{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GUIAM3U4UPACBCJVVC75E6JCOU","short_pith_number":"pith:GUIAM3U4","canonical_record":{"source":{"id":"1912.06861","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-14T15:10:11Z","cross_cats_sorted":[],"title_canon_sha256":"ef22bbaf92342a6bbe79a880a1a2c2c39d4f1c6fc1343bed4093d42b0dfe4b61","abstract_canon_sha256":"84a42d170c498fe8bd4986f710da667828d712ad7cea1c74a4898489103b5c52"},"schema_version":"1.0"},"canonical_sha256":"3510066e9ca3c0208935a8bfd2792275334122594ad9354a4d875f50bc125337","source":{"kind":"arxiv","id":"1912.06861","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.06861","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"arxiv_version","alias_value":"1912.06861v2","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.06861","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"pith_short_12","alias_value":"GUIAM3U4UPAC","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"GUIAM3U4UPACBCJV","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"GUIAM3U4","created_at":"2026-07-05T02:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GUIAM3U4UPACBCJVVC75E6JCOU","target":"record","payload":{"canonical_record":{"source":{"id":"1912.06861","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-14T15:10:11Z","cross_cats_sorted":[],"title_canon_sha256":"ef22bbaf92342a6bbe79a880a1a2c2c39d4f1c6fc1343bed4093d42b0dfe4b61","abstract_canon_sha256":"84a42d170c498fe8bd4986f710da667828d712ad7cea1c74a4898489103b5c52"},"schema_version":"1.0"},"canonical_sha256":"3510066e9ca3c0208935a8bfd2792275334122594ad9354a4d875f50bc125337","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:26:26.067460Z","signature_b64":"LpzqUVtuS+gjpCGaU2KiHM4sQduECPm3QS/YH96pCs7n3LoI6/AHMsTXS8R1LwuA0QmfJi6L0tCmWk4hMlQsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3510066e9ca3c0208935a8bfd2792275334122594ad9354a4d875f50bc125337","last_reissued_at":"2026-07-05T02:26:26.066989Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:26:26.066989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.06861","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":"2026-07-05T02:26:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UhjZAP5PvErhiJC7TrotGAE/sLKVOObPpIAS7XNUdlKqeAQW5d1tPz4ZSf+a1z8awLypRdX1eMY4JcuKFBzQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:56:11.024918Z"},"content_sha256":"e88b7d5be3c613f1e078aab085f4de720c4f10e6cf559f203a11696c3d3a3bfb","schema_version":"1.0","event_id":"sha256:e88b7d5be3c613f1e078aab085f4de720c4f10e6cf559f203a11696c3d3a3bfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GUIAM3U4UPACBCJVVC75E6JCOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A subclass of the Cowen-Douglas class and similarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hyun-Kyoung Kwon, Jaydeb Sarkar, Jing Xu, Kui Ji","submitted_at":"2019-12-14T15:10:11Z","abstract_excerpt":"We consider a subclass of the Cowen-Douglas class in which the problem of deciding whether two operators are similar becomes more manageable. A similarity criterion for Cowen-Douglas operators is known to be dependent on the trace of the curvatures of the corresponding eigenvector bundles. Unless the given eignvector bundle is a line bundle, the computation of the curvatures, in general, is not so simple as one might hope. By using a structure theorem given in \\cite{JW}, we reduce the problem of finding the trace of the curvatures to looking at the curvatures of the associated line bundles. Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.06861","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/1912.06861/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":"2026-07-05T02:26:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jshwrJotVZ1HLREb82Tdm/7aR6ILP2QYkt6yqTyMgco3JmpPurEYxR1TN26Orm2e41T5QZmHCHQV/NhAQGwdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:56:11.025417Z"},"content_sha256":"5a42c36e967c335f20edfc4c856a285efdabf11327e7259127932bad0446fca8","schema_version":"1.0","event_id":"sha256:5a42c36e967c335f20edfc4c856a285efdabf11327e7259127932bad0446fca8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUIAM3U4UPACBCJVVC75E6JCOU/bundle.json","state_url":"https://pith.science/pith/GUIAM3U4UPACBCJVVC75E6JCOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUIAM3U4UPACBCJVVC75E6JCOU/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":"2026-08-05T18:56:11Z","links":{"resolver":"https://pith.science/pith/GUIAM3U4UPACBCJVVC75E6JCOU","bundle":"https://pith.science/pith/GUIAM3U4UPACBCJVVC75E6JCOU/bundle.json","state":"https://pith.science/pith/GUIAM3U4UPACBCJVVC75E6JCOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUIAM3U4UPACBCJVVC75E6JCOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GUIAM3U4UPACBCJVVC75E6JCOU","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":"84a42d170c498fe8bd4986f710da667828d712ad7cea1c74a4898489103b5c52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-14T15:10:11Z","title_canon_sha256":"ef22bbaf92342a6bbe79a880a1a2c2c39d4f1c6fc1343bed4093d42b0dfe4b61"},"schema_version":"1.0","source":{"id":"1912.06861","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.06861","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"arxiv_version","alias_value":"1912.06861v2","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.06861","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"pith_short_12","alias_value":"GUIAM3U4UPAC","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"GUIAM3U4UPACBCJV","created_at":"2026-07-05T02:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"GUIAM3U4","created_at":"2026-07-05T02:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:5a42c36e967c335f20edfc4c856a285efdabf11327e7259127932bad0446fca8","target":"graph","created_at":"2026-07-05T02:26:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.06861/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a subclass of the Cowen-Douglas class in which the problem of deciding whether two operators are similar becomes more manageable. A similarity criterion for Cowen-Douglas operators is known to be dependent on the trace of the curvatures of the corresponding eigenvector bundles. Unless the given eignvector bundle is a line bundle, the computation of the curvatures, in general, is not so simple as one might hope. By using a structure theorem given in \\cite{JW}, we reduce the problem of finding the trace of the curvatures to looking at the curvatures of the associated line bundles. Mo","authors_text":"Hyun-Kyoung Kwon, Jaydeb Sarkar, Jing Xu, Kui Ji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-14T15:10:11Z","title":"A subclass of the Cowen-Douglas class and similarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.06861","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:e88b7d5be3c613f1e078aab085f4de720c4f10e6cf559f203a11696c3d3a3bfb","target":"record","created_at":"2026-07-05T02:26:26Z","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":"84a42d170c498fe8bd4986f710da667828d712ad7cea1c74a4898489103b5c52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-14T15:10:11Z","title_canon_sha256":"ef22bbaf92342a6bbe79a880a1a2c2c39d4f1c6fc1343bed4093d42b0dfe4b61"},"schema_version":"1.0","source":{"id":"1912.06861","kind":"arxiv","version":2}},"canonical_sha256":"3510066e9ca3c0208935a8bfd2792275334122594ad9354a4d875f50bc125337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3510066e9ca3c0208935a8bfd2792275334122594ad9354a4d875f50bc125337","first_computed_at":"2026-07-05T02:26:26.066989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:26:26.066989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LpzqUVtuS+gjpCGaU2KiHM4sQduECPm3QS/YH96pCs7n3LoI6/AHMsTXS8R1LwuA0QmfJi6L0tCmWk4hMlQsCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:26:26.067460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.06861","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e88b7d5be3c613f1e078aab085f4de720c4f10e6cf559f203a11696c3d3a3bfb","sha256:5a42c36e967c335f20edfc4c856a285efdabf11327e7259127932bad0446fca8"],"state_sha256":"3119adbe25d4586452414e030ef786356761f3987b6d1ba010cbafeafbe0407f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+6v3aFeb8STSC7K9qslOdaRt0NFzX+vNaTEfOLTXp+/faTS5m6IGb8S18XwWqV2U1UDv/Neqv9Rgt6P18M7Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T18:56:11.039248Z","bundle_sha256":"d307bc7443121fb25ed6ad211a3dbbd955db536a1adfbf2bcf96384e19be8f40"}}