{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5ONVXJOSMA6AIAB3S2WJR6MIWK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8960a6996f61313f14f9c0dd7c267810fbc6b9e873bff4a21c7e5c9451d84c01","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-05T07:55:24Z","title_canon_sha256":"3766e2974577ceb4075f612aced44e17d1e763b1d2c81cda8624f41d0d8e8407"},"schema_version":"1.0","source":{"id":"1207.1182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1182","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1182v2","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1182","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"5ONVXJOSMA6A","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5ONVXJOSMA6AIAB3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5ONVXJOS","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:e6d9bc9e3d4841648433995e0452ffbc73d93e88d372121c8449921fbc4a05b1","target":"graph","created_at":"2026-05-18T02:58:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of K\\\"ahler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds and also a construction of global canonical family of holomorphic $(n,0)$-forms on the deformation spaces of Calabi-Yau manifolds. Similar constructions are also applied to the deformation spaces of compact K\\\"ahler manifolds.","authors_text":"Kefeng Liu, Sheng Rao, Xiaokui Yang","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-05T07:55:24Z","title":"Quasi-isometry and deformations of Calabi-Yau manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1182","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:979d7e88d1b1655ae2ccf0f4f0d485cf404f3d30180eba7b85e234bba33af2dc","target":"record","created_at":"2026-05-18T02:58:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8960a6996f61313f14f9c0dd7c267810fbc6b9e873bff4a21c7e5c9451d84c01","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-05T07:55:24Z","title_canon_sha256":"3766e2974577ceb4075f612aced44e17d1e763b1d2c81cda8624f41d0d8e8407"},"schema_version":"1.0","source":{"id":"1207.1182","kind":"arxiv","version":2}},"canonical_sha256":"eb9b5ba5d2603c04003b96ac98f988b283303c20c8d6c744cdef675c0e1e5595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb9b5ba5d2603c04003b96ac98f988b283303c20c8d6c744cdef675c0e1e5595","first_computed_at":"2026-05-18T02:58:57.823416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:57.823416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V6p45zWNCO3sj6Qo/atGu1lnjXVrCfmLJ2GsXONQ231LUUr3yW/wrNYpiXQhxDGPA/YNCS1fgPaU9mgFRsRkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:57.824570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:979d7e88d1b1655ae2ccf0f4f0d485cf404f3d30180eba7b85e234bba33af2dc","sha256:e6d9bc9e3d4841648433995e0452ffbc73d93e88d372121c8449921fbc4a05b1"],"state_sha256":"361f28972b33b3aadb2047718771a211bbcdac388fb71794d2ddbda122513629"}