{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CRXW2MFIJCPRH3OM4ZH4UFTYH2","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":"0fbe7654f975ad557d71a822cd8f0f238d1db1f3fc1059d7acbf98bb86b56a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-03T18:45:48Z","title_canon_sha256":"fc9143a41a2aaa5cc78bb411691b32b5d0d14b20e9ca4dcd5be3d3dd78b72d21"},"schema_version":"1.0","source":{"id":"1411.0600","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0600","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0600v3","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0600","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"pith_short_12","alias_value":"CRXW2MFIJCPR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CRXW2MFIJCPRH3OM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CRXW2MFI","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:3e185fc416a12ae6b74682e1c92d131f02d2a61d6e0d2fe48df9a10f0fe46228","target":"graph","created_at":"2026-05-18T02:21:26Z","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":"In this paper, we give a general boundary Schwarz lemma for holomorphic mappings between unit balls in any dimensions. It is proved that if the mapping $f\\in C^{1+\\alpha}$ at $z_0\\in \\partial \\mathbb B^n$ with $f(z_0)=w_0\\in \\partial \\mathbb B^N$ for any $n,N\\geq 1$, then the Jacobian matrix $J_f(z_0)$ maps the tangent space $T_{z_0}(\\partial \\mathbb B^n)$ to $T_{w_0}(\\partial \\mathbb B^N)$, and the holomorphic tangent space $T^{(1,0)}_{z_0}(\\partial \\mathbb B^n)$ to $T^{(1,0)}_{w_0}(\\partial \\mathbb B^N)$ as well.","authors_text":"Yang Liu, Yifei Pan, Zhihua Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-03T18:45:48Z","title":"A boundary Schwarz Lemma for holomorphic mappings between unit balls of different dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0600","kind":"arxiv","version":3},"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":"sha256:8cc13ff907ccdecfea54b27fc4fdc948efdc2a65e759c11a652a04417dcbcd3a","target":"record","created_at":"2026-05-18T02:21:26Z","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":"0fbe7654f975ad557d71a822cd8f0f238d1db1f3fc1059d7acbf98bb86b56a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-03T18:45:48Z","title_canon_sha256":"fc9143a41a2aaa5cc78bb411691b32b5d0d14b20e9ca4dcd5be3d3dd78b72d21"},"schema_version":"1.0","source":{"id":"1411.0600","kind":"arxiv","version":3}},"canonical_sha256":"146f6d30a8489f13edcce64fca16783eb331995d573d83d5a00609584414bfbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"146f6d30a8489f13edcce64fca16783eb331995d573d83d5a00609584414bfbb","first_computed_at":"2026-05-18T02:21:26.462705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:26.462705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D/HpcjXqx0Um05rtAv6P6SEs8Fqrq+K9/7v1rB+7+u9evtH5WcRVidrNu2odxm23wdaH+bifIW+crP0GmxyyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:26.463271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0600","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cc13ff907ccdecfea54b27fc4fdc948efdc2a65e759c11a652a04417dcbcd3a","sha256:3e185fc416a12ae6b74682e1c92d131f02d2a61d6e0d2fe48df9a10f0fe46228"],"state_sha256":"0210e7be3e2ca86a6e608d975608dc6ed04c4a1533c5aabe0dffe26f5aa20aeb"}