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Here, $\\lambda>0$ is the coupling parameter, $\\delta_p$ is the Dirac measure with pole at $p$ and $n_i\\in \\mathbb{N},$ for $i=1, \\dots, N.$ When $N=1, 2$ many results are"},"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":"1805.09970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-25T03:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"c52eb0b092a08e8f3bf92884117a71f6cd5a4302879fda144713fbeca9bdae82","abstract_canon_sha256":"4e2fe46ee3789b88c475e71d7d443c8782b02293e763f26865d12d62b5727d60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:58.629338Z","signature_b64":"BmSgQyitO6DGy8/x27C4CwYSNncvHoIm5yWUD6xTbbECM6ei18w3Amc+it6tBI1kDXq58dr5781NFFsKN4XaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"238443466021e8459de2ba445f5d6feecf688c47d86f643a702de0e2444d9b58","last_reissued_at":"2026-05-18T00:14:58.628733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:58.628733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple Solutions for the Non-Abelian Chern--Simons--Higgs Vortex Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriella Tarantello, Xiaosen Han","submitted_at":"2018-05-25T03:56:32Z","abstract_excerpt":"In this paper we study the existence of multiple solutions for the non-Abelian Chern--Simons--Higgs $(N\\times N)$-system: \\[ \\Delta u_i=\\lambda\\left(\\sum_{j=1}^N\\sum_{k=1}^N K_{kj}K_{ji}\\re^{u_j}\\re^{u_k}-\\sum_{j=1}^N K_{ji}\\re^{u_j}\\right)+4\\pi\\sum_{j=1}^{n_i}\\delta_{p_{ij}},\\quad i=1,\\dots, N; \\] over a doubly periodic domain $\\Omega$, with coupling matrix $K$ given by the Cartan matrix of $SU(N+1),$ (see \\eqref{k1} below). Here, $\\lambda>0$ is the coupling parameter, $\\delta_p$ is the Dirac measure with pole at $p$ and $n_i\\in \\mathbb{N},$ for $i=1, \\dots, N.$ When $N=1, 2$ many results are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09970","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":"1805.09970","created_at":"2026-05-18T00:14:58.628825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.09970v1","created_at":"2026-05-18T00:14:58.628825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09970","created_at":"2026-05-18T00:14:58.628825+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOCEGRTAEHUE","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOCEGRTAEHUELHPC","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOCEGRTA","created_at":"2026-05-18T12:32:22.470017+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/EOCEGRTAEHUELHPCXJCF6XLP53","json":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53.json","graph_json":"https://pith.science/api/pith-number/EOCEGRTAEHUELHPCXJCF6XLP53/graph.json","events_json":"https://pith.science/api/pith-number/EOCEGRTAEHUELHPCXJCF6XLP53/events.json","paper":"https://pith.science/paper/EOCEGRTA"},"agent_actions":{"view_html":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53","download_json":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53.json","view_paper":"https://pith.science/paper/EOCEGRTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.09970&json=true","fetch_graph":"https://pith.science/api/pith-number/EOCEGRTAEHUELHPCXJCF6XLP53/graph.json","fetch_events":"https://pith.science/api/pith-number/EOCEGRTAEHUELHPCXJCF6XLP53/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53/action/storage_attestation","attest_author":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53/action/author_attestation","sign_citation":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53/action/citation_signature","submit_replication":"https://pith.science/pith/EOCEGRTAEHUELHPCXJCF6XLP53/action/replication_record"}},"created_at":"2026-05-18T00:14:58.628825+00:00","updated_at":"2026-05-18T00:14:58.628825+00:00"}