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Let $Q_{\\rho }$ be the Husimi function of a density operator $\\rho $ on $% \\mathcal{P}_{N}$. We prove an isospectral version of Lieb-Solovej inequality: if $\\rho ^{\\downarrow }$ is obtained by placing the eigenvalues of $\\rho $ in decreasing order along the monomial basis, then \\begin{equation*} \\int_{\\mathbb{C}}\\Phi (Q_{\\rho }(z))\\,dm(z)\\leq \\int_{\\mathbb{C}}\\Phi (Q_{\\rho ^{\\downarrow }}(z))\\,dm(z) \\end{equatio"},"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":"2608.12248","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-08-12T16:46:26Z","cross_cats_sorted":["math-ph","math.CA","math.FA","math.MP"],"title_canon_sha256":"5e58ff8a5a706177763312fde473911552dc2c4afd84faa7d32738d71bfab791","abstract_canon_sha256":"f5f9fe1b69ab049f0b37bb01e004a63b6cd2976bed403378634c42db4002d851"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T01:30:36.682418Z","signature_b64":"XhsTD0pcQyjt6NnXTmRxCArq+1VYi3AymwtLEMBnlXhuwuiwzB2A4Ttkd7b0VK14cuD1Fy3bfnYYN4JK4b5WCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5bddcc8bc67a58f58d8f58d1c010b8641799cba05bba962afe2fd399bfe89c0","last_reissued_at":"2026-08-13T01:30:36.680099Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T01:30:36.680099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isospectral majorization and isoperimetric inequalities for coherent states on the Bloch sphere","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CA","math.FA","math.MP"],"primary_cat":"quant-ph","authors_text":"Luis Daniel Abreu","submitted_at":"2026-08-12T16:46:26Z","abstract_excerpt":"Let $\\mathcal{P}_{N}$ be the $(N+1)$-dimensional Hilbert space of analytic polynomials of degree at most $N$. This is the natural environment to define $SU(2)$ (Bloch) coherent states. Let $Q_{\\rho }$ be the Husimi function of a density operator $\\rho $ on $% \\mathcal{P}_{N}$. We prove an isospectral version of Lieb-Solovej inequality: if $\\rho ^{\\downarrow }$ is obtained by placing the eigenvalues of $\\rho $ in decreasing order along the monomial basis, then \\begin{equation*} \\int_{\\mathbb{C}}\\Phi (Q_{\\rho }(z))\\,dm(z)\\leq \\int_{\\mathbb{C}}\\Phi (Q_{\\rho ^{\\downarrow }}(z))\\,dm(z) \\end{equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12248","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12248/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.12248","created_at":"2026-08-13T01:30:36.681320+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.12248v1","created_at":"2026-08-13T01:30:36.681320+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.12248","created_at":"2026-08-13T01:30:36.681320+00:00"},{"alias_kind":"pith_short_12","alias_value":"2W65ZSF4M6SY","created_at":"2026-08-13T01:30:36.681320+00:00"},{"alias_kind":"pith_short_16","alias_value":"2W65ZSF4M6SY6WGY","created_at":"2026-08-13T01:30:36.681320+00:00"},{"alias_kind":"pith_short_8","alias_value":"2W65ZSF4","created_at":"2026-08-13T01:30:36.681320+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/2W65ZSF4M6SY6WGY6WGRYAILQZ","json":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ.json","graph_json":"https://pith.science/api/pith-number/2W65ZSF4M6SY6WGY6WGRYAILQZ/graph.json","events_json":"https://pith.science/api/pith-number/2W65ZSF4M6SY6WGY6WGRYAILQZ/events.json","paper":"https://pith.science/paper/2W65ZSF4"},"agent_actions":{"view_html":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ","download_json":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ.json","view_paper":"https://pith.science/paper/2W65ZSF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.12248&json=true","fetch_graph":"https://pith.science/api/pith-number/2W65ZSF4M6SY6WGY6WGRYAILQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2W65ZSF4M6SY6WGY6WGRYAILQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ/action/storage_attestation","attest_author":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ/action/author_attestation","sign_citation":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ/action/citation_signature","submit_replication":"https://pith.science/pith/2W65ZSF4M6SY6WGY6WGRYAILQZ/action/replication_record"}},"created_at":"2026-08-13T01:30:36.681320+00:00","updated_at":"2026-08-13T01:30:36.681320+00:00"}