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We say that $A\\in\\mathcal A$ is $\\varphi$-symmetric if $\\varphi(A)=A$, $A$ is $\\varphi$-antisymmetric if $\\varphi(A)=-A$, and $A$ has a $\\zeta=e^{i\\theta}$ $\\varphi$-phase symmetry if $\\varphi(A)=\\zeta A$.\n  Our main result is a new projection charact"},"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":"2412.20795","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-12-30T08:33:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"61d0b49a89d4ce6a817e53ed48ccc8d5166de9ac98cd5f8ce802a90b715ce6f6","abstract_canon_sha256":"1f9db496935f7a051909e5e5850fbaa7fc1622c004fb31196bc04670cedb0401"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:22.395490Z","signature_b64":"Z35apD6NYbieihsMVA3x/OufFxZL1tcdw4aDUCbJkNAJG2Y2WSylL0ngJK8qWjsYALmhBEIlK7rDjzSJLpapAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad53184045a82a7c15273430858cfd2e55997e6260e3b1ff4c920f2ec7aa4d85","last_reissued_at":"2026-07-05T09:55:22.395003Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:22.395003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Projection Characterization and Symmetry Bootstrap for Elements of a von Neumann Algebra that are Nearby Commuting Elements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"David Herrera","submitted_at":"2024-12-30T08:33:54Z","abstract_excerpt":"We define a symmetry map $\\varphi$ on a unital $C^\\ast$-algebra $\\mathcal A$ to be an $\\mathbb{R}$-linear map on $\\mathcal A$ that generalizes transformations on matrices like: transpose, adjoint, complex-conjugation, conjugation by a unitary matrix, and their compositions. 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