{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MB75NJEZFDLN27RIUGFWDSPXVX","short_pith_number":"pith:MB75NJEZ","canonical_record":{"source":{"id":"2405.08002","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-05-06T14:08:02Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"219e06b49d942cda52445d9ecfe0d712da80a10370f475a09a3630b326377fc2","abstract_canon_sha256":"22646f90110954ddd194abe71162d6a1fcc7ea50234c123e66af9927c097e335"},"schema_version":"1.0"},"canonical_sha256":"607fd6a49928d6dd7e28a18b61c9f7adec295c821a29d3f3579687ac9236091c","source":{"kind":"arxiv","id":"2405.08002","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.08002","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"2405.08002v2","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.08002","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"MB75NJEZFDLN","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"pith_short_16","alias_value":"MB75NJEZFDLN27RI","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"pith_short_8","alias_value":"MB75NJEZ","created_at":"2026-07-05T11:38:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MB75NJEZFDLN27RIUGFWDSPXVX","target":"record","payload":{"canonical_record":{"source":{"id":"2405.08002","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-05-06T14:08:02Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"219e06b49d942cda52445d9ecfe0d712da80a10370f475a09a3630b326377fc2","abstract_canon_sha256":"22646f90110954ddd194abe71162d6a1fcc7ea50234c123e66af9927c097e335"},"schema_version":"1.0"},"canonical_sha256":"607fd6a49928d6dd7e28a18b61c9f7adec295c821a29d3f3579687ac9236091c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:00.217649Z","signature_b64":"V7XYQXLo0lTig72EpnSDAvOGafiQWbgbaDjgO99uDkX56u/gOHgi2EqAsHJ0tMdqTAlv0jiTzZerQKR86h5vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"607fd6a49928d6dd7e28a18b61c9f7adec295c821a29d3f3579687ac9236091c","last_reissued_at":"2026-07-05T11:38:00.217134Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:00.217134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.08002","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9cVn0qBbGs3mShcJTLvlRoWFB1MlOIENLzg9yB8g3GWWuXGhqWOcgrv5pfxxF+kUojzgzeqgZsUIQaG851+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:42:10.212973Z"},"content_sha256":"48c86e55b5361869ec06b7979a4bf4cb3d64c6b80aa623236141a2df7260277c","schema_version":"1.0","event_id":"sha256:48c86e55b5361869ec06b7979a4bf4cb3d64c6b80aa623236141a2df7260277c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MB75NJEZFDLN27RIUGFWDSPXVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brown-Halmos type Theorems on the proper images of bounded symmetric domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Gargi Ghosh, Subrata Shyam Roy","submitted_at":"2024-05-06T14:08:02Z","abstract_excerpt":"Let $\\Omega\\subseteq\\mathbb C^n$ be a bounded symmetric domain and $f :\\Omega \\to \\Omega^\\prime\\subseteq \\mathbb C^n$ be a proper holomorphic mapping which is factored by a finite complex reflection group $G.$ We identify a family of reproducing kernel Hilbert spaces on $\\Omega^\\prime$ arising naturally from the isotypic decomposition of the regular representation of $G$ on the Hardy space $H^2(\\Omega).$ Each element of this family can be realized as a closed subspace of some $L^2$-space on the \\v{S}ilov boundary of $\\Omega^\\prime$. The reproducing kernel Hilbert space associated to the sign r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08002","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.08002/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J00Y4HFgeefDXFjcambGPzeCuYairKWMm24iTH/AyQzsTEDU3KrxRFO44Omi1raLrKyr/nsEsg5rMmLdiHlpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:42:10.213457Z"},"content_sha256":"2410afc2ec77bc540a86fd001993178f520e3125f48641cc6c731220c0efa5c1","schema_version":"1.0","event_id":"sha256:2410afc2ec77bc540a86fd001993178f520e3125f48641cc6c731220c0efa5c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MB75NJEZFDLN27RIUGFWDSPXVX/bundle.json","state_url":"https://pith.science/pith/MB75NJEZFDLN27RIUGFWDSPXVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MB75NJEZFDLN27RIUGFWDSPXVX/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":"2026-08-08T07:42:10Z","links":{"resolver":"https://pith.science/pith/MB75NJEZFDLN27RIUGFWDSPXVX","bundle":"https://pith.science/pith/MB75NJEZFDLN27RIUGFWDSPXVX/bundle.json","state":"https://pith.science/pith/MB75NJEZFDLN27RIUGFWDSPXVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MB75NJEZFDLN27RIUGFWDSPXVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MB75NJEZFDLN27RIUGFWDSPXVX","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":"22646f90110954ddd194abe71162d6a1fcc7ea50234c123e66af9927c097e335","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-05-06T14:08:02Z","title_canon_sha256":"219e06b49d942cda52445d9ecfe0d712da80a10370f475a09a3630b326377fc2"},"schema_version":"1.0","source":{"id":"2405.08002","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.08002","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"2405.08002v2","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.08002","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"MB75NJEZFDLN","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"pith_short_16","alias_value":"MB75NJEZFDLN27RI","created_at":"2026-07-05T11:38:00Z"},{"alias_kind":"pith_short_8","alias_value":"MB75NJEZ","created_at":"2026-07-05T11:38:00Z"}],"graph_snapshots":[{"event_id":"sha256:2410afc2ec77bc540a86fd001993178f520e3125f48641cc6c731220c0efa5c1","target":"graph","created_at":"2026-07-05T11:38:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.08002/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Omega\\subseteq\\mathbb C^n$ be a bounded symmetric domain and $f :\\Omega \\to \\Omega^\\prime\\subseteq \\mathbb C^n$ be a proper holomorphic mapping which is factored by a finite complex reflection group $G.$ We identify a family of reproducing kernel Hilbert spaces on $\\Omega^\\prime$ arising naturally from the isotypic decomposition of the regular representation of $G$ on the Hardy space $H^2(\\Omega).$ Each element of this family can be realized as a closed subspace of some $L^2$-space on the \\v{S}ilov boundary of $\\Omega^\\prime$. The reproducing kernel Hilbert space associated to the sign r","authors_text":"Gargi Ghosh, Subrata Shyam Roy","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-05-06T14:08:02Z","title":"Brown-Halmos type Theorems on the proper images of bounded symmetric domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08002","kind":"arxiv","version":2},"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":"sha256:48c86e55b5361869ec06b7979a4bf4cb3d64c6b80aa623236141a2df7260277c","target":"record","created_at":"2026-07-05T11:38:00Z","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":"22646f90110954ddd194abe71162d6a1fcc7ea50234c123e66af9927c097e335","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-05-06T14:08:02Z","title_canon_sha256":"219e06b49d942cda52445d9ecfe0d712da80a10370f475a09a3630b326377fc2"},"schema_version":"1.0","source":{"id":"2405.08002","kind":"arxiv","version":2}},"canonical_sha256":"607fd6a49928d6dd7e28a18b61c9f7adec295c821a29d3f3579687ac9236091c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607fd6a49928d6dd7e28a18b61c9f7adec295c821a29d3f3579687ac9236091c","first_computed_at":"2026-07-05T11:38:00.217134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:00.217134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V7XYQXLo0lTig72EpnSDAvOGafiQWbgbaDjgO99uDkX56u/gOHgi2EqAsHJ0tMdqTAlv0jiTzZerQKR86h5vCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:00.217649Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.08002","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48c86e55b5361869ec06b7979a4bf4cb3d64c6b80aa623236141a2df7260277c","sha256:2410afc2ec77bc540a86fd001993178f520e3125f48641cc6c731220c0efa5c1"],"state_sha256":"b698590480b120f53b5613bcf8643397c10ea6b5288bd402981bcc236674115f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKZ5Qz8pyRY2FHvyt+ABnD01Vov8zfHq6PStZj2v7BCYUwTNd2b221RkEaeFU58cNyql1HLvf06wd8iCmSzgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T07:42:10.216778Z","bundle_sha256":"dab3fd9bfacc22ccaeefe681e5c5d234978c606b7ff815e8adef7261c945b139"}}