{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:CNQKO3U73Y4NHBRVY3PQIDXF7C","short_pith_number":"pith:CNQKO3U7","canonical_record":{"source":{"id":"2012.13535","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2020-12-25T07:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"f77470230850f77ad42359a2ee234ea2c0806728e8a7df2538ec4a0beb63262e","abstract_canon_sha256":"9902ede36771bd477b1077a0f57ac3eab39b40a74932dce1c018980fbb3c0e1a"},"schema_version":"1.0"},"canonical_sha256":"1360a76e9fde38d38635c6df040ee5f8adf40aa80c31930689e2e64f84677283","source":{"kind":"arxiv","id":"2012.13535","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.13535","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"2012.13535v2","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.13535","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"CNQKO3U73Y4N","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"CNQKO3U73Y4NHBRV","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"CNQKO3U7","created_at":"2026-07-05T06:01:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:CNQKO3U73Y4NHBRVY3PQIDXF7C","target":"record","payload":{"canonical_record":{"source":{"id":"2012.13535","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2020-12-25T07:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"f77470230850f77ad42359a2ee234ea2c0806728e8a7df2538ec4a0beb63262e","abstract_canon_sha256":"9902ede36771bd477b1077a0f57ac3eab39b40a74932dce1c018980fbb3c0e1a"},"schema_version":"1.0"},"canonical_sha256":"1360a76e9fde38d38635c6df040ee5f8adf40aa80c31930689e2e64f84677283","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:01:08.644863Z","signature_b64":"yPGUKhVsrg+Y6k9Qs+ephUpXKc+EtLMNuLPsWVVmYdurICey5mMf7Vy+IQj9nBnEO1B+4Ei4l9MNAoPs3Q0pBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1360a76e9fde38d38635c6df040ee5f8adf40aa80c31930689e2e64f84677283","last_reissued_at":"2026-07-05T06:01:08.644433Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:01:08.644433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.13535","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":"2026-07-05T06:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KE8D9kX0oCW8EPDJnjAU2RlYc/JocVcsQv+3EbK2YrZ72i7MEEvTOMsrqhMmIhHxmk75GJFnZHP7WVfbbl0WDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T00:41:00.861401Z"},"content_sha256":"cd12146f7e45937de9b666bf857a52318483329957c89db61b109aae5f67d002","schema_version":"1.0","event_id":"sha256:cd12146f7e45937de9b666bf857a52318483329957c89db61b109aae5f67d002"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:CNQKO3U73Y4NHBRVY3PQIDXF7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the similarity of restriction of the operator to an invariant subspace","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinesh Kumar Keshari, Jing Xu, Kui Ji, Shanshan Ji","submitted_at":"2020-12-25T07:17:13Z","abstract_excerpt":"Let $M_{z}$ be the multiplication operator on the Bergman space and $M_{I}$ denote the restriction of $M_{z}$ to an invariant subspace $I$. A question raised by K. Zhu is that when are two restriction operators $M_{I}$ and $M_{J}$ are similar? In this note, we give some sufficient conditions of this problem in a general case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.13535","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/2012.13535/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":"2026-07-05T06:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESG8mMXdDUtR9GHF+LV/GpmKBq22xC2X7TB6sRbfsLX7xbiWrd5qPxEvbBKBb/vvSpNWbfAM+Pqxjfqyi9EOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T00:41:00.861936Z"},"content_sha256":"2fc355c071876fbcb71bbcc09fbb3ff5d15a03d894ed23d4ecc8007af99ed4a4","schema_version":"1.0","event_id":"sha256:2fc355c071876fbcb71bbcc09fbb3ff5d15a03d894ed23d4ecc8007af99ed4a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C/bundle.json","state_url":"https://pith.science/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C/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":"2026-08-20T00:41:00Z","links":{"resolver":"https://pith.science/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C","bundle":"https://pith.science/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C/bundle.json","state":"https://pith.science/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNQKO3U73Y4NHBRVY3PQIDXF7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CNQKO3U73Y4NHBRVY3PQIDXF7C","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":"9902ede36771bd477b1077a0f57ac3eab39b40a74932dce1c018980fbb3c0e1a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2020-12-25T07:17:13Z","title_canon_sha256":"f77470230850f77ad42359a2ee234ea2c0806728e8a7df2538ec4a0beb63262e"},"schema_version":"1.0","source":{"id":"2012.13535","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.13535","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"2012.13535v2","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.13535","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"CNQKO3U73Y4N","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"CNQKO3U73Y4NHBRV","created_at":"2026-07-05T06:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"CNQKO3U7","created_at":"2026-07-05T06:01:08Z"}],"graph_snapshots":[{"event_id":"sha256:2fc355c071876fbcb71bbcc09fbb3ff5d15a03d894ed23d4ecc8007af99ed4a4","target":"graph","created_at":"2026-07-05T06:01:08Z","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/2012.13535/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $M_{z}$ be the multiplication operator on the Bergman space and $M_{I}$ denote the restriction of $M_{z}$ to an invariant subspace $I$. A question raised by K. Zhu is that when are two restriction operators $M_{I}$ and $M_{J}$ are similar? In this note, we give some sufficient conditions of this problem in a general case.","authors_text":"Dinesh Kumar Keshari, Jing Xu, Kui Ji, Shanshan Ji","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2020-12-25T07:17:13Z","title":"On the similarity of restriction of the operator to an invariant subspace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.13535","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:cd12146f7e45937de9b666bf857a52318483329957c89db61b109aae5f67d002","target":"record","created_at":"2026-07-05T06:01:08Z","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":"9902ede36771bd477b1077a0f57ac3eab39b40a74932dce1c018980fbb3c0e1a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2020-12-25T07:17:13Z","title_canon_sha256":"f77470230850f77ad42359a2ee234ea2c0806728e8a7df2538ec4a0beb63262e"},"schema_version":"1.0","source":{"id":"2012.13535","kind":"arxiv","version":2}},"canonical_sha256":"1360a76e9fde38d38635c6df040ee5f8adf40aa80c31930689e2e64f84677283","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1360a76e9fde38d38635c6df040ee5f8adf40aa80c31930689e2e64f84677283","first_computed_at":"2026-07-05T06:01:08.644433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:01:08.644433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yPGUKhVsrg+Y6k9Qs+ephUpXKc+EtLMNuLPsWVVmYdurICey5mMf7Vy+IQj9nBnEO1B+4Ei4l9MNAoPs3Q0pBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:01:08.644863Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.13535","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd12146f7e45937de9b666bf857a52318483329957c89db61b109aae5f67d002","sha256:2fc355c071876fbcb71bbcc09fbb3ff5d15a03d894ed23d4ecc8007af99ed4a4"],"state_sha256":"10a8d362f0548c50330d9c8c758f679b5a8ec009e8c05336e2db8e45c6aa8ee0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mm5pI8sEXt/1g52phwNVNcZAgtioStYAmUmm0GegAscfPhV/u6JM7gwInogaZsyG/5JMVj/nCJlpZeEftN+cCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T00:41:00.866885Z","bundle_sha256":"35b303d75a66583b9de9b7e40cfab09c0d59b43c33560e24d10a829eaf58d57e"}}