{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LXUSSFW5CA7JMCIBABZFJGU7XW","short_pith_number":"pith:LXUSSFW5","canonical_record":{"source":{"id":"1304.0252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-31T20:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"47e821e02a2efcb12d50a1ad042b872fdd1e163a49d4fa9e26563aac334eb07b","abstract_canon_sha256":"f174eab8bac3ee67d251462612b66f62d797859c5602ae5a6dfe0396fa3f861d"},"schema_version":"1.0"},"canonical_sha256":"5de92916dd103e9609010072549a9fbdae121a0ad616ad32d45635c70182d0de","source":{"kind":"arxiv","id":"1304.0252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0252","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0252v1","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0252","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"LXUSSFW5CA7J","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LXUSSFW5CA7JMCIB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LXUSSFW5","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LXUSSFW5CA7JMCIBABZFJGU7XW","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-31T20:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"47e821e02a2efcb12d50a1ad042b872fdd1e163a49d4fa9e26563aac334eb07b","abstract_canon_sha256":"f174eab8bac3ee67d251462612b66f62d797859c5602ae5a6dfe0396fa3f861d"},"schema_version":"1.0"},"canonical_sha256":"5de92916dd103e9609010072549a9fbdae121a0ad616ad32d45635c70182d0de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:17.478034Z","signature_b64":"18sHx+ptOfDx5/6Cmdx+Cbdj/cbPhr52WgiL3tk8x8Jcksq7VsmnE7BimmjElM0nRkhY3Pgq2Y8baNmIem29BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de92916dd103e9609010072549a9fbdae121a0ad616ad32d45635c70182d0de","last_reissued_at":"2026-05-18T03:29:17.476029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:17.476029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0252","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":"2026-05-18T03:29:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mg+zw9qclvELHjp5/e3uPEx+qUpG+aaKCwmMstIgmvTOe5MIW8tY/8/4Suljq6IcDJS5FIlVV2t07QWyfgHrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:43:21.632790Z"},"content_sha256":"410fed7b35cdae305cf88ea2c0897fdd81715fea6116b0ea86841b812a8309c5","schema_version":"1.0","event_id":"sha256:410fed7b35cdae305cf88ea2c0897fdd81715fea6116b0ea86841b812a8309c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LXUSSFW5CA7JMCIBABZFJGU7XW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Maria Trybula","submitted_at":"2013-03-31T20:39:12Z","abstract_excerpt":"We consider a proper holomorphic map form D to G domains in C^n and show that it induces a unitary isomorphism between the Bergman space A^2(G) and some subspace of A^2(D). Using this isomorphism we construct orthogonal projection onto that subspace and we derive Bells transformation formula for the Bergman kernel under proper holomorphic mappings. As a consequence of the formula we get that the tetrablock is not a Lu Qi-Keng domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0252","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":"2026-05-18T03:29:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qo+4/BGQClA1qk1SaaTv3bkXn/662ZLUeYRj26BQ7PjmqWl6wqtuYvP6MZvdiApWP1BmeJSzyFyusTkWLxuyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:43:21.633127Z"},"content_sha256":"1c8c02552f95d0f1c7875f3edac51b8c05d2cbe54ffb16710c525e3ab49c5bcb","schema_version":"1.0","event_id":"sha256:1c8c02552f95d0f1c7875f3edac51b8c05d2cbe54ffb16710c525e3ab49c5bcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXUSSFW5CA7JMCIBABZFJGU7XW/bundle.json","state_url":"https://pith.science/pith/LXUSSFW5CA7JMCIBABZFJGU7XW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXUSSFW5CA7JMCIBABZFJGU7XW/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":"2026-06-22T22:43:21Z","links":{"resolver":"https://pith.science/pith/LXUSSFW5CA7JMCIBABZFJGU7XW","bundle":"https://pith.science/pith/LXUSSFW5CA7JMCIBABZFJGU7XW/bundle.json","state":"https://pith.science/pith/LXUSSFW5CA7JMCIBABZFJGU7XW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXUSSFW5CA7JMCIBABZFJGU7XW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LXUSSFW5CA7JMCIBABZFJGU7XW","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":"f174eab8bac3ee67d251462612b66f62d797859c5602ae5a6dfe0396fa3f861d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-31T20:39:12Z","title_canon_sha256":"47e821e02a2efcb12d50a1ad042b872fdd1e163a49d4fa9e26563aac334eb07b"},"schema_version":"1.0","source":{"id":"1304.0252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0252","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0252v1","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0252","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"LXUSSFW5CA7J","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LXUSSFW5CA7JMCIB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LXUSSFW5","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:1c8c02552f95d0f1c7875f3edac51b8c05d2cbe54ffb16710c525e3ab49c5bcb","target":"graph","created_at":"2026-05-18T03:29:17Z","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 consider a proper holomorphic map form D to G domains in C^n and show that it induces a unitary isomorphism between the Bergman space A^2(G) and some subspace of A^2(D). Using this isomorphism we construct orthogonal projection onto that subspace and we derive Bells transformation formula for the Bergman kernel under proper holomorphic mappings. As a consequence of the formula we get that the tetrablock is not a Lu Qi-Keng domain.","authors_text":"Maria Trybula","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-31T20:39:12Z","title":"Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0252","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":"sha256:410fed7b35cdae305cf88ea2c0897fdd81715fea6116b0ea86841b812a8309c5","target":"record","created_at":"2026-05-18T03:29:17Z","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":"f174eab8bac3ee67d251462612b66f62d797859c5602ae5a6dfe0396fa3f861d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-31T20:39:12Z","title_canon_sha256":"47e821e02a2efcb12d50a1ad042b872fdd1e163a49d4fa9e26563aac334eb07b"},"schema_version":"1.0","source":{"id":"1304.0252","kind":"arxiv","version":1}},"canonical_sha256":"5de92916dd103e9609010072549a9fbdae121a0ad616ad32d45635c70182d0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de92916dd103e9609010072549a9fbdae121a0ad616ad32d45635c70182d0de","first_computed_at":"2026-05-18T03:29:17.476029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:17.476029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"18sHx+ptOfDx5/6Cmdx+Cbdj/cbPhr52WgiL3tk8x8Jcksq7VsmnE7BimmjElM0nRkhY3Pgq2Y8baNmIem29BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:17.478034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:410fed7b35cdae305cf88ea2c0897fdd81715fea6116b0ea86841b812a8309c5","sha256:1c8c02552f95d0f1c7875f3edac51b8c05d2cbe54ffb16710c525e3ab49c5bcb"],"state_sha256":"e0749c8e3afdf9f38f91b36fec76481dd352ff29dd4a2eb5881c320413b22c8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wAD4iMFpct7kpc7HSf7GGtHaLVx6Ov6Wy5SWsWED15TaLSJJ7mVmIyBf9TB3rMFvA5G2mYPn8fQkyqXzsQNZDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:43:21.635026Z","bundle_sha256":"ac815f409e966d12f680f02963d7d6824b35bf46551866b3d4f4f0c011456cca"}}