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For a weight $\\balpha$, let $M_C^{\\balpha}(\\bt,\\blambda)$ be the moduli space of $\\balpha$-stable $(\\bt,\\blambda)$-parabolic connections on $C$ and let $RP_r(C,\\bt)_{\\ba}$ be the moduli space of representations of the fundamental group $\\pi_1(C\\setminus\\{t_1,...,t_n\\},*)$ with the local monodromy data $\\ba$ for a certain $\\ba\\in\\C^{nr}$. Then we prove that the morphism $\\RH:M_C^{\\balpha}(\\bt,"},"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":"math/0602004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-02-01T01:54:15Z","cross_cats_sorted":[],"title_canon_sha256":"261fe42b0e54dd3730f62292c39798be5311d4842d85217b426210217bb1bf9c","abstract_canon_sha256":"31625c24071df3b7a844d3cee0f1e471f7cf85e5a4918712b3391a716a130124"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:06.414703Z","signature_b64":"4NVxjVpnNJ4FgejRYsh5maQHky58Qp581x+e4njbqn/c8bNqpp438K28nFdVxCmayPmUT1ho8jviZdduOZkwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beaea39600b8eb61e0aae15b19d40f47c2cbd698a2251710b38e22cf7eee02d9","last_reissued_at":"2026-05-18T03:54:06.414061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:06.414061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli of parabolic connections on a curve and Riemann-Hilbert correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michi-aki Inaba","submitted_at":"2006-02-01T01:54:15Z","abstract_excerpt":"Let $(C,\\bt)$ ($\\bt=(t_1,...,t_n)$) be an $n$-pointed smooth projective curve of genus $g$ and take an element $\\blambda=(\\lambda^{(i)}_j)\\in\\C^{nr}$ such that $-\\sum_{i,j}\\lambda^{(i)}_j=d\\in\\mathbf{Z}$. For a weight $\\balpha$, let $M_C^{\\balpha}(\\bt,\\blambda)$ be the moduli space of $\\balpha$-stable $(\\bt,\\blambda)$-parabolic connections on $C$ and let $RP_r(C,\\bt)_{\\ba}$ be the moduli space of representations of the fundamental group $\\pi_1(C\\setminus\\{t_1,...,t_n\\},*)$ with the local monodromy data $\\ba$ for a certain $\\ba\\in\\C^{nr}$. Then we prove that the morphism $\\RH:M_C^{\\balpha}(\\bt,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602004","kind":"arxiv","version":2},"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":"math/0602004","created_at":"2026-05-18T03:54:06.414197+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0602004v2","created_at":"2026-05-18T03:54:06.414197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602004","created_at":"2026-05-18T03:54:06.414197+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2XKHFQAXDVW","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2XKHFQAXDVWDYFK","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2XKHFQA","created_at":"2026-05-18T12:25:54.717736+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/X2XKHFQAXDVWDYFK4FNRTVAPI7","json":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7.json","graph_json":"https://pith.science/api/pith-number/X2XKHFQAXDVWDYFK4FNRTVAPI7/graph.json","events_json":"https://pith.science/api/pith-number/X2XKHFQAXDVWDYFK4FNRTVAPI7/events.json","paper":"https://pith.science/paper/X2XKHFQA"},"agent_actions":{"view_html":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7","download_json":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7.json","view_paper":"https://pith.science/paper/X2XKHFQA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0602004&json=true","fetch_graph":"https://pith.science/api/pith-number/X2XKHFQAXDVWDYFK4FNRTVAPI7/graph.json","fetch_events":"https://pith.science/api/pith-number/X2XKHFQAXDVWDYFK4FNRTVAPI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7/action/storage_attestation","attest_author":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7/action/author_attestation","sign_citation":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7/action/citation_signature","submit_replication":"https://pith.science/pith/X2XKHFQAXDVWDYFK4FNRTVAPI7/action/replication_record"}},"created_at":"2026-05-18T03:54:06.414197+00:00","updated_at":"2026-05-18T03:54:06.414197+00:00"}