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Let $\\mathscr{N}$ be a complete nest on a complex and separable Hilbert space $H$. Suppose that $M$ belongs to $\\mathscr{N}$ with $\\{0\\}\\neq M\\neq\\ H$ and write $\\hat{M}$ for $M$ or $M^{\\bot}$. Our main result is: for any $\\Omega\\in alg\\mathscr{N}$ with $\\Omega=P(\\hat{M})\\Omega P(\\hat{M})$, if $\\Omega |_{\\hat{M}}$ i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.1434","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-09T00:35:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8bc59039af9c87a384ebedfd534e2d1ad19aa321a0b974535cedc6e1c8674bb9","abstract_canon_sha256":"d62274e621a41f3cc4e245c6d212392d57e9ca7342f643f8f204f99e449b9847"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:00.814755Z","signature_b64":"jee3pgLd7Bue6n/AHHyXJmo0hB1FTUxh26rPqTyNRv18+C7pKlWAKei4uiwbtD9eQmkMoy5o9Dvn3TtDtv14DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32188acd917135d5bf378535a1bb9dc279784d1bf701b3b0a0ca0f543a1a5cea","last_reissued_at":"2026-05-18T00:31:00.814213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:00.814213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"All-derivable points in nest algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Wu Junde, Zhang Lin, Zhu Jun","submitted_at":"2010-08-09T00:35:04Z","abstract_excerpt":"Suppose that $\\mathscr{A}$ is an operator algebra on a Hilbert space $H$. 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Our main result is: for any $\\Omega\\in alg\\mathscr{N}$ with $\\Omega=P(\\hat{M})\\Omega P(\\hat{M})$, if $\\Omega |_{\\hat{M}}$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1434","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.1434","created_at":"2026-05-18T00:31:00.814300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.1434v3","created_at":"2026-05-18T00:31:00.814300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1434","created_at":"2026-05-18T00:31:00.814300+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIMIVTMROE25","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIMIVTMROE25LPZX","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIMIVTMR","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ","json":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ.json","graph_json":"https://pith.science/api/pith-number/GIMIVTMROE25LPZXQU22DO45YJ/graph.json","events_json":"https://pith.science/api/pith-number/GIMIVTMROE25LPZXQU22DO45YJ/events.json","paper":"https://pith.science/paper/GIMIVTMR"},"agent_actions":{"view_html":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ","download_json":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ.json","view_paper":"https://pith.science/paper/GIMIVTMR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.1434&json=true","fetch_graph":"https://pith.science/api/pith-number/GIMIVTMROE25LPZXQU22DO45YJ/graph.json","fetch_events":"https://pith.science/api/pith-number/GIMIVTMROE25LPZXQU22DO45YJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ/action/storage_attestation","attest_author":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ/action/author_attestation","sign_citation":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ/action/citation_signature","submit_replication":"https://pith.science/pith/GIMIVTMROE25LPZXQU22DO45YJ/action/replication_record"}},"created_at":"2026-05-18T00:31:00.814300+00:00","updated_at":"2026-05-18T00:31:00.814300+00:00"}