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In this paper, we proved that the topological solutions of \\eqref{0.1} are uniquely determined by the location of their vortices provided the coupling parameter $\\varepsilon$ is small and the collapsing velocity of vortices $p_i^\\varepsilon$ "},"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":"1412.8317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-29T11:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"19db414c3f391f3671d951ab47fb93f8efebd4432708d53d5d51bf47ad1d367f","abstract_canon_sha256":"afdcd472d2c67185b75a7b2c9311acec8fdeabf12d7c41c92e35aee5bdb17e7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:23.497564Z","signature_b64":"J5eV3k91omRYDcbnK848RkjpYsAsf5/IJ3QoyWsXlqyf2CSodD3crJltoWtctYjD2/G5fpIBgi/0rMDl86h1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b28d01dc44d0c05c02c683535c1673864361657052f33c1f7e2e36903b0fee27","last_reissued_at":"2026-05-18T02:30:23.497084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:23.497084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of topological solutions of self-dual Chern-Simons equation with collapsing vortices","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":"2014-12-29T11:42:18Z","abstract_excerpt":"We consider the following Chern-Simons equation, \\begin{equation} \\label{0.1} \\Delta u+\\frac 1{\\varepsilon^2} e^u(1-e^u)=4\\pi\\sum_{i=1}^N \\delta_{p_i^\\varepsilon},\\quad \\text{in}\\quad \\Omega, \\end{equation} where $\\Omega$ is a 2-dimensional flat torus, $\\varepsilon>0$ is a coupling parameter and $\\delta_p$ stands for the Dirac measure concentrated at $p$. In this paper, we proved that the topological solutions of \\eqref{0.1} are uniquely determined by the location of their vortices provided the coupling parameter $\\varepsilon$ is small and the collapsing velocity of vortices $p_i^\\varepsilon$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8317","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":"1412.8317","created_at":"2026-05-18T02:30:23.497135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.8317v1","created_at":"2026-05-18T02:30:23.497135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8317","created_at":"2026-05-18T02:30:23.497135+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKGQDXCE2DAF","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKGQDXCE2DAFYAWG","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKGQDXCE","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/WKGQDXCE2DAFYAWGQNJVYFTTQZ","json":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ.json","graph_json":"https://pith.science/api/pith-number/WKGQDXCE2DAFYAWGQNJVYFTTQZ/graph.json","events_json":"https://pith.science/api/pith-number/WKGQDXCE2DAFYAWGQNJVYFTTQZ/events.json","paper":"https://pith.science/paper/WKGQDXCE"},"agent_actions":{"view_html":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ","download_json":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ.json","view_paper":"https://pith.science/paper/WKGQDXCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.8317&json=true","fetch_graph":"https://pith.science/api/pith-number/WKGQDXCE2DAFYAWGQNJVYFTTQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/WKGQDXCE2DAFYAWGQNJVYFTTQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ/action/storage_attestation","attest_author":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ/action/author_attestation","sign_citation":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ/action/citation_signature","submit_replication":"https://pith.science/pith/WKGQDXCE2DAFYAWGQNJVYFTTQZ/action/replication_record"}},"created_at":"2026-05-18T02:30:23.497135+00:00","updated_at":"2026-05-18T02:30:23.497135+00:00"}