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In this paper, (i) we completely classify the solutions and obtain the quantization result:\n$$\\sum_{j=1}^n a_{ij}\\int_{\\R^2}e^{u_j} dx = 4\\pi (2+\\gamma_i+\\gamma_{n+1-i}), \\;\\;\\forall\\; 1\\leq i \\leq n.$$\nThis generalizes the classification result by Jost and Wang fo"},"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":"1111.0390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-02T05:36:02Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"64c341821896b2e592dca49899dcb94c401e81895d9eb9db55660852f23633e2","abstract_canon_sha256":"defcd828f9e7fda077421ac6c3fa06356593a8dd6c75b8b061bfbfba81801d18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:48.607106Z","signature_b64":"UWOxQR+uax1GdWo2hQcr+4YTWi09ffVdJLN53hvmlmPwqoQd4Mdrfm5YpDpSbcQhB/a1ibifw1EjAUekHeuvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a92c7dace3f3eab2f55b4d4dace833adeeb7ffc74f2648adab1b3330946acb67","last_reissued_at":"2026-05-18T01:59:48.606413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:48.606413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Dong Ye, Juncheng Wei","submitted_at":"2011-11-02T05:36:02Z","abstract_excerpt":"We consider the following Toda system\n\\Delta u_i + \\D \\sum_{j = 1}^n a_{ij}e^{u_j} = 4\\pi\\gamma_{i}\\delta_{0}  \\text{in}\\mathbb R^2,   \\int_{\\mathbb R^2}e^{u_i} dx < \\infty,   \\forall 1\\leq i \\leq n,\nwhere $\\gamma_{i} > -1$, $\\delta_0$ is Dirac measure at 0, and the coefficients $a_{ij}$ form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:\n$$\\sum_{j=1}^n a_{ij}\\int_{\\R^2}e^{u_j} dx = 4\\pi (2+\\gamma_i+\\gamma_{n+1-i}), \\;\\;\\forall\\; 1\\leq i \\leq n.$$\nThis generalizes the classification result by Jost and Wang fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0390","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":"1111.0390","created_at":"2026-05-18T01:59:48.606523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0390v1","created_at":"2026-05-18T01:59:48.606523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0390","created_at":"2026-05-18T01:59:48.606523+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEWH3LHD6PVL","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEWH3LHD6PVLF5K3","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEWH3LHD","created_at":"2026-05-18T12:26:44.992195+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/VEWH3LHD6PVLF5K3JVG2Z2BTVX","json":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX.json","graph_json":"https://pith.science/api/pith-number/VEWH3LHD6PVLF5K3JVG2Z2BTVX/graph.json","events_json":"https://pith.science/api/pith-number/VEWH3LHD6PVLF5K3JVG2Z2BTVX/events.json","paper":"https://pith.science/paper/VEWH3LHD"},"agent_actions":{"view_html":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX","download_json":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX.json","view_paper":"https://pith.science/paper/VEWH3LHD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0390&json=true","fetch_graph":"https://pith.science/api/pith-number/VEWH3LHD6PVLF5K3JVG2Z2BTVX/graph.json","fetch_events":"https://pith.science/api/pith-number/VEWH3LHD6PVLF5K3JVG2Z2BTVX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX/action/storage_attestation","attest_author":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX/action/author_attestation","sign_citation":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX/action/citation_signature","submit_replication":"https://pith.science/pith/VEWH3LHD6PVLF5K3JVG2Z2BTVX/action/replication_record"}},"created_at":"2026-05-18T01:59:48.606523+00:00","updated_at":"2026-05-18T01:59:48.606523+00:00"}