{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:WFASZV4Z3SPF5RIXQZYGVP6X5O","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":"a78e889b950d4f4a1197d61d41b0d320b2b8b3939cceb0bfb6a6829ce2970d30","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2000-03-24T13:35:24Z","title_canon_sha256":"1a1ef28a44d404a2ae5712ed2c08a1a927483aef649dcedf433038072834046b"},"schema_version":"1.0","source":{"id":"math/0003149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0003149","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/0003149v2","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0003149","created_at":"2026-05-18T02:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"WFASZV4Z3SPF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"WFASZV4Z3SPF5RIX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"WFASZV4Z","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:095cadb5a2b53aa15b93876fd190e0e14c0a8d0dbf322d1fcd90afae9870f9c0","target":"graph","created_at":"2026-05-18T02:42:46Z","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 construct a family of integral kernels for solving the \\bar\\partial equation with C^k and Holder estimates in thin tubes around totally real submanifolds in complex Eulidean spaces (theorems 1.1 and 3.1). Combining this with the proof of a theorem of Serre we solve the d-equation with estimates for holomorphic forms in such tubes (theorem 5.1). We apply these techniques and a method of Moser to approximate C^k-diffeomorphisms between totally real submanifolds in C^n in the C^k-topology by biholomorphic mappings in tubes, by unimodular and symplectic biholomorphic mappings, and by holomorphi","authors_text":"Erik Low, Franc Forstneric, Nils {\\O}vrelid","cross_cats":[],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2000-03-24T13:35:24Z","title":"Solving the $d$ and $\\bar\\partial$-equation in thin tubes and applications to mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0003149","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:b336fe39e23535f29164fb8850ca8c309aaa1a67ae95b98393fcf5ecc307fc4c","target":"record","created_at":"2026-05-18T02:42:46Z","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":"a78e889b950d4f4a1197d61d41b0d320b2b8b3939cceb0bfb6a6829ce2970d30","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2000-03-24T13:35:24Z","title_canon_sha256":"1a1ef28a44d404a2ae5712ed2c08a1a927483aef649dcedf433038072834046b"},"schema_version":"1.0","source":{"id":"math/0003149","kind":"arxiv","version":2}},"canonical_sha256":"b1412cd799dc9e5ec51786706abfd7ebac8cb331427ed88ae0f12b334d6f7b14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1412cd799dc9e5ec51786706abfd7ebac8cb331427ed88ae0f12b334d6f7b14","first_computed_at":"2026-05-18T02:42:46.915698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:46.915698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8H1nFGt00M/URX5UPx680NvlACzNhXXTDAig9taUQCurrN3/Jj6/vVjlV1g+wqjZkqfSI81uRNyffxNauVnEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:46.916114Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0003149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b336fe39e23535f29164fb8850ca8c309aaa1a67ae95b98393fcf5ecc307fc4c","sha256:095cadb5a2b53aa15b93876fd190e0e14c0a8d0dbf322d1fcd90afae9870f9c0"],"state_sha256":"31178f41f99c7c5499b9212eca250abd961c0554719e43e5d0c59b0aeceb2846"}