{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:W73W2MCLRCO4VELVLXF776XYZU","short_pith_number":"pith:W73W2MCL","canonical_record":{"source":{"id":"1802.04126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:37:19Z","cross_cats_sorted":[],"title_canon_sha256":"50ea165d970bcf07127cd6a8b892033cfea4f2651047bc223af3c0644d7f7257","abstract_canon_sha256":"47f8e76ae327493acc92abe8e5493f1b7d18e9ae9d8ba19d1cb6a33421fc8be2"},"schema_version":"1.0"},"canonical_sha256":"b7f76d304b889dca91755dcbfffaf8cd164ac16fce9c592443db9379a696167d","source":{"kind":"arxiv","id":"1802.04126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04126","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04126v1","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04126","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"W73W2MCLRCO4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W73W2MCLRCO4VELV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W73W2MCL","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:W73W2MCLRCO4VELVLXF776XYZU","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:37:19Z","cross_cats_sorted":[],"title_canon_sha256":"50ea165d970bcf07127cd6a8b892033cfea4f2651047bc223af3c0644d7f7257","abstract_canon_sha256":"47f8e76ae327493acc92abe8e5493f1b7d18e9ae9d8ba19d1cb6a33421fc8be2"},"schema_version":"1.0"},"canonical_sha256":"b7f76d304b889dca91755dcbfffaf8cd164ac16fce9c592443db9379a696167d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:46.738673Z","signature_b64":"jnCuSNI/6tFV2hqGH5qwpCQuSL3pEosOeTXAPcIt2OJxn31yFNB8G0eBw0+Q8m2M9XIqZP1kxpV40jHtehSsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7f76d304b889dca91755dcbfffaf8cd164ac16fce9c592443db9379a696167d","last_reissued_at":"2026-05-18T00:23:46.738239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:46.738239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04126","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":"2026-05-18T00:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4O6AZklmQ/Dsp7Yd7DwKMJIJBk98k4JI0rHdMJrD+FARzQ35KcFbstppa5jZrkZCPkeTuOqvCLVxncOvCOFvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T01:57:51.450123Z"},"content_sha256":"26f9536d30a1cb52e10c5d606277a159c1aeebb11a248510c798aa38115d1a8b","schema_version":"1.0","event_id":"sha256:26f9536d30a1cb52e10c5d606277a159c1aeebb11a248510c798aa38115d1a8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:W73W2MCLRCO4VELVLXF776XYZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of proper holomorphic mappings between certain unbounded non-hyperbolic domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Lei Wang, Zhenhan Tu","submitted_at":"2018-02-12T15:37:19Z","abstract_excerpt":"The Fock-Bargmann-Hartogs domain $D_{n,m}(\\mu)$ ($\\mu>0$) in $\\mathbb{C}^{n+m}$ is defined by the inequality $\\|w\\|^2<e^{-\\mu\\|z\\|^2},$ where $(z,w)\\in \\mathbb{C}^n\\times \\mathbb{C}^m$, which is an unbounded non-hyperbolic domain in $\\mathbb{C}^{n+m}$. Recently, Tu-Wang obtained the rigidity result that proper holomorphic self-mappings of $D_{n,m}(\\mu)$ are automorphisms for $m\\geq 2$, and found a counter-example to show that the rigidity result isn't true for $D_{n,1}(\\mu)$. In this article, we obtain a classification of proper holomorphic mappings between $D_{n,1}(\\mu)$ and $D_{N,1}(\\mu)$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04126","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":"2026-05-18T00:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4XgziaXC2tjhmXvSd1wCO6q2GobWLCMg5Jajv+Yc36PTrpBT5aYZ9aIvIG8WDeVzn6p0D27jra/axM7ucHMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T01:57:51.450481Z"},"content_sha256":"9957abb13f6334c6e1c74f296ee8561d7a78eb42a1918af298d1c8d653464d7d","schema_version":"1.0","event_id":"sha256:9957abb13f6334c6e1c74f296ee8561d7a78eb42a1918af298d1c8d653464d7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W73W2MCLRCO4VELVLXF776XYZU/bundle.json","state_url":"https://pith.science/pith/W73W2MCLRCO4VELVLXF776XYZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W73W2MCLRCO4VELVLXF776XYZU/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":"2026-06-29T01:57:51Z","links":{"resolver":"https://pith.science/pith/W73W2MCLRCO4VELVLXF776XYZU","bundle":"https://pith.science/pith/W73W2MCLRCO4VELVLXF776XYZU/bundle.json","state":"https://pith.science/pith/W73W2MCLRCO4VELVLXF776XYZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W73W2MCLRCO4VELVLXF776XYZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:W73W2MCLRCO4VELVLXF776XYZU","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":"47f8e76ae327493acc92abe8e5493f1b7d18e9ae9d8ba19d1cb6a33421fc8be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:37:19Z","title_canon_sha256":"50ea165d970bcf07127cd6a8b892033cfea4f2651047bc223af3c0644d7f7257"},"schema_version":"1.0","source":{"id":"1802.04126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04126","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04126v1","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04126","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"W73W2MCLRCO4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W73W2MCLRCO4VELV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W73W2MCL","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:9957abb13f6334c6e1c74f296ee8561d7a78eb42a1918af298d1c8d653464d7d","target":"graph","created_at":"2026-05-18T00:23:46Z","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":"The Fock-Bargmann-Hartogs domain $D_{n,m}(\\mu)$ ($\\mu>0$) in $\\mathbb{C}^{n+m}$ is defined by the inequality $\\|w\\|^2<e^{-\\mu\\|z\\|^2},$ where $(z,w)\\in \\mathbb{C}^n\\times \\mathbb{C}^m$, which is an unbounded non-hyperbolic domain in $\\mathbb{C}^{n+m}$. Recently, Tu-Wang obtained the rigidity result that proper holomorphic self-mappings of $D_{n,m}(\\mu)$ are automorphisms for $m\\geq 2$, and found a counter-example to show that the rigidity result isn't true for $D_{n,1}(\\mu)$. In this article, we obtain a classification of proper holomorphic mappings between $D_{n,1}(\\mu)$ and $D_{N,1}(\\mu)$ wi","authors_text":"Lei Wang, Zhenhan Tu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:37:19Z","title":"Classification 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":"1802.04126","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":"sha256:26f9536d30a1cb52e10c5d606277a159c1aeebb11a248510c798aa38115d1a8b","target":"record","created_at":"2026-05-18T00:23:46Z","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":"47f8e76ae327493acc92abe8e5493f1b7d18e9ae9d8ba19d1cb6a33421fc8be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:37:19Z","title_canon_sha256":"50ea165d970bcf07127cd6a8b892033cfea4f2651047bc223af3c0644d7f7257"},"schema_version":"1.0","source":{"id":"1802.04126","kind":"arxiv","version":1}},"canonical_sha256":"b7f76d304b889dca91755dcbfffaf8cd164ac16fce9c592443db9379a696167d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7f76d304b889dca91755dcbfffaf8cd164ac16fce9c592443db9379a696167d","first_computed_at":"2026-05-18T00:23:46.738239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:46.738239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jnCuSNI/6tFV2hqGH5qwpCQuSL3pEosOeTXAPcIt2OJxn31yFNB8G0eBw0+Q8m2M9XIqZP1kxpV40jHtehSsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:46.738673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26f9536d30a1cb52e10c5d606277a159c1aeebb11a248510c798aa38115d1a8b","sha256:9957abb13f6334c6e1c74f296ee8561d7a78eb42a1918af298d1c8d653464d7d"],"state_sha256":"4a3cd39e60c66b12cee9d165b9b8fffc5141cf0a102cc3e257366b7e5cf2aba1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiSGt/tpHVM2s/grUXEaLEmDJ65NWR4qwaUQfpktQDFp2sPcDSfs9DyB1SKP2r51iflMrGOHU3UE2oRpYDUiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T01:57:51.452489Z","bundle_sha256":"de61e979bd89868840034466762e249d1c0f00f4789c8f4166d0b0b16e7ae1b1"}}