{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OXPVDVOCG67JS77BMZCFJXY2FT","short_pith_number":"pith:OXPVDVOC","schema_version":"1.0","canonical_sha256":"75df51d5c237be997fe1664454df1a2cfc0612931359931241f6810a0e0f3853","source":{"kind":"arxiv","id":"1905.00347","version":1},"attestation_state":"computed","paper":{"title":"On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Yang, Lipeng Duan","submitted_at":"2019-05-01T15:27:48Z","abstract_excerpt":"For the following Ginzburg-Landau system in ${\\mathbb R}^2$\n  \\begin{align*}\n  \\begin{cases}\n  -\\Delta w^+ +\\Big[A_+\\big(|w^+|^2-{t^+}^2\\big)+B\\big(|w^-|^2-{t^-}^2\\big)\\Big]w^+=0,\n  \\\\[3mm] -\\Delta w^- +\\Big[A_-\\big(|w^-|^2-{t^-}^2\\big)+B\\big(|w^+|^2-{t^+}^2\\big)\\Big]w^-=0, \\end{cases} \\end{align*} with constraints $ A_+, A_->0$, $B<0$, $B^2<A_+A_-$ and $t^+, t^->0$, we will concern its linearized operator ${\\mathcal L}$ around the radially symmetric solution $w(x)=(w^+, w^-): {\\mathbb R}^2 \\rightarrow\\mathbb{C}^2$ of degree pair $(1, 1)$ and prove the non-degeneracy result: the kernel of ${\\m"},"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":"1905.00347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-01T15:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"c7ac41911a329cc60c696829c7d8cca41209c2826024b05b19b5adb7db4738a1","abstract_canon_sha256":"e5d84536ad89ae18e4a199b195356776acf5e1f1a6686af00629bfd211caf2fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:13.098115Z","signature_b64":"7NfbEmmL/PAWS3xfub6xAFfejtD6a1cCJ7K1hjq3+Hg3OGZbxQrWCo0sL4PzT1EaxVFgsGVEA1B76njUk+JSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75df51d5c237be997fe1664454df1a2cfc0612931359931241f6810a0e0f3853","last_reissued_at":"2026-05-17T23:47:13.097678Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:13.097678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Yang, Lipeng Duan","submitted_at":"2019-05-01T15:27:48Z","abstract_excerpt":"For the following Ginzburg-Landau system in ${\\mathbb R}^2$\n  \\begin{align*}\n  \\begin{cases}\n  -\\Delta w^+ +\\Big[A_+\\big(|w^+|^2-{t^+}^2\\big)+B\\big(|w^-|^2-{t^-}^2\\big)\\Big]w^+=0,\n  \\\\[3mm] -\\Delta w^- +\\Big[A_-\\big(|w^-|^2-{t^-}^2\\big)+B\\big(|w^+|^2-{t^+}^2\\big)\\Big]w^-=0, \\end{cases} \\end{align*} with constraints $ A_+, A_->0$, $B<0$, $B^2<A_+A_-$ and $t^+, t^->0$, we will concern its linearized operator ${\\mathcal L}$ around the radially symmetric solution $w(x)=(w^+, w^-): {\\mathbb R}^2 \\rightarrow\\mathbb{C}^2$ of degree pair $(1, 1)$ and prove the non-degeneracy result: the kernel of ${\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00347","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":"1905.00347","created_at":"2026-05-17T23:47:13.097748+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.00347v1","created_at":"2026-05-17T23:47:13.097748+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00347","created_at":"2026-05-17T23:47:13.097748+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXPVDVOCG67J","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXPVDVOCG67JS77B","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXPVDVOC","created_at":"2026-05-18T12:33:24.271573+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/OXPVDVOCG67JS77BMZCFJXY2FT","json":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT.json","graph_json":"https://pith.science/api/pith-number/OXPVDVOCG67JS77BMZCFJXY2FT/graph.json","events_json":"https://pith.science/api/pith-number/OXPVDVOCG67JS77BMZCFJXY2FT/events.json","paper":"https://pith.science/paper/OXPVDVOC"},"agent_actions":{"view_html":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT","download_json":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT.json","view_paper":"https://pith.science/paper/OXPVDVOC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.00347&json=true","fetch_graph":"https://pith.science/api/pith-number/OXPVDVOCG67JS77BMZCFJXY2FT/graph.json","fetch_events":"https://pith.science/api/pith-number/OXPVDVOCG67JS77BMZCFJXY2FT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT/action/storage_attestation","attest_author":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT/action/author_attestation","sign_citation":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT/action/citation_signature","submit_replication":"https://pith.science/pith/OXPVDVOCG67JS77BMZCFJXY2FT/action/replication_record"}},"created_at":"2026-05-17T23:47:13.097748+00:00","updated_at":"2026-05-17T23:47:13.097748+00:00"}