{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DCRYQY75DYM47TMYKHB62RVB6H","short_pith_number":"pith:DCRYQY75","schema_version":"1.0","canonical_sha256":"18a38863fd1e19cfcd9851c3ed46a1f1e633360dfc515c02b2037b09217ed499","source":{"kind":"arxiv","id":"1406.6753","version":4},"attestation_state":"computed","paper":{"title":"A differential-geometric approach to deformations of pairs $(X,E)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Kwokwai Chan, Yat-Hin Suen","submitted_at":"2014-06-26T02:46:07Z","abstract_excerpt":"This article gives an exposition of the deformation theory for pairs $(X, E)$, where $X$ is a compact complex manifold and $E$ is a holomorphic vector bundle over $X$, adapting an analytic viewpoint \\`{a} la Kodaira-Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer--Cartan equation and differential graded Lie algebra (DGLA) governing the deformation problem, and express them in terms of differential-geometric notions such as the connection and curvature of $E$, obtaining a chain level refinement of the classical results that the tangent space and o"},"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":"1406.6753","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-06-26T02:46:07Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"e0681fddd5f83a3bbab3436e8cc19d14d85b24f2977a2c13fa805fd62cf7718f","abstract_canon_sha256":"b123291496ce4b883ee6dd7b738d9696953fb0764b1c09a679e9fc64aff9a2ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.049006Z","signature_b64":"rLSbl4bdPGvrjNv0KUgsrLv7KM/B+MDcjUexAJJWjxGMFAtChTbA95Pp7SAJakD99O55fHjAgyOZUXQ5W12LAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18a38863fd1e19cfcd9851c3ed46a1f1e633360dfc515c02b2037b09217ed499","last_reissued_at":"2026-05-18T01:20:54.048403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.048403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A differential-geometric approach to deformations of pairs $(X,E)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Kwokwai Chan, Yat-Hin Suen","submitted_at":"2014-06-26T02:46:07Z","abstract_excerpt":"This article gives an exposition of the deformation theory for pairs $(X, E)$, where $X$ is a compact complex manifold and $E$ is a holomorphic vector bundle over $X$, adapting an analytic viewpoint \\`{a} la Kodaira-Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer--Cartan equation and differential graded Lie algebra (DGLA) governing the deformation problem, and express them in terms of differential-geometric notions such as the connection and curvature of $E$, obtaining a chain level refinement of the classical results that the tangent space and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6753","kind":"arxiv","version":4},"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":"1406.6753","created_at":"2026-05-18T01:20:54.048508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.6753v4","created_at":"2026-05-18T01:20:54.048508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6753","created_at":"2026-05-18T01:20:54.048508+00:00"},{"alias_kind":"pith_short_12","alias_value":"DCRYQY75DYM4","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DCRYQY75DYM47TMY","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DCRYQY75","created_at":"2026-05-18T12:28:25.294606+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/DCRYQY75DYM47TMYKHB62RVB6H","json":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H.json","graph_json":"https://pith.science/api/pith-number/DCRYQY75DYM47TMYKHB62RVB6H/graph.json","events_json":"https://pith.science/api/pith-number/DCRYQY75DYM47TMYKHB62RVB6H/events.json","paper":"https://pith.science/paper/DCRYQY75"},"agent_actions":{"view_html":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H","download_json":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H.json","view_paper":"https://pith.science/paper/DCRYQY75","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.6753&json=true","fetch_graph":"https://pith.science/api/pith-number/DCRYQY75DYM47TMYKHB62RVB6H/graph.json","fetch_events":"https://pith.science/api/pith-number/DCRYQY75DYM47TMYKHB62RVB6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H/action/storage_attestation","attest_author":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H/action/author_attestation","sign_citation":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H/action/citation_signature","submit_replication":"https://pith.science/pith/DCRYQY75DYM47TMYKHB62RVB6H/action/replication_record"}},"created_at":"2026-05-18T01:20:54.048508+00:00","updated_at":"2026-05-18T01:20:54.048508+00:00"}