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E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\\leq n$ is given by \\begin{equation*} -\\psi_{1}\\left(mn+1\\right)+\\frac{m+n}{mn+1}\\psi_{1}\\left(n\\right)-\\frac{(m+1)(m+2n+1)}{4n^{2}(mn+1)}, \\end{equation*} where $\\psi_{1}(\\cdot)$ is the trigamma function. We give a proof of this formula."},"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":"1706.08199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-26T00:59:54Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","quant-ph"],"title_canon_sha256":"6e3df34e7c74420941859be83674762ff107bed9124200220c49571c7f9229ee","abstract_canon_sha256":"bcabed2592a6b173586176c0fbb0bfd66e6138285ad1665f25c00187043096c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:17.818577Z","signature_b64":"fTLxYgzU1rNgxjQKNG0//4yO8PApaymekunATjYicTS6bv/l/cn97YCYUfnxMgkMey+zCy1vNfG6UXfJcZyZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8302590cb5c17b6618926ba4774f76dfb52d379e515da266d9eaaccc2b19f613","last_reissued_at":"2026-05-18T00:38:17.817883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:17.817883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Lu wei","submitted_at":"2017-06-26T00:59:54Z","abstract_excerpt":"It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\\leq n$ is given by \\begin{equation*} -\\psi_{1}\\left(mn+1\\right)+\\frac{m+n}{mn+1}\\psi_{1}\\left(n\\right)-\\frac{(m+1)(m+2n+1)}{4n^{2}(mn+1)}, \\end{equation*} where $\\psi_{1}(\\cdot)$ is the trigamma function. We give a proof of this formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08199","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":""},"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":"1706.08199","created_at":"2026-05-18T00:38:17.818027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.08199v2","created_at":"2026-05-18T00:38:17.818027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08199","created_at":"2026-05-18T00:38:17.818027+00:00"},{"alias_kind":"pith_short_12","alias_value":"QMBFSDFVYF5W","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QMBFSDFVYF5WMGES","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QMBFSDFV","created_at":"2026-05-18T12:31:39.905425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.30941","citing_title":"Revisiting the Page curve and its moments. 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