{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2VYSSFHXJAZYOETIXBOXTXUEEL","short_pith_number":"pith:2VYSSFHX","canonical_record":{"source":{"id":"1412.3527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-12-11T03:28:12Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9402d1d2cb25f7e5cd32476a1c772962c020eb72d652b5033ae4d79a3c03fcdc","abstract_canon_sha256":"ce42e962354dbe7dd12efa5335ae849776e1ae0b0c0c93cbe6ec464681b2ec51"},"schema_version":"1.0"},"canonical_sha256":"d5712914f74833871268b85d79de8422dc589a7e0a6a74dee15e5babbb76db47","source":{"kind":"arxiv","id":"1412.3527","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3527","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3527v1","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3527","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"2VYSSFHXJAZY","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2VYSSFHXJAZYOETI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2VYSSFHX","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2VYSSFHXJAZYOETIXBOXTXUEEL","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-12-11T03:28:12Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9402d1d2cb25f7e5cd32476a1c772962c020eb72d652b5033ae4d79a3c03fcdc","abstract_canon_sha256":"ce42e962354dbe7dd12efa5335ae849776e1ae0b0c0c93cbe6ec464681b2ec51"},"schema_version":"1.0"},"canonical_sha256":"d5712914f74833871268b85d79de8422dc589a7e0a6a74dee15e5babbb76db47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:30.893395Z","signature_b64":"hk/7eEOIBWPuuGiJT1TSbn/Ymz3QGq0Mcn5K/78st9LMVxujygFI5sGtr2N+wMnrWNVahNI+Klk/q/QIpH5kBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5712914f74833871268b85d79de8422dc589a7e0a6a74dee15e5babbb76db47","last_reissued_at":"2026-05-18T02:31:30.892953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:30.892953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3527","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFeFnAbmTio6kGUv4RFJ4cyDBW/x3l2R4qasyvuFuI/8cnY80UWdstkoEB6kCqnnbX4ogBCPUbNnOasM1WZSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T02:58:59.075212Z"},"content_sha256":"67049073978fc15a58b824e2dd44bd2b462d1ee2d9e2360d8f61dff4c5b48764","schema_version":"1.0","event_id":"sha256:67049073978fc15a58b824e2dd44bd2b462d1ee2d9e2360d8f61dff4c5b48764"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2VYSSFHXJAZYOETIXBOXTXUEEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Lei Wang, Zhenhan Tu","submitted_at":"2014-12-11T03:28:12Z","abstract_excerpt":"The Fock-Bargmann-Hartogs domain $D_{n,m}(\\mu)$ ($\\mu>0$) in $\\mathbf{C}^{n+m}$ is defined by the inequality $\\|w\\|^2<e^{-\\mu\\|z\\|^2},$ where $(z,w)\\in \\mathbf{C}^n\\times \\mathbf{C}^m$, which is an unbounded non-hyperbolic domain in $\\mathbf{C}^{n+m}$. Recently, Yamamori gave an explicit formula for the Bergman kernel of the Fock-Bargmann-Hartogs domains in terms of the polylogarithm functions and Kim-Ninh-Yamamori determined the automorphism group of the domain $D_{n,m}(\\mu)$. In this article, we obtain rigidity results on proper holomorphic mappings between two equidimensional Fock-Bargmann-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3527","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZokylSSx9OlHDgj0yhniFR3D/EgHePJBGVo2FAZGjQ0vPSi8xvF3f0x2kQiFkasqcUEZUFqB1+URq+2CBYafCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T02:58:59.075570Z"},"content_sha256":"933f36af38518ecb493aa7849bc9c0e89d73e8019ef48d381091cadaa47673f3","schema_version":"1.0","event_id":"sha256:933f36af38518ecb493aa7849bc9c0e89d73e8019ef48d381091cadaa47673f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VYSSFHXJAZYOETIXBOXTXUEEL/bundle.json","state_url":"https://pith.science/pith/2VYSSFHXJAZYOETIXBOXTXUEEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VYSSFHXJAZYOETIXBOXTXUEEL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T02:58:59Z","links":{"resolver":"https://pith.science/pith/2VYSSFHXJAZYOETIXBOXTXUEEL","bundle":"https://pith.science/pith/2VYSSFHXJAZYOETIXBOXTXUEEL/bundle.json","state":"https://pith.science/pith/2VYSSFHXJAZYOETIXBOXTXUEEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VYSSFHXJAZYOETIXBOXTXUEEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2VYSSFHXJAZYOETIXBOXTXUEEL","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":"ce42e962354dbe7dd12efa5335ae849776e1ae0b0c0c93cbe6ec464681b2ec51","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-12-11T03:28:12Z","title_canon_sha256":"9402d1d2cb25f7e5cd32476a1c772962c020eb72d652b5033ae4d79a3c03fcdc"},"schema_version":"1.0","source":{"id":"1412.3527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3527","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3527v1","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3527","created_at":"2026-05-18T02:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"2VYSSFHXJAZY","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2VYSSFHXJAZYOETI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2VYSSFHX","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:933f36af38518ecb493aa7849bc9c0e89d73e8019ef48d381091cadaa47673f3","target":"graph","created_at":"2026-05-18T02:31:30Z","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":"The Fock-Bargmann-Hartogs domain $D_{n,m}(\\mu)$ ($\\mu>0$) in $\\mathbf{C}^{n+m}$ is defined by the inequality $\\|w\\|^2<e^{-\\mu\\|z\\|^2},$ where $(z,w)\\in \\mathbf{C}^n\\times \\mathbf{C}^m$, which is an unbounded non-hyperbolic domain in $\\mathbf{C}^{n+m}$. Recently, Yamamori gave an explicit formula for the Bergman kernel of the Fock-Bargmann-Hartogs domains in terms of the polylogarithm functions and Kim-Ninh-Yamamori determined the automorphism group of the domain $D_{n,m}(\\mu)$. In this article, we obtain rigidity results on proper holomorphic mappings between two equidimensional Fock-Bargmann-","authors_text":"Lei Wang, Zhenhan Tu","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-12-11T03:28:12Z","title":"Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3527","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":"sha256:67049073978fc15a58b824e2dd44bd2b462d1ee2d9e2360d8f61dff4c5b48764","target":"record","created_at":"2026-05-18T02:31:30Z","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":"ce42e962354dbe7dd12efa5335ae849776e1ae0b0c0c93cbe6ec464681b2ec51","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-12-11T03:28:12Z","title_canon_sha256":"9402d1d2cb25f7e5cd32476a1c772962c020eb72d652b5033ae4d79a3c03fcdc"},"schema_version":"1.0","source":{"id":"1412.3527","kind":"arxiv","version":1}},"canonical_sha256":"d5712914f74833871268b85d79de8422dc589a7e0a6a74dee15e5babbb76db47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5712914f74833871268b85d79de8422dc589a7e0a6a74dee15e5babbb76db47","first_computed_at":"2026-05-18T02:31:30.892953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:30.892953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hk/7eEOIBWPuuGiJT1TSbn/Ymz3QGq0Mcn5K/78st9LMVxujygFI5sGtr2N+wMnrWNVahNI+Klk/q/QIpH5kBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:30.893395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67049073978fc15a58b824e2dd44bd2b462d1ee2d9e2360d8f61dff4c5b48764","sha256:933f36af38518ecb493aa7849bc9c0e89d73e8019ef48d381091cadaa47673f3"],"state_sha256":"7d09ae9d8e251f1992739ae3cc8c33da1898f80be5bc0c5ab7bc777eb4648552"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlIEUXw7FeZSfPjL+USUb5gIHipIeYe6bjyRCNIgIlCXMKLqJPbelUIiW3hRnJD6I/OSHYZQ6VvLZ8A3gtDDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T02:58:59.077420Z","bundle_sha256":"f1476f5cae8485fcb7733fcfb8f788b7baf386dbe5c5f88a811da42650b1f142"}}