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Abreu asked whether the spectrum of the Laplace operator $\\Delta_g$ on $\\mathcal{C}^\\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to trans"},"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":"0908.0727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-08-05T20:49:35Z","cross_cats_sorted":["math.SG","math.SP"],"title_canon_sha256":"3a57bde9fb3d562dc45209dfaff5101b9f08a3d21161b594cc1b291e32fcb729","abstract_canon_sha256":"a65f62dde3d40e8d13b4a2cc7e7b5926e6c0b0b79bd70ad430da2f0c2ecaf089"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:29.775511Z","signature_b64":"NZIeehnusO0mGhDXCp+b8teXFY972X6J4WGEO8hVnjZQKasBjy99B3OePEgjbiMPocb0pgkJ8VzzUwkV9CQwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88c060ff2f9649d554d35f5b2a08b83de43b3fd663e56117cd97d449bf105d0a","last_reissued_at":"2026-05-18T03:53:29.774756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:29.774756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hearing Delzant polytopes from the equivariant spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG","math.SP"],"primary_cat":"math.DG","authors_text":"Emily B. 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