{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WVL7N2NDKQT6X5IIOBSDU64MYU","short_pith_number":"pith:WVL7N2ND","schema_version":"1.0","canonical_sha256":"b557f6e9a35427ebf50870643a7b8cc514ff8b857b87f6cb41b2bc5afa7f4051","source":{"kind":"arxiv","id":"1401.1251","version":1},"attestation_state":"computed","paper":{"title":"Existence of non-topological solutions for a skew-symmetric Chern-Simons system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Genggeng Huang","submitted_at":"2014-01-07T00:47:17Z","abstract_excerpt":"We investigate the existence of non-topological solutions $(u_1,u_2)$ satisfying\n  $$u_{i}(x)=-2\\beta_i\\ln|x|+O(1),\\quad\\text{as }|x|\\rightarrow +\\infty,$$ such that $\\beta_i>1$ and\n  $$(\\beta_1-1)(\\beta_2-1)>(N_1+1)(N_2+1),$$\n  for a skew-symmetric Chern-Simons system. By the bubbling analysis and the Leray-Schauder degree theory, we get the existence results except for a finite set of curves: $$\\frac{N_1}{\\beta_1+N_1}+\\frac{N_2}{\\beta_2+N_2}=\\frac{k-1}{k},k=2,\\cdots,\\max(N_1,N_2).$$ This generalizes a previous work by Choe-Kim-Lin \\cite{ChoeKimLin2011}."},"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":"1401.1251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-07T00:47:17Z","cross_cats_sorted":[],"title_canon_sha256":"d52ff8aaca3e60c68571c8bb600611d09098ead4bc1a165be56776db8bd9dbb9","abstract_canon_sha256":"35a5b0a26306d61966ea162d6236e71346c6a927cadd03a8493862961132cf6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:09.259895Z","signature_b64":"vLTIAMl3Jc/OHSuj0owhXUfiRYRfqmcmvg9/d5Cet6F4Yzg+dU+U2wbhwwC5DzRkhAHz3vrWIt+PdfhE4kwYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b557f6e9a35427ebf50870643a7b8cc514ff8b857b87f6cb41b2bc5afa7f4051","last_reissued_at":"2026-05-18T03:03:09.259394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:09.259394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of non-topological solutions for a skew-symmetric Chern-Simons system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Genggeng Huang","submitted_at":"2014-01-07T00:47:17Z","abstract_excerpt":"We investigate the existence of non-topological solutions $(u_1,u_2)$ satisfying\n  $$u_{i}(x)=-2\\beta_i\\ln|x|+O(1),\\quad\\text{as }|x|\\rightarrow +\\infty,$$ such that $\\beta_i>1$ and\n  $$(\\beta_1-1)(\\beta_2-1)>(N_1+1)(N_2+1),$$\n  for a skew-symmetric Chern-Simons system. By the bubbling analysis and the Leray-Schauder degree theory, we get the existence results except for a finite set of curves: $$\\frac{N_1}{\\beta_1+N_1}+\\frac{N_2}{\\beta_2+N_2}=\\frac{k-1}{k},k=2,\\cdots,\\max(N_1,N_2).$$ This generalizes a previous work by Choe-Kim-Lin \\cite{ChoeKimLin2011}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1251","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":"1401.1251","created_at":"2026-05-18T03:03:09.259468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.1251v1","created_at":"2026-05-18T03:03:09.259468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1251","created_at":"2026-05-18T03:03:09.259468+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVL7N2NDKQT6","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVL7N2NDKQT6X5II","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVL7N2ND","created_at":"2026-05-18T12:28:54.890064+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/WVL7N2NDKQT6X5IIOBSDU64MYU","json":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU.json","graph_json":"https://pith.science/api/pith-number/WVL7N2NDKQT6X5IIOBSDU64MYU/graph.json","events_json":"https://pith.science/api/pith-number/WVL7N2NDKQT6X5IIOBSDU64MYU/events.json","paper":"https://pith.science/paper/WVL7N2ND"},"agent_actions":{"view_html":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU","download_json":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU.json","view_paper":"https://pith.science/paper/WVL7N2ND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.1251&json=true","fetch_graph":"https://pith.science/api/pith-number/WVL7N2NDKQT6X5IIOBSDU64MYU/graph.json","fetch_events":"https://pith.science/api/pith-number/WVL7N2NDKQT6X5IIOBSDU64MYU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU/action/storage_attestation","attest_author":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU/action/author_attestation","sign_citation":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU/action/citation_signature","submit_replication":"https://pith.science/pith/WVL7N2NDKQT6X5IIOBSDU64MYU/action/replication_record"}},"created_at":"2026-05-18T03:03:09.259468+00:00","updated_at":"2026-05-18T03:03:09.259468+00:00"}