{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ACP4T2XNDIPHUYHMUWAXN5ABHU","short_pith_number":"pith:ACP4T2XN","schema_version":"1.0","canonical_sha256":"009fc9eaed1a1e7a60eca58176f4013d35b0837fc4932b417b6d4f6d4ce83c1b","source":{"kind":"arxiv","id":"1403.2348","version":1},"attestation_state":"computed","paper":{"title":"On Non-topological Solutions of the ${\\bf G}_2$ Chern-Simons System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Juncheng Wei, Weiwei Ao","submitted_at":"2014-03-10T19:10:23Z","abstract_excerpt":"For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form: \\begin{equation}\\label{e001} \\left\\{\\begin{array}{c} \\Delta u_1+(\\sum_{i=1}^2K_{1i}e^{u_i} -\\sum_{i=1}^2\\sum_{j=1}^2e^{u_i}K_{1i}e^{u_j}K_{ij})=4\\pi\\displaystyle \\sum_{j=1}^{N_1}\\delta_{p_j}\\\\ \\Delta u_2+ (\\sum_{i=1}^2K_{2i}e^{u_i}-\\sum_{i=1}^2\\sum_{j=1}^2e^{u_i}K_{2i}e^{u_j}K_{ij})=4\\pi\\displaystyle \\sum_{j=1}^{N_2}\\delta_{q_j} \\end{array} \\right.\\mbox{in}\\; \\mathbb{R}^2, \\end{equation} where $K$ is the Cartan matrix of rank $2$. There are three Cartan matrix of rank 2: ${\\bf A}_2$, ${\\bf B}_2$ "},"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":"1403.2348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-10T19:10:23Z","cross_cats_sorted":[],"title_canon_sha256":"283a477c4aa56df84ff3b12536c6ff6e414bbe7f66b0481161b438d02574c197","abstract_canon_sha256":"5c02a64e5bb8bfeb02f75bc1889338fb1ab69a78ecf0a2497a9a28084334e359"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:44.750639Z","signature_b64":"7XXSaVrh+EBLn6vt22Y32t8c6DYu2FvLO6fJRxSCNrIJROdYnEmy4KTIGYe0wsAu9sDDVR4WFMW6nsX6EmqyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"009fc9eaed1a1e7a60eca58176f4013d35b0837fc4932b417b6d4f6d4ce83c1b","last_reissued_at":"2026-05-18T02:56:44.749929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:44.749929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Non-topological Solutions of the ${\\bf G}_2$ Chern-Simons System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Juncheng Wei, Weiwei Ao","submitted_at":"2014-03-10T19:10:23Z","abstract_excerpt":"For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form: \\begin{equation}\\label{e001} \\left\\{\\begin{array}{c} \\Delta u_1+(\\sum_{i=1}^2K_{1i}e^{u_i} -\\sum_{i=1}^2\\sum_{j=1}^2e^{u_i}K_{1i}e^{u_j}K_{ij})=4\\pi\\displaystyle \\sum_{j=1}^{N_1}\\delta_{p_j}\\\\ \\Delta u_2+ (\\sum_{i=1}^2K_{2i}e^{u_i}-\\sum_{i=1}^2\\sum_{j=1}^2e^{u_i}K_{2i}e^{u_j}K_{ij})=4\\pi\\displaystyle \\sum_{j=1}^{N_2}\\delta_{q_j} \\end{array} \\right.\\mbox{in}\\; \\mathbb{R}^2, \\end{equation} where $K$ is the Cartan matrix of rank $2$. There are three Cartan matrix of rank 2: ${\\bf A}_2$, ${\\bf B}_2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2348","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":"1403.2348","created_at":"2026-05-18T02:56:44.750016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.2348v1","created_at":"2026-05-18T02:56:44.750016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2348","created_at":"2026-05-18T02:56:44.750016+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACP4T2XNDIPH","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACP4T2XNDIPHUYHM","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACP4T2XN","created_at":"2026-05-18T12:28:19.803747+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/ACP4T2XNDIPHUYHMUWAXN5ABHU","json":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU.json","graph_json":"https://pith.science/api/pith-number/ACP4T2XNDIPHUYHMUWAXN5ABHU/graph.json","events_json":"https://pith.science/api/pith-number/ACP4T2XNDIPHUYHMUWAXN5ABHU/events.json","paper":"https://pith.science/paper/ACP4T2XN"},"agent_actions":{"view_html":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU","download_json":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU.json","view_paper":"https://pith.science/paper/ACP4T2XN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.2348&json=true","fetch_graph":"https://pith.science/api/pith-number/ACP4T2XNDIPHUYHMUWAXN5ABHU/graph.json","fetch_events":"https://pith.science/api/pith-number/ACP4T2XNDIPHUYHMUWAXN5ABHU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU/action/storage_attestation","attest_author":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU/action/author_attestation","sign_citation":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU/action/citation_signature","submit_replication":"https://pith.science/pith/ACP4T2XNDIPHUYHMUWAXN5ABHU/action/replication_record"}},"created_at":"2026-05-18T02:56:44.750016+00:00","updated_at":"2026-05-18T02:56:44.750016+00:00"}