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We also prove a lower bound on $\\sup_{\\Vert \\Psi\\Vert =1}\\langle \\Phi,\\gamma_{2}^{\\Psi}\\Phi\\rangle$ for fixed $\\Phi$, and state a conjecture motivated by these results."},"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":"2505.21167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-27T13:21:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c0df82de550300f3833fbdf1d9f13a9fa8dd85d89886fdfa4117e70cc2c2479b","abstract_canon_sha256":"a6c0ff3ef94006d70db6cbb02e4e31cd4f855dce7a36609bb6c2c280f0815507"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:24.849205Z","signature_b64":"4At+UGia/O3ijtyX5B7mrasbkdlqawKkLcMeedQzaLYjzNL+zrhG8S8bniv+s809k4JoRAUhEDIieamXYcppCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f83e40f858290b3c9a476bcbb3a4c72d2834aba709a9cc4b19cb0bbb468d1408","last_reissued_at":"2026-07-05T11:10:24.848667Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:24.848667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Correlational Bound for Eigenvalues of Fermionic 2-Body Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Martin Ravn Christiansen","submitted_at":"2025-05-27T13:21:51Z","abstract_excerpt":"We prove that the eigenvalues of a 2-body operator $\\gamma_{2}^{\\Psi}$ associated to a fermionic $N$-particle state $\\Psi$ are highly constrained by the structure of the corresponding eigenvectors: If $\\Phi=\\sum_{k=1}^{\\infty}\\lambda_{k}u_{k}\\wedge v_{k}$ is the canonical form of an eigenvector $\\Phi$ with eigenvalue $\\Lambda$, then $\\Lambda\\leq(1+\\frac{N-2}{2}\\sum_{k=1}^{\\infty}\\lambda_{k}^{4})^{-1}N$. 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