{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HT6ODRJ46YYR263QDHBTTGCWUA","short_pith_number":"pith:HT6ODRJ4","canonical_record":{"source":{"id":"1811.05761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-14T13:16:55Z","cross_cats_sorted":[],"title_canon_sha256":"87fc33dc32335341f566f6c7aad9c498d0f20a8da69319cd2de848eed8068cab","abstract_canon_sha256":"d5ff82d990c51b6e16d3b7cd97a65d8d9e27fb7324cd3be7d990193a88110d8d"},"schema_version":"1.0"},"canonical_sha256":"3cfce1c53cf6311d7b7019c3399856a03661d26267851e84dedab395fd21f910","source":{"kind":"arxiv","id":"1811.05761","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05761","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05761v1","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05761","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"HT6ODRJ46YYR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HT6ODRJ46YYR263Q","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HT6ODRJ4","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HT6ODRJ46YYR263QDHBTTGCWUA","target":"record","payload":{"canonical_record":{"source":{"id":"1811.05761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-14T13:16:55Z","cross_cats_sorted":[],"title_canon_sha256":"87fc33dc32335341f566f6c7aad9c498d0f20a8da69319cd2de848eed8068cab","abstract_canon_sha256":"d5ff82d990c51b6e16d3b7cd97a65d8d9e27fb7324cd3be7d990193a88110d8d"},"schema_version":"1.0"},"canonical_sha256":"3cfce1c53cf6311d7b7019c3399856a03661d26267851e84dedab395fd21f910","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:42.142945Z","signature_b64":"k5hb382LbZ9OOQJDIxuzG2ybcbz7huPrM9/kroGPjdbzgBMfsRQUCngvhUNHF+ToQqG0Gd3s6YNRDDA1vpBQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cfce1c53cf6311d7b7019c3399856a03661d26267851e84dedab395fd21f910","last_reissued_at":"2026-05-18T00:00:42.142484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:42.142484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.05761","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":"2026-05-18T00:00:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXj593L1/btQldNpb6ZkUNT0SfP85ZzWLluvTYLIlHTV8+BEPkfYNDRSBYqTIJ03rpza+JOD+rvb4i2p95cvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:57:42.135242Z"},"content_sha256":"e1c007dcaff8399b7b3f57717a484069155dab986859aeaeeed266f3baaa269f","schema_version":"1.0","event_id":"sha256:e1c007dcaff8399b7b3f57717a484069155dab986859aeaeeed266f3baaa269f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HT6ODRJ46YYR263QDHBTTGCWUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random weighted shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Guozheng Cheng, Sen Zhu, Xiang Fang","submitted_at":"2018-11-14T13:16:55Z","abstract_excerpt":"In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$, defined as $Te_n=w_ne_{n+1}$, where $\\{e_n\\}_{n=1}^\\infty$ form an orthonormal basis of a complex Hilbert space, by a sequence of i.i.d. random variables $\\{X_n\\}_{n=1}^{\\infty}$; that is, $w_n=X_n$. This paper answers basic questions concerning such a model. We propose that this model can be studied in comparison with the classical Hardy/Bergman/Dirichlet sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05761","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":"2026-05-18T00:00:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQDVoO6O7e68ZYg/96f3CRJwMTUdEKVOH+pAVswGV26BbO1Xbm/XCSzyb705oUovStpHay8f3UUh8xP6+ENbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:57:42.135739Z"},"content_sha256":"fb5ea1f05f1b27ec3c02581199b6c8aa70457417f2c0479948d1739473683ade","schema_version":"1.0","event_id":"sha256:fb5ea1f05f1b27ec3c02581199b6c8aa70457417f2c0479948d1739473683ade"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HT6ODRJ46YYR263QDHBTTGCWUA/bundle.json","state_url":"https://pith.science/pith/HT6ODRJ46YYR263QDHBTTGCWUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HT6ODRJ46YYR263QDHBTTGCWUA/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":"2026-06-24T05:57:42Z","links":{"resolver":"https://pith.science/pith/HT6ODRJ46YYR263QDHBTTGCWUA","bundle":"https://pith.science/pith/HT6ODRJ46YYR263QDHBTTGCWUA/bundle.json","state":"https://pith.science/pith/HT6ODRJ46YYR263QDHBTTGCWUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HT6ODRJ46YYR263QDHBTTGCWUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HT6ODRJ46YYR263QDHBTTGCWUA","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":"d5ff82d990c51b6e16d3b7cd97a65d8d9e27fb7324cd3be7d990193a88110d8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-14T13:16:55Z","title_canon_sha256":"87fc33dc32335341f566f6c7aad9c498d0f20a8da69319cd2de848eed8068cab"},"schema_version":"1.0","source":{"id":"1811.05761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05761","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05761v1","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05761","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"HT6ODRJ46YYR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HT6ODRJ46YYR263Q","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HT6ODRJ4","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:fb5ea1f05f1b27ec3c02581199b6c8aa70457417f2c0479948d1739473683ade","target":"graph","created_at":"2026-05-18T00:00:42Z","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":"In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$, defined as $Te_n=w_ne_{n+1}$, where $\\{e_n\\}_{n=1}^\\infty$ form an orthonormal basis of a complex Hilbert space, by a sequence of i.i.d. random variables $\\{X_n\\}_{n=1}^{\\infty}$; that is, $w_n=X_n$. This paper answers basic questions concerning such a model. We propose that this model can be studied in comparison with the classical Hardy/Bergman/Dirichlet sp","authors_text":"Guozheng Cheng, Sen Zhu, Xiang Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-14T13:16:55Z","title":"Random weighted shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05761","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:e1c007dcaff8399b7b3f57717a484069155dab986859aeaeeed266f3baaa269f","target":"record","created_at":"2026-05-18T00:00:42Z","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":"d5ff82d990c51b6e16d3b7cd97a65d8d9e27fb7324cd3be7d990193a88110d8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-14T13:16:55Z","title_canon_sha256":"87fc33dc32335341f566f6c7aad9c498d0f20a8da69319cd2de848eed8068cab"},"schema_version":"1.0","source":{"id":"1811.05761","kind":"arxiv","version":1}},"canonical_sha256":"3cfce1c53cf6311d7b7019c3399856a03661d26267851e84dedab395fd21f910","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cfce1c53cf6311d7b7019c3399856a03661d26267851e84dedab395fd21f910","first_computed_at":"2026-05-18T00:00:42.142484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:42.142484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k5hb382LbZ9OOQJDIxuzG2ybcbz7huPrM9/kroGPjdbzgBMfsRQUCngvhUNHF+ToQqG0Gd3s6YNRDDA1vpBQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:42.142945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1c007dcaff8399b7b3f57717a484069155dab986859aeaeeed266f3baaa269f","sha256:fb5ea1f05f1b27ec3c02581199b6c8aa70457417f2c0479948d1739473683ade"],"state_sha256":"4916b0c7c3df6a9382fc19ad072be8d3f0bae6aa75881c211e8682db4b6643ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Axtb18sg2Yc1AlLogKvI2QcX1h7KBdgVYfLCKvKWbdCEj5MyPLRgsSHyomhAVHS4eq5w1osayEs4wd7p+ZN1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:57:42.138012Z","bundle_sha256":"4b5ed306c0cebf7aad075a1cc9cf7f5ecda6f6c1d04753f72930e13b63128ae6"}}