIGavDddkAGE0+5oIWL1jk1zbcdC9IYyKpbBzpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e4c5b85e5c0001fff4e29819a0f2acb69e959081e974eabd0aa3e6b4a2425cf","last_reissued_at":"2026-05-18T03:03:23.607072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:23.607072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions without any symmetry for semilinear elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Pacard, Juncheng Wei, Monica Musso, Weiwei Ao","submitted_at":"2014-01-01T10:46:00Z","abstract_excerpt":"We prove the existence of infinitely many solitary waves for the nonlinear Klein-Gordon or Schr\\\"odinger equation $$ \\Delta u-u+ u^3 =0 , $$ in ${\\bf R}^2$, which have finite energy and whose maximal group of symmetry reduces to the identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0271","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":""},"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":"1401.0271","created_at":"2026-05-18T03:03:23.607218+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0271v1","created_at":"2026-05-18T03:03:23.607218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0271","created_at":"2026-05-18T03:03:23.607218+00:00"},{"alias_kind":"pith_short_12","alias_value":"NZGFXBPFYAAB","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NZGFXBPFYAAB772O","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NZGFXBPF","created_at":"2026-05-18T12:28:41.024544+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/NZGFXBPFYAAB772OFGAZUDZKZN","json":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN.json","graph_json":"https://pith.science/api/pith-number/NZGFXBPFYAAB772OFGAZUDZKZN/graph.json","events_json":"https://pith.science/api/pith-number/NZGFXBPFYAAB772OFGAZUDZKZN/events.json","paper":"https://pith.science/paper/NZGFXBPF"},"agent_actions":{"view_html":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN","download_json":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN.json","view_paper":"https://pith.science/paper/NZGFXBPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0271&json=true","fetch_graph":"https://pith.science/api/pith-number/NZGFXBPFYAAB772OFGAZUDZKZN/graph.json","fetch_events":"https://pith.science/api/pith-number/NZGFXBPFYAAB772OFGAZUDZKZN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/action/storage_attestation","attest_author":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/action/author_attestation","sign_citation":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/action/citation_signature","submit_replication":"https://pith.science/pith/NZGFXBPFYAAB772OFGAZUDZKZN/action/replication_record"}},"created_at":"2026-05-18T03:03:23.607218+00:00","updated_at":"2026-05-18T03:03:23.607218+00:00"}