{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5NLCC36LLVP46ZOTA2VRIAK5CX","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":"feee6ebc9dc05e2831ae7c3cc1c52514b5d80ed218cc5a8768950c31b544af21","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-15T03:39:53Z","title_canon_sha256":"56727f9b8380628ece41e0142021264e4da3d47fdb9260b419cb05db6431233a"},"schema_version":"1.0","source":{"id":"1409.4148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4148","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4148v1","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4148","created_at":"2026-05-18T02:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"5NLCC36LLVP4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5NLCC36LLVP46ZOT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5NLCC36L","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:757809e43a0dec87bcd90ab82a35eb1865154a1115c6821762eeac5503fc6234","target":"graph","created_at":"2026-05-18T02:42:52Z","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":"Let $X$ be a Stein manifold of complex dimension at least two, $F : X \\rightarrow \\mathbb{C}^n$ a local biholomorphism, and $q \\in F(X)$. In this paper we formulate sufficient conditions involving only objects naturally associated to $q$, in order for the fiber over $q$ to be finite. Assume that $F^{-1}(l)$ is 1-connected for the generic complex line $l$ containing $q$, and $F^{-1}(l)$ has finitely many components whenever $l$ is an exceptional line through $q$. Using arguments from topology and differential geometry, we establish a sharp estimate on the size of $F^{-1}(q)$. It follows that fo","authors_text":"Frederico Xavier, Xiaoyang Chen","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-15T03:39:53Z","title":"Finiteness of prescribed fibers of local biholomorphisms: a geometric approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4148","kind":"arxiv","version":1},"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:fe392f6d39784d79be6227de48e87275637cc8b9524fc887fdd9c51892c4159b","target":"record","created_at":"2026-05-18T02:42:52Z","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":"feee6ebc9dc05e2831ae7c3cc1c52514b5d80ed218cc5a8768950c31b544af21","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-15T03:39:53Z","title_canon_sha256":"56727f9b8380628ece41e0142021264e4da3d47fdb9260b419cb05db6431233a"},"schema_version":"1.0","source":{"id":"1409.4148","kind":"arxiv","version":1}},"canonical_sha256":"eb56216fcb5d5fcf65d306ab14015d15fa37ecaf2449d276d401d39bfdb01876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb56216fcb5d5fcf65d306ab14015d15fa37ecaf2449d276d401d39bfdb01876","first_computed_at":"2026-05-18T02:42:52.927398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:52.927398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h8Tz9f6F3VDXaslAdSd8a4MQxjOUlToEvf0MRRsyASrmPqrqFD4W/95dUvHwwuk94zxv5CVu7t1X7kkiNGAhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:52.927848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe392f6d39784d79be6227de48e87275637cc8b9524fc887fdd9c51892c4159b","sha256:757809e43a0dec87bcd90ab82a35eb1865154a1115c6821762eeac5503fc6234"],"state_sha256":"d62e3dfae97244b8a1617bdfb372037073b59a20d6c7b8f60d80255a135c0429"}